## MCQ (Single Correct Answer)

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by x, its efficiency de...

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.
The...

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is $$\left(\mathrm{given}...

$$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is...

Heat energy of $735 \mathrm{~J}$ is given to a diatomic gas allowing the gas to expand at constant pressure.
Each gas molecule rotates around an inte...

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initia...

The pressure of a gas changes linearly with volume from $$\mathrm{A}$$ to $$\mathrm{B}$$ as shown in figure. If no heat is supplied to or extracted fr...

The correct relation between $$\gamma = {{{c_p}} \over {{c_v}}}$$ and temperature T is :

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$
Assertion A: Efficiency of ...

A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} \mathrm{C}$. The ratio of average kinetic energy per mo...

The pressure $$(\mathrm{P})$$ and temperature ($$\mathrm{T})$$ relationship of an ideal gas obeys the equation
$$\mathrm{PT}^{2}=$$ constant. The vol...

Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. I...

Heat energy of 184 kJ is given to ice of mass 600 g at $$-12^\circ \mathrm{C}$$. Specific heat of ice is $$\mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}}$$ an...

At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average speed in the gas. Then, the val...

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If $$d Q$$ and $$d W$$ represent th...

Match List I with List II
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.tg td{border-color:black;border-style:solid;border-width:1px;font-family...

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions...

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrati...

The root mean square velocity of molecules of gas is

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink sam...

A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will t...

Let $$\gamma_1$$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $$\gamma_...

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $$\mathrm{T_3 > T_2 > T_1}$$ a...

1 g of a liquid is converted to vapour at 3 $$\times$$ 10$$^5$$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm$...

Given below are two statements :
Statement I : The temperature of a gas is $$-73^\circ$$C. When the gas is heated to $$527^\circ$$C, the root mean squ...

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then redu...

The root mean square speed of smoke particles of mass $$5 \times 10^{-17} \mathrm{~kg}$$ in their Brownian motion in air at NTP is approximately. [Giv...

A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat to be transferred to the gas to...

Sun light falls normally on a surface of area $$36 \mathrm{~cm}^{2}$$ and exerts an average force of $$7.2 \times 10^{-9} \mathrm{~N}$$ within a time ...

A Carnot engine has efficiency of $$50 \%$$. If the temperature of sink is reduced by $$40^{\circ} \mathrm{C}$$, its efficiency increases by $$30 \%$$...

Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : T...

In $$1^{\text {st }}$$ case, Carnot engine operates between temperatures $$300 \mathrm{~K}$$ and $$100 \mathrm{~K}$$. In $$2^{\text {nd }}$$ case, as ...

Which statements are correct about degrees of freedom ?
(A) A molecule with n degrees of freedom has n$$^{2}$$ different ways of storing energy.
(B) E...

If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A_{2}$$ are the cross sectional...

Read the following statements :
A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the ...

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1: 4$$, then
A. The r.m.s. ...

An ice cube of dimensions $$60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}$$ is placed in an insulation box of wall thickness $$1 \math...

A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :...

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $$40 \mathrm{~K}$$ at constant pressure. The increase in the internal ener...

A monoatomic gas at pressure $$\mathrm{P}$$ and volume $$\mathrm{V}$$ is suddenly compressed to one eighth of its original volume. The final pressure ...

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $$\sqrt2$$ times the speed ...

Let $$\eta_{1}$$ is the efficiency of an engine at $$T_{1}=447^{\circ} \mathrm{C}$$ and $$\mathrm{T}_{2}=147^{\circ} \mathrm{C}$$ while $$\eta_{2}$$ i...

A certain amount of gas of volume $$\mathrm{V}$$ at $$27^{\circ} \mathrm{C}$$ temperature and pressure $$2 \times 10^{7} \mathrm{Nm}^{-2}$$ expands is...

Following statements are given :
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic e...

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a li...

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In...

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters h...

Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the pr...

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is :

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperatu...

