QBManager

PHXI12:THERMODYNAMICS

371465 During an adiabatic expansion, the increase in volume is associated with which of the following possibilities regarding pressure and temperature ?
$P r e s s u r e T e m p e r a t u r e$

1

\begin{matrix} I n c r e a s e & I n c r e a s e \end{matrix}

2

\begin{matrix} D e c r e a s e & D e c r e a s e \end{matrix}

3

\begin{matrix} I n c r e a s e & D e c r e a s e \end{matrix}

4

\begin{matrix} D e c r e a s e & I n c r e a s e \end{matrix}

Explanation:

$P V^{γ} =$ const $\Rightarrow V^{γ} \propto \frac{1}{P}$
$T V^{γ - 1} =$ const $\Rightarrow V^{γ - 1} \propto \frac{1}{T}$

PHXI12:THERMODYNAMICS

371466 In a thermodynamic system, ' $W$ ' represents the work done by the system and ' $Δ U$ ' is the increase in internal energy. Which of the following statements is true?

1 In an isothermal process,

Δ U = W

2 In an adiabatic process,

Δ U = - W

3 In an isothermal process,

Δ U = - W

4 In an adiabatic process,

Δ U = W

.

Explanation:

According to the first law of thermodynamics
$Δ Q = Δ U + Δ W$
In adiabatic process
$Δ U = - Δ W$

MHTCET - 2022

PHXI12:THERMODYNAMICS

371467 During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{P}}{C_{V}}$ for the gas is

1

\frac{4}{3}

2

2

3

\frac{5}{3}

4

\frac{3}{2}

Explanation:

Given adiabatic process $P \propto T^{3}$ .
Ideal gas equation $\Rightarrow T = \frac{P V}{n R}$
$P \propto T^{3}$
$P \propto (P V)^{3} \Rightarrow P^{2} V^{3} = P V^{\frac{3}{2}} =$ constant
Comparing with $P V^{γ} =$ constant
Hence, $γ = \frac{3}{2}$ .

PHXI12:THERMODYNAMICS

371468 Assertion :
Air quickly leaking out of a balloon becomes cooler.
Reason :
The leaking air undergoes adiabatic expansion

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Both Assertion and Reason are incorrect.

4 Assertion is incorrect but Reason is correct.

AIIMS - 2005

PHXI12:THERMODYNAMICS

371469 A monoatomic gas $(γ = \frac{5}{3})$ is suddenly compressed to $1 / 8$ of its volume adiabatically. If the initial pressure is $P$ , then the final pressure of the gas is

1

\frac{24}{5} P

2

8 P

3

\frac{40}{3} P

4

32 P

Explanation:

For adiabatic process, $P V^{γ} = constant ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P V^{γ} = P_{2} {(\frac{V}{8})}^{γ},$ $(∵ V_{2} = \frac{V}{8})$
$P = \frac{P_{2}}{8^{γ}}$ or $P_{2} = 8^{γ} P$
$∴ P_{2} = 8^{5 / 3} P$ $(∵ γ = \frac{5}{3})$
$\Rightarrow P_{2} = 32 P$ .
So correct option is (4)

PHXI12:THERMODYNAMICS

371465 During an adiabatic expansion, the increase in volume is associated with which of the following possibilities regarding pressure and temperature ?
$P r e s s u r e T e m p e r a t u r e$

1

\begin{matrix} I n c r e a s e & I n c r e a s e \end{matrix}

2

\begin{matrix} D e c r e a s e & D e c r e a s e \end{matrix}

3

\begin{matrix} I n c r e a s e & D e c r e a s e \end{matrix}

4

\begin{matrix} D e c r e a s e & I n c r e a s e \end{matrix}

Explanation:

$P V^{γ} =$ const $\Rightarrow V^{γ} \propto \frac{1}{P}$
$T V^{γ - 1} =$ const $\Rightarrow V^{γ - 1} \propto \frac{1}{T}$

PHXI12:THERMODYNAMICS

371466 In a thermodynamic system, ' $W$ ' represents the work done by the system and ' $Δ U$ ' is the increase in internal energy. Which of the following statements is true?

1 In an isothermal process,

Δ U = W

2 In an adiabatic process,

Δ U = - W

3 In an isothermal process,

Δ U = - W

4 In an adiabatic process,

Δ U = W

.

Explanation:

According to the first law of thermodynamics
$Δ Q = Δ U + Δ W$
In adiabatic process
$Δ U = - Δ W$

MHTCET - 2022

PHXI12:THERMODYNAMICS

371467 During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{P}}{C_{V}}$ for the gas is

1

\frac{4}{3}

2

2

3

\frac{5}{3}

4

\frac{3}{2}

Explanation:

Given adiabatic process $P \propto T^{3}$ .
Ideal gas equation $\Rightarrow T = \frac{P V}{n R}$
$P \propto T^{3}$
$P \propto (P V)^{3} \Rightarrow P^{2} V^{3} = P V^{\frac{3}{2}} =$ constant
Comparing with $P V^{γ} =$ constant
Hence, $γ = \frac{3}{2}$ .

PHXI12:THERMODYNAMICS

371468 Assertion :
Air quickly leaking out of a balloon becomes cooler.
Reason :
The leaking air undergoes adiabatic expansion

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Both Assertion and Reason are incorrect.

