Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 41 :

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

800 W
1200 W
600 W
500 W

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(1)

$d Q = d U + d W$

$\frac{d U}{d t} = \frac{d Q}{d t} - \frac{d W}{d t}$

$\frac{d U}{d t} = 1000 - 200 = 800 W$

Q 42 :

Given below are two statements: [2023]

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are true
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Statement I is true but Statement II is false

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(2)

$Statement I: Δ Q > 0$

According to the first law of thermodynamics,

$Δ Q = Δ U + W$

If $Δ Q > 0$ , $Δ U < 0$ and $W > 0$ is also possible.

Hence $Δ T < 0$ , so temperature decreases.

$Statement I is false$

$Statement II: W > 0$

$∴$ $\int P d V > 0$

Therefore, volume of the system must increase during positive work done by the system.

$Statement II is true$

Q 43 :

Consider two containers $A$ and $B$ containing monoatomic gases at the same pressure $(P)$ , volume $(V)$ and temperature $(T)$ . The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume, while the gas in $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is: [2023]

$8$
$8^{1 / 2}$
$\frac{1}{8}$
$4$

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(4)

$Isothermal process, T = constant$

$P V = n R T = constant$

$P_{1} V_{1} = P_{2} V_{2}$

$P V = P_{A} (\frac{V}{8})$

$P_{A} = 8 P$

$Adiabatic process, P V^{γ} = constant$

$γ for monoatomic gas is \frac{5}{3}$

$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$\frac{P_{B}}{P} = {(\frac{V_{1}}{V_{2}})}^{γ} = {(\frac{V}{V / 8})}^{5 / 3}$

$P_{B} = 32 P$

$\frac{P_{B}}{P_{A}} = \frac{32 P}{8 P} = 4$

Q 44 :

A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

There is no heat supplied to the system
The temperature of the gas increases
The change in the internal energy is equal to the work done on the gas
There is no change in the internal energy

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(4)

$(1) Δ Q = 0$

$(2) Δ Q = Δ U + Δ W \Rightarrow Δ U = - Δ W$

$Adiabatic compression (V ↓)$

$Δ W = - ve \Rightarrow Δ U = + ve$

$Δ U ↑ \Rightarrow T ↑$

$Δ U \neq 0$

Q 45 :

1 kg of water at $100 ° C$ is converted into steam at $100 ° C$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{- 3} m^{3}$ as a liquid to ${1.671 m}^{3}$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation $=2257 kJ/kg$ , atmospheric pressure $= {1×10}^{5} Pa$ ) [2023]

+ 2090 kJ
- 2090 kJ
- 2426 kJ
+ 2476 kJ

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(1)

$Δ Q = Δ U + Δ W$

$∴$ $Δ U = Δ Q - Δ W = m L_{v} - P Δ V$

$= {(1 kg)(2257×10}^{3} J/kg)$

$- (1 \times 10^{5} Pa) ({1.671 m}^{3} - 1 \times 10^{- 3} m^{3})$

$= 2257 \times 10^{3} J - 167 \times 10^{3} J$ $= 2090 kJ$

Q 46 :

The thermodynamic process, in which internal energy of the system remains constant is [2023]

Isochoric
Isothermal
Adiabatic
Isobaric

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(2)

$T = constant \Rightarrow U = constant$

Q 47 :

The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

$P_{0} {(4)}^{1 / γ}$
$P_{0} {(4)}^{γ}$
$P_{0}$
$4 P_{0}$

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(2)

$As gas is suddenly compressed, the process is adiabatic.$

$Equation of gas for adiabatic process is P V^{γ} = constant$

$\Rightarrow P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$\Rightarrow P_{0} V_{0}^{γ} = P_{2} {(\frac{V_{0}}{4})}^{γ}$

$\Rightarrow P_{2} = P_{0} {(4)}^{γ}$

$Option (2) is correct.$

Q 48 :

A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

100 J
300 J
Zero
200 J

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(2)

$On P - V scale, area of loop = work done$

$\Rightarrow W = + \frac{1}{2} (2) \times 300$ $\Rightarrow W = 300 J$

Q 49 :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

0%

300

Q 50 :

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_{1}$ to $P_{2}$ is $α$ Joule ( $P_{1} = 21.7 Pa$ and $P_{2} = 30 Pa$ , $C_{v} = 21 J/K.mol$ , $R = 8.3 J/mol.K$ ). The value of $α$ is _______. [2026]

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(4)

Topic Question Set

Q 41 :

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

Q 44 :

A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

Q 46 :

The thermodynamic process, in which internal energy of the system remains constant is [2023]

Q 47 :

The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

Q 48 :

A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

Q 49 :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

0%

Q 50 :

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_{1}$ to $P_{2}$ is $α$ Joule ( $P_{1} = 21.7 Pa$ and $P_{2} = 30 Pa$ , $C_{v} = 21 J/K.mol$ , $R = 8.3 J/mol.K$ ). The value of $α$ is _______. [2026]

[IMAGE 60]

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