In van der Waal equation $$\left[ {P + {a \over {{V^2}}}} \right]$$ [V $$-$$ b] = RT; P is pressure, V is volume, R is universal gas constant and T is...

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC a...

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic...

Given below are two statements :
Statement I : When $$\mu$$ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2...

For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows :
...

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0$$^\circ$$C.
B. The mean free path of gas molecules decreases if ...

A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to...

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$$^\circ$$C. The ratio of their average kinetic energy pe...

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly ...

A copper block of mass 5.0 kg is heated to a temperature of 500$$^\circ$$C and is placed on a large ice block. What is the maximum amount of ice that ...

The ratio of specific heats $$\left( {{{{C_P}} \over {{C_V}}}} \right)$$ in terms of degree of freedom (f) is given by :

The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K...

A Carnot engine takes 5000 kcal of heat from a reservoir at 727$$^\circ$$C and gives heat to a sink at 127$$^\circ$$C. The work done by the engine is...

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms$$-$$1. What will be the rise in the temperature of the nail if one four...

A Carnot engine whose heat sinks at 27$$^\circ$$C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to in...

Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K t...

Two thin metallic spherical shells of radii r1 and r2 (r1 > r2) are placed with their centres coinciding. A material of thermal conductivity K is f...

A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen wi...

A reversible engine has an efficiency of $${1 \over 4}$$. If the temperature of the sink is reduced by 58$$^\circ$$C, its efficiency becomes double. C...

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p0 at v =0 i...

if the rms speed of oxygen molecules at 0$$^\circ$$C is 160 m/s, find the rms speed of hydrogen molecules at 0$$^\circ$$C.

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall?[Given 1 cal = 4.2 J and spe...

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$$^\circ$$C. What load will the balloon carry on rising to a height a...

An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is :

The temperature of equal masses of three different liquids x, y and z are 10$$^\circ$$C, 20$$^\circ$$C and 30$$^\circ$$C respectively. The temperature...

A cylindrical container of volume 4.0 $$\times$$ 10$$-$$3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of ...

A refrigerator consumes an average 35W power to operate between temperature $$-$$10$$^\circ$$C to 25$$^\circ$$C. If there is no loss of energy then ho...

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal e...

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then :...

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$$^\circ$$ C to 37$$^\circ$$ C. If the ideal gas is ...

Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half ...

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $$\times$$ 10$$-$$9 J per molecule...

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $$\to$...

A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the bod...

A heat engine has an efficiency of $${1 \over 6}$$. When the temperature of sink is reduced by 62$$^\circ$$C, its efficiency get doubled. The temperat...

Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :...

For a gas CP $$-$$ CV = R in a state P and CP $$-$$ CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectiv...

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabati...

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is ...

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

The correct relation between the degrees of freedom f and the ratio of specific heat $$\gamma$$ is :

Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperat...

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$$^\circ$$ C to 50$$^\circ$$ C when no work is done is ____...

The entropy of any system is given by $$S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$$ where $$\alpha$$ and $$\beta$$ ...

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule...

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats) :

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 &...

The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use $$\...

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? (kB is Boltzmann cons...

If one mole of the polyatomic gas is having two vibrational modes and $$\beta$$ is the ratio of molar specific heats for polyatomic gas $$\left( {\bet...

Which one is the correct option for the two different thermodynamic processes?...

A polyatomic ideal gas has 24 vibrational modes. What is the value of $$\gamma$$?

Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees o...

Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combinat...

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the sou...

Calculate the value of mean free path ($$\lambda$$) for oxygen molecules at temperature 27$$^\circ$$C and pressure 1.01 $$\times$$ 105 Pa. Assume the ...

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of met...

In thermodynamics, heat and work are :

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T....

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U $$=$$ 3PV + 4. The gas is :

The temperature $$\theta$$ at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures $$\th...

Given below are two statements :Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.Statem...

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is :...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : When a rod lying freely is heated,...

