Heat and Thermodynamics · Physics · JEE Advanced

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1 \mathrm{~kg}$ of the substance from $-73^{\circ} \mathrm{C}$ to $27^{\circ} \mathrm{C}$ is $n k$, the value of $n$ is ________.

[Given: $0 \mathrm{~K}=-273{ }^{\circ} \mathrm{C}$.]

A metal rod AB of length 10x has its one end A in ice at 0$$^\circ$$C and the other end B in water at 100$$^\circ$$C. If a point P on the rod is maintained at 400$$^\circ$$C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of $$\lambda x$$ from the ice end A, find the value of $$\lambda$$. (Neglect any heat loss to the surrounding.)

One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}$, as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

[ $\mathcal{R}$ is the gas constant.]

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

Which one of the following options is correct?

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

One mole of a monatomic ideal gas is taken along two cyclic processes E $$\to$$ F $$\to$$ G $$\to$$ E and E $$\to$$ F $$\to$$ H $$\to$$ E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists :

Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as shown in the figure. One of the blocks has thermal conductivity $$\kappa $$ and the other 2$$\kappa $$. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in configuration-I. The time to transport the same amount of heat in configuration-II is

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T, respectively. The temperature of the middle (i.e. second) plate under steady state condition is

One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II:

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

	Column I		Column II
(A)	An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened.	(P)	The temperature of the gas decreases
(B)	An ideal monatomic gas expands to twice its original volume such that its pressure P $$\propto$$ $$\frac{1}{\mathrm{V}^2}$$, where V is the volume of the gas	(Q)	The temperature of the gas increase or remains constant.
(C)	An ideal monoatomic gas expands to twice its original volume such that its pressure P $$\propto$$ $$\frac{1}{\mathrm{V}^{4/3}}$$, where V is its volume	(R)	The gas loses heat
(D)	An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph	(S)	The gas gains heat

An ideal gas is expanding such that PT$$^2$$ = constant. The coefficient of volume expansion of the gas is

STATEMENT 1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

Because

STATEMENT 2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

In the given $P-V$ diagram, a monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7$ ].

Which of the following statement(s) is(are) correct?

The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is(are) correct to a reasonable approximation.

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P₀. Choose the correct option(s) from the following:

The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then,

$$C_V$$ and $$C_P$$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then