4.5
(100k+ )
1

### JEE Main 2021 (Online) 1st September Evening Shift

Numerical
The average translational kinetic energy of N2 gas molecules at .............$$^\circ$$C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given kB = 1.38 $$\times$$ 10$$-$$23 J/K) (Fill the nearest integer).

## Explanation

Given, the average translational kinetic energy of dinitrogen (N2) = Kinetic energy of an electron .... (i)

Translational kinetic energy of dinitrogen (N2)

$$KE = {3 \over 2}{K_B}T$$

Here, T = temperature of the gas,

and KB = Boltzmann constant.

Kinetic energy of an electron = eV

Given, the potential differential of an electron, V = 0.1 V

Substituting the values in the Eq. (i), we get

$${3 \over 2}{K_B}T = eV$$

$$\Rightarrow {3 \over 2} \times 1.38 \times {10^{ - 23}} \times T = 1.6 \times {10^{ - 19}} \times (0.1)$$

$$T = 773K = 773 - 273^\circ C = 500^\circ C$$
2

### JEE Main 2021 (Online) 1st September Evening Shift

Numerical
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 gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $${x \over {10}}$$. Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol$$-$$1 K$$-$$1)

## Explanation

Given, the number of diatomic moles, n = 3 mol

The increase in temperature of the diatomic mole,

$$\Delta$$T = 40$$^\circ$$C

Now, the degree of freedom

f = linear + rotational + no oscillation

f = 3 + 2 + 0 $$\Rightarrow$$ f = 5

Change in internal energy,

$$\Delta$$U = nCv$$\Delta$$T .... (i)

where, $${C_v} = {f \over 2}R = {5 \over 2}R$$

Substituting the value in Eq. (i), we get

$$\Delta U = {{5R} \over 2}nR\Delta T$$

Now, work done by the gas for isobaric process,

$$W = p\Delta V = nR\Delta T$$

The ratio of the change in internal energy to the work done by the gas,

$${{\Delta U} \over W} = {{{5 \over 2}nR\Delta T} \over {nR\Delta T}}$$

$$= {{\Delta U} \over W} = {5 \over 2}$$

Multiply and divide the above equation with 5, we get

$${{\Delta U} \over W} = {{5 \times 5} \over {2 \times 5}} = {{25} \over {10}}$$

Comparing with given equation, $${{\Delta U} \over W} = {x \over {10}}$$

The value of the x = 25.
3

### JEE Main 2021 (Online) 31st August Evening Shift

Numerical
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 pressure is 200 kPa. The absolute value of the workdone by the gas in the process = _____________ J.

## Explanation

v = 1.5

p1v1v = p2v2v

(200) (1200)1.5 = P2 (300)1.5

P2 = 200 [4]3/2 = 1600 kPa

$$\left| {W.D.} \right| = {{{p_2}{v_2} - {p_1}{v_1}} \over {v - 1}} = \left( {{{480 - 240} \over {0.5}}} \right) = 480$$ J
4

### JEE Main 2021 (Online) 27th August Evening Shift

Numerical
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 reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be ______________ K.

## Explanation

Qin = 300 J ; Qout = 240 J

Work done = Qin $$-$$ Qout = 300 $$-$$ 240 = 60 J

Efficiency = $${W \over {{Q_{in}}}} = {{60} \over {300}} = {1 \over 5}$$

efficiency = $$1 - {{{T_2}} \over {{T_1}}}$$

$${1 \over 5} = 1 - {{400} \over {{T_1}}} \Rightarrow {{400} \over {{T_1}}} = {4 \over 5}$$

T1 = 500 k

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12