A diatomic gas, having $${C_p} = {7 \over 2}R$$ and $${C_v} = {5 \over 2}R$$, is heated at constant pressure. The ratio dU : dQ : dW :

If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original ...

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

Match List I with List II.
List I
List II
(a)
Isothermal
(i)
Pressure constant
(b)
Isochor...

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.A $$ \to $$ B : Isothermal expansion at tem...

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$$\al...

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a
molecule varies with T as :

Three rods of identical cross-section and lengths are made of three different materials of thermal
conductivity K1
, K2
and K3
, respecrtively. They ...

Molecules of an ideal gas are known to have three translational degrees of freedom and two
rotational degrees of freedom.The gas is maintained at a te...

Two different wires having lengths L1 and L2,
and respective temperature coefficient of linear
expansion $$\alpha $$1 and $$\alpha $$2, are joined end...

In an adiabatic process, the density of a
diatomic gas becomes 32 times its initial value.
The final pressure of the gas is found to be n
times the in...

A bullet of mass 5 g, travelling with a speed of
210 m/s, strikes a fixed wooden target. One half
of its kinetic energy is converted into heat in
the ...

Three different processes that can occur in an
ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A $$ \to $$ B,
A $$ \to...

Number of molecules in a volume of 4 cm3 of
a perfect monoatomic gas at some temperature
T and at a pressure of 2 cm of mercury is close
to? (Given, m...

Match the thermodynamic processes taking place in a system with the correct conditions. In the
table : $$\Delta $$Q is the heat supplied, $$\Delta $$W...

The specific heat of water = 4200 J kg-1K-1 and the latent heat of ice = 3.4 $$ \times $$ 105 J kg–1. 100 grams of ice at 0oC is placed in 200 g of wa...

Match the $${{{C_P}} \over {{C_V}}}$$ ratio for ideal gases with different type of molecules :
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A metallic sphere cools from 50oC to 40o in 300 s. If atmospheric temperature around is 20oC,
then the sphere’s temperature after the next 5 minutes w...

To raise the temperature of a certain mass of gas by 50oC at a constant pressure, 160 calories of
heat is required. When the same mass of gas is coole...

A calorimeter of water equivalent 20 g contains 180 g of water at 25oC. ‘m’ grams of steam at
100oC is mixed in it till the temperature of the mixure ...

A balloon filled with helium (32oC and 1.7 atm.)
bursts. Immediately afterwards the expansion
of helium can be considered as

Consider a gas of triatomic molecules. The
molecules are assumed to be triangular and
made of massless rigid rods whose vertices
are occupied by atom...

When the temperature of a metal wire is
increased from 0oC to 10oC, its length
increases by 0.02%. The percentage change in
its mass density will be c...

A heat engine is involved with exchange of heat
of 1915 J, – 40J, + 125 J and –Q J, during one
cycle achieving an efficiency of 50.0%. The
value of Q ...

An ideal gas in a closed container is slowly
heated. As its temperature increases, which of
the following statements are true?
(A) the mean free path ...

A gas mixture consists of 3 moles of oxygen
and 5 moles of argon at temperature T.
Assuming the gases to be ideal and the oxygen
bond to be rigid, the...

Two gases-argon (atomic radius 0.07 nm,
atomic weight 40) and xenon (atomic radius
0.1 nm, atomic weight 140) have the same
number density and are at ...

Consider two ideal diatomic gases A and B at
some temperature T. Molecules of the gas A are
rigid, and have a mass m. Molecules of the gas
B have an a...

Which of the following is an equivalent cyclic
process corresponding to the thermodynamic cyclic
given in the figure ? where, 1 $$ \to $$ 2 is adiabat...

A carnot engine having an efficiency of $${1 \over {10}}$$ is
being used as a refrigerator. If the work done
on the refrigerator is 10 J, the amount o...

Consider a mixture of n moles of helium gas
and 2n moles of oxygen gas (molecules taken
to be rigid) as an ideal gas. Its CP/CV value
will be :...

The plot that depicts the behavior of the mean
free time t (time between two successive
collisions) for the molecules of an ideal gas, as
a function o...

A thermodynamic cycle xyzx is shown on a V-T diagram.
The P-V diagram that best describes this cycle
is : (Diagrams are schematic and not to scale)...

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other
engine to produce work) between temperature, T1
and...

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean
collision time between the gas molecule changes from $${\ta...

Two moles of an ideal gas with $${{{C_P}} \over {{C_V}}} = {5 \over 3}$$
are mixed with 3 moles of another ideal gas
with $${{{C_P}} \over {{C_V}}} = ...

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma $$ = 1.40, the work done by air is : (31.4 = 4.6555) [Take air to...

A Carnot engine has an efficiency of $${1 \over 6}$$. When the temperature of the sink is reduced by 62ºC, its efficiency
is doubled. The temperatures...

One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature
averaged) resistance of 20 $$\Omega $$. The rms v...

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be
the heat energy absorbed by the gas, in this p...

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the
internal energy of the gas along the path ...

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant vo...

When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1
oC–1
) is added to M2 gram of water at 50C, finally
no ice is left and the water is at 0°C. ...

One mole of ideal gas passes through a process where pressure and volume obey the relation
$$P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over ...

Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm–2. If the surface
has an area of 25 cm2, the momentum tran...

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
$$\Delta $$T. the heat required to produ...

A cylinder with fixed capacity of 67.2 lit
contains helium gas at STP. The amount of heat
needed to raise the temperature of the gas by
20°C is : [Giv...

A 25 × 10–3 m3 volume cylinder is filled with
1 mol of O2 gas at room temperature (300K).
The molecular diameter of O2, and its root
mean square speed...

n moles of an ideal gas with constant volume
heat capcity CV undergo an isobaric expansion
by certain volume. The ratio of the work done
in the proces...

50 W/m2 energy density of sunlight is normally
incident on the surface of a solar panel. Some
part of incident energy (25%) is reflected from
the surf...

The specific heats, CP and CV of a gas of
diatomic molecules, A, are given (in units of
J mol–1 K–1) by 29 and 22, respectively.
Another gas of diato...

An HCl molecule has rotational, translational
and vibrational motions. If the rms velocity of
HCl molecules in its gaseous phase is $$\overline v $$ ,...

Following figure shows two processes A and
B for a gas. If $$\Delta $$QA and $$\Delta $$QB are the amount of
heat absorbed by the system in two cases,...

For a given gas at 1 atm pressure, rms speed
of the molecule is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will ...

The given diagram shows four processes i.e.,
isochoric, isobaric, isothermal and adiabatic.
The correct assignment of the processes, in the
same order...

The temperature, at which the root mean square
velocity of hydrogen molecules equals their
escape velocity from the earth, is closest to :
[Boltzmann ...

Two identical breakers A and B contain equal
volumes of two different liquids at 60°C each
and left to cool down. Liquid in A has density
of 8 × 102 k...

A thermally insulated vessel contains 150g of
water at 0°C. Then the air from the vessel is
pumped out adiabatically. A fraction of water
turns into i...

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $$ \times $$ 1...

An ideal gas occupies a volume of 2m3 at a pressure of 3 $$ \times $$ 106 Pa. The energy of the gas is :

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inn...

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ...

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of ...

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperat...

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is th...

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In thi...

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total inte...

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = ...

Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The a...

Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20oC to 90oC. Work done
by gas is close to – (Gas constant R = 8.31 ...

Two kg of a monoatomic gas is at a pressure of 4 $$ \times $$ 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due ...

An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a tem...

A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given that the thermal conductivity...

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other r...

Two Carnot engines A and B are operated in series. The first one, A, receives heat at T1 (= 600 K) and rejects to a reservoir at temperature T2. The s...

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules i...

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of the...

Temperature difference of 120oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and leng...

A gas can be taken from A to B via two different processes ACB and ADB.
When path ACB is used 60 J of heat flows into the system and 30 J of work is...

Two moles of helium are mixed with n moles of hydrogen. If $${{Cp} \over {Cv}} = {3 \over 2}$$ for the mixture, then the value of n is :

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path...

Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a
volume 2 V. Calculate (a) the final temperature of...

The mass of a hydrogen molecule is 3.32 $$\times$$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of ...

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. ...

A Carnot's engine works as a refrigerator between $$250$$ K and $$300$$ K. It receives $$500$$ cal heat from the reservoir at the lower temperature. T...

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $${27^ \circ }C.$$ The wo...

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n mole...

For the P-V diagram given for an ideal gas,
out of the following which one correctly represents the T-P diagram ?
...

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :
(Take Cv = 1.5...

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :
...

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $$ \ti...

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for n...

A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336×103 J kg−1....

Which of the following shows the correct relationship between the pressure ‘P’ and density $$\rho $$ of an ideal gas at constant temperature ?

The ratio of work done by an ideal monoatomic gas to the heat supplied to it
in an isobaric process is :

200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of...

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $$C$$ remains constant. If during this process the relation...

A pendulum clock loses $$12$$ $$s$$ a day if the temperature is $${40^ \circ }C$$ and gains $$4$$ $$s$$ a day if the temperature is $${20^ \circ }C.$$...

$$'n'$$ moles of an ideal gas undergoes a process $$A$$ $$ \to $$ $$B$$ as shown in the figure. The maximum temperature of the gas during the process ...

A solid body of constant heat capacity $$1$$ $$J/{}^ \circ C$$ is being heated by keeping it in contact with reservoirs in two ways:
$$(i)$$ Sequenti...

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molec...

Consider a spherical shell of radius $$R$$ at temperature $$T$$. The black body radiation inside it can be considered as an ideal gas of photons with ...

The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by ...

Three rods of Copper, Brass and Steel are welded together to form a $$Y$$ shaped structure. Area of cross - section of each rod $$ = 4c{m^2}.$$ End of...

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liqui...

One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic. The temperatures at $$A, B$$ ...

The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted ...

If a piece of metal is heated to temperature $$\theta $$ and then allowed to cool in a room which is at temperature $${\theta _0},$$ the graph between...

A Carnot engine, whose efficiency is $$40\% $$, takes in heat from a source maintained at a temperature of $$500$$ $$K.$$ It is desired to have an eng...

Helium gas goes through a cycle $$ABCD$$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Ass...

A liquid in a beaker has temperature $$\theta \left( t \right)$$ at time $$t$$ and $${\theta _0}$$ is temperature of surroundings, then according to N...

A wooden wheel of radius $$R$$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross...

Three perfect gases at absolute temperatures $${T_1},\,{T_2}$$ and $${T_3}$$ are mixed. The masses of molecules are $${m_1},{m_2}$$ and $${m_3}$$ and ...

A Carnot engine operating between temperatures $${{T_1}}$$ and $${{T_2}}$$ has efficiency $${1 \over 6}$$. When $${T_2}$$ is lowered by $$62$$ $$K$$ i...

A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It is moving with speed $$v$$ and ...

$$100g$$ of water is heated from $${30^ \circ }C$$ to $${50^ \circ }C$$. Ignoring the slight expansion of the water, the change in its internal energy...

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas in...

Statement - 1: The temperature dependence of resistance is usually given as $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$$ The resistance of wir...

One $$kg$$ of a diatomic gas is at a pressure of $$8 \times {10^4}\,N/{m^2}.$$ The density of the gas is $$4kg/{m^3}$$. What is the energy of the gas ...

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $$\theta $$ along the leng...

Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.
Assuming the gas to be ideal the work done on the ga...

Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.
The work done on the gas in taking it from $$D$$ to ...

Two moles of helium gas are taken over the cycle $$ABCD$$, as shown in the $$P$$-$$T$$ diagram.
The net work done on the gas in the cycle $$ABCDA$$ ...

The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of sound in helium $$(He)$$ at t...

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${V_1}$$ and contains ideal gas ...

A Carnot engine, having an efficiency of $$\eta = 1/10$$ as heat engine, is used as a refrigerator . If the work done on the system is $$10$$ $$J$$, ...

If $${C_p}$$ and $${C_v}$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ ...

One end of a thermally insulated rod is kept at a temperature $${T_1}$$ and the other at $${T_2}$$. The rod is composed of two sections of length $${L...

The work of $$146$$ $$kJ$$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increas...

Assuming the Sun to be a spherical body of radius $$R$$ at a temperature of $$TK$$, evaluate the total radiant powered incident of Earth at a distance...

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $${T_0},$$ while Box contai...

A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio $${{Cp} \over {{C_v}}}$$ of the mixture is

A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delta {U_2}$$ are the changes in i...

The figure shows a system of two concentric spheres of radii $${r_1}$$ and $${r_2}$$ are kept at temperatures $${T_1}$$ and $${T_2}$$, respectively. T...

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
...

One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is ...

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received...

Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ volume $$\left( {{V_1},{V_2}} \r...

Which of the following statements is correct for any thermodynamic system ?

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$...

''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $${C_p}/{C_V}$$ for ...

Which of the following parameters does not characterize the thermodynamic state of mattter?

A carnot engine takes $$3 \times {10^6}$$ cal. of heat from a reservoir at $${627^ \circ }C,$$ and gives it to a sink at $${27^ \circ }C$$. The work d...

According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \thet...

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Which statement is incorrect?

Infrared radiation is detected by

Heat given to a body which raises its temperature by $${1^ \circ }C$$ is

Which of the following is more close to a black body?

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

Even Carnot engine cannot give $$100\% $$ efficiency because we cannot

At what temperature is the $$r.m.s$$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $${47^ \circ }C?$$

Two spheres of the same material have radii $$1$$ $$m$$ and $$4$$ $$m$$ and temperatures $$4000$$ $$K$$ and $$2000$$ $$K$$ respectively. The ratio of ...

1 mole of a gas with $$\gamma = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma = 5/3,$$ then the value of $$\gamma $$ for the resulting mixtu...

## Numerical

A water heater of power $2000 \mathrm{~W}$ is used to heat water. The specific heat capacity of water is $4200 \mathrm{~J}$ $\mathrm{kg}^{-1} \mathrm{...

A faulty thermometer reads $5^{\circ} \mathrm{C}$ in melting ice and $95^{\circ} \mathrm{C}$ in stream. The correct temperature on absolute scale will...

A body cools from 60$$^\circ$$C to 40$$^\circ$$C in 6 minutes. If, temperature of surroundings is 10$$^\circ$$C. Then, after the next 6 minutes, its t...

A hole is drilled in a metal sheet. At $$\mathrm{27^\circ
C}$$, the diameter of hole is 5 cm. When the sheet is heated to $$\mathrm{177^\circ
C}$$...

The pressure $$\mathrm{P}_{1}$$ and density $$\mathrm{d}_{1}$$ of diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes suddenly to $$\mathrm{P}_{2...

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $$\frac{\alpha^...

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. Th...

A block of ice of mass 120 g at temperature 0$$^\circ$$C is put in 300 g of water at 25$$^\circ$$C. The x g of ice melts as the temperature of the wat...

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they a...

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates ar...

300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227$$^\circ$$C, then the temperature of sink will be _____...

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

A diatomic gas ($$\gamma$$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

In a carnot engine, the temperature of reservoir is 527$$^\circ$$C and that of sink is 200 K. If the work done by the engine when it transfers heat fr...

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$$^\circ$$C to 70$$^\circ$$C. If geyser operates on a gas burner, the rate of combu...

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J hea...

When a gas filled in a closed vessel is heated by raising the temperature by 1$$^\circ$$C, its pressure increases by 0.4%. The initial temperature of ...

A steam engine intakes 50 g of steam at 100$$^\circ$$C per minute and cools it down to 20$$^\circ$$C. If latent heat of vaporization of steam is 540 c...

A monoatomic gas performs a work of $${Q \over {4}}$$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R ...

In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference ($$\Delta$$T) of the water and surroundings ...

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$$^\circ$$C. Th amount of heat required to double the speed of its molecules is __...

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0$$^\circ$$C without changing the pressure of the gas. The molecules in the ga...

The average translational kinetic energy of N2 gas molecules at .............$$^\circ$$C becomes equal to the K.E. of an electron accelerated from res...

A sample of gas with $$\gamma$$ = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3 to 300 cm3. If the initial...

A heat engine operates between a cold reservoir at temperature T2 = 400 K and a hot reservoir at temperature T1. It takes 300 J of heat from the hot r...

A rod CD of thermal resistance 10.0 KW$$-$$1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 2...

A system consists of two types of gas molecules A and B having same number density 2 $$\times$$ 1025/m3. The diameter of A and B are 10 $$\mathop A\li...

In 5 minutes, a body cools from 75$$^\circ$$C to 65$$^\circ$$C at room temperature of 25$$^\circ$$C. The temperature of body at the end of next 5 minu...

One mole of an ideal gas at 27$$^\circ$$ is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be ________...

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ $$\pi$$J....

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made...

For an ideal heat engine, the temperature of the source is 127$$^\circ$$C. In order to have 60% efficiency the temperature of the sink should be _____...

1 mole of rigid diatomic gas performs a work of $${Q \over 5}$$ when heat Q is supplied to it. The molar heat capacity of the gas during this transfor...

The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $$V = K{T^{{2 \over 3}}}$$. The workdone when temp...

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber c...

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is double...

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then chan...

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100$$^\circ$...

The root mean square speed of molecules of a given mass of a gas at 27$$^\circ$$C and 1 atmosphere pressure is 200 ms$$-$$1. The root mean square spee...

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The
percentage efficiency of the engine is close to _______...

Initially a gas of diatomic molecules is contained in a cylinder of volume V1
at a pressure P1
and
temperature 250 K. Assuming that 25% of the molec...

A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and
it is decreasing at a rate of 102 A s–1. The va...

Nitrogen gas is at 300oC temperature. The
temperature (in K) at which the rms speed of a
H2 molecule would be equal to the rms speed
of a nitrogen mol...

The change in the magnitude of the volume of an ideal gas when a small additional pressure $$\Delta $$P is
applied at a constant temperature, is the s...

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas
at 400 K is added to it, the final equilibrium temp...

If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice,
how much heat (in calories) is released to the surr...

A bakelite beaker has volume capacity of 500 cc at 30oC. When it is partially filled with Vm
volume
(at 30oC) of mercury, it is found that the unfill...

An engine takes in 5 moles of air at 20oC and
1 atm, and compresses it adiabatically to
1/10th of the original volume. Assuming air to
be a diatomic i...

Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V1 to V2 = $${{{V_1...

Three containers C1, C2 and C3 have water at
different temperatures. The table below shows
the final temperature T when different amounts
of water (gi...

M grams of steam at 100oC is mixed with 200 g of ice at its melting point in a thermally insulated
container. If it produced liquid water at 40oC [hea...

A non-isotropic solid metal cube has coefficients of linear expansion as : 5 $$ \times $$ 10-5/oC along the x-axis and 5 $$ \times $$ 10-6/oC along th...

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine
performs 1200 J of work per cycle. The heat energy (in J) ...

## MCQ (More than One Correct Answer)

Which of the following is incorrect regarding the first law of thermodynamics?