4 Assertion is incorrect but Reason is correct.

AIIMS - 2005

PHXI12:THERMODYNAMICS

371469 A monoatomic gas $(γ = \frac{5}{3})$ is suddenly compressed to $1 / 8$ of its volume adiabatically. If the initial pressure is $P$ , then the final pressure of the gas is

1

\frac{24}{5} P

2

8 P

3

\frac{40}{3} P

4

32 P

Explanation:

For adiabatic process, $P V^{γ} = constant ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P V^{γ} = P_{2} {(\frac{V}{8})}^{γ},$ $(∵ V_{2} = \frac{V}{8})$
$P = \frac{P_{2}}{8^{γ}}$ or $P_{2} = 8^{γ} P$
$∴ P_{2} = 8^{5 / 3} P$ $(∵ γ = \frac{5}{3})$
$\Rightarrow P_{2} = 32 P$ .
So correct option is (4)

PHXI12:THERMODYNAMICS

371465 During an adiabatic expansion, the increase in volume is associated with which of the following possibilities regarding pressure and temperature ?
$P r e s s u r e T e m p e r a t u r e$

1

\begin{matrix} I n c r e a s e & I n c r e a s e \end{matrix}

2

\begin{matrix} D e c r e a s e & D e c r e a s e \end{matrix}

3

\begin{matrix} I n c r e a s e & D e c r e a s e \end{matrix}

4

\begin{matrix} D e c r e a s e & I n c r e a s e \end{matrix}

Explanation:

$P V^{γ} =$ const $\Rightarrow V^{γ} \propto \frac{1}{P}$
$T V^{γ - 1} =$ const $\Rightarrow V^{γ - 1} \propto \frac{1}{T}$

PHXI12:THERMODYNAMICS

371466 In a thermodynamic system, ' $W$ ' represents the work done by the system and ' $Δ U$ ' is the increase in internal energy. Which of the following statements is true?

1 In an isothermal process,

Δ U = W

2 In an adiabatic process,

Δ U = - W

3 In an isothermal process,

Δ U = - W

4 In an adiabatic process,

Δ U = W

.

Explanation:

According to the first law of thermodynamics
$Δ Q = Δ U + Δ W$
In adiabatic process
$Δ U = - Δ W$

MHTCET - 2022

PHXI12:THERMODYNAMICS

371467 During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{P}}{C_{V}}$ for the gas is

1

\frac{4}{3}

2

2

3

\frac{5}{3}

4

\frac{3}{2}

Explanation:

Given adiabatic process $P \propto T^{3}$ .
Ideal gas equation $\Rightarrow T = \frac{P V}{n R}$
$P \propto T^{3}$
$P \propto (P V)^{3} \Rightarrow P^{2} V^{3} = P V^{\frac{3}{2}} =$ constant
Comparing with $P V^{γ} =$ constant
Hence, $γ = \frac{3}{2}$ .

PHXI12:THERMODYNAMICS

371468 Assertion :
Air quickly leaking out of a balloon becomes cooler.
Reason :
The leaking air undergoes adiabatic expansion

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Both Assertion and Reason are incorrect.

4 Assertion is incorrect but Reason is correct.

AIIMS - 2005

PHXI12:THERMODYNAMICS

371469 A monoatomic gas $(γ = \frac{5}{3})$ is suddenly compressed to $1 / 8$ of its volume adiabatically. If the initial pressure is $P$ , then the final pressure of the gas is

1

\frac{24}{5} P

2

8 P

3

\frac{40}{3} P

4

32 P

Explanation:

For adiabatic process, $P V^{γ} = constant ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P V^{γ} = P_{2} {(\frac{V}{8})}^{γ},$ $(∵ V_{2} = \frac{V}{8})$
$P = \frac{P_{2}}{8^{γ}}$ or $P_{2} = 8^{γ} P$
$∴ P_{2} = 8^{5 / 3} P$ $(∵ γ = \frac{5}{3})$
$\Rightarrow P_{2} = 32 P$ .
So correct option is (4)

PHXI12:THERMODYNAMICS

371465 During an adiabatic expansion, the increase in volume is associated with which of the following possibilities regarding pressure and temperature ?
$P r e s s u r e T e m p e r a t u r e$

1

\begin{matrix} I n c r e a s e & I n c r e a s e \end{matrix}

2

\begin{matrix} D e c r e a s e & D e c r e a s e \end{matrix}

3

\begin{matrix} I n c r e a s e & D e c r e a s e \end{matrix}

4

\begin{matrix} D e c r e a s e & I n c r e a s e \end{matrix}

Explanation:

$P V^{γ} =$ const $\Rightarrow V^{γ} \propto \frac{1}{P}$
$T V^{γ - 1} =$ const $\Rightarrow V^{γ - 1} \propto \frac{1}{T}$

PHXI12:THERMODYNAMICS

371466 In a thermodynamic system, ' $W$ ' represents the work done by the system and ' $Δ U$ ' is the increase in internal energy. Which of the following statements is true?

1 In an isothermal process,

Δ U = W

2 In an adiabatic process,

Δ U = - W

3 In an isothermal process,

Δ U = - W

4 In an adiabatic process,

Δ U = W

.

Explanation:

According to the first law of thermodynamics
$Δ Q = Δ U + Δ W$
In adiabatic process
$Δ U = - Δ W$

MHTCET - 2022

PHXI12:THERMODYNAMICS

371467 During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{P}}{C_{V}}$ for the gas is

1

\frac{4}{3}

2

2

3

\frac{5}{3}

4

\frac{3}{2}

Explanation:

Given adiabatic process $P \propto T^{3}$ .
Ideal gas equation $\Rightarrow T = \frac{P V}{n R}$
$P \propto T^{3}$
$P \propto (P V)^{3} \Rightarrow P^{2} V^{3} = P V^{\frac{3}{2}} =$ constant
Comparing with $P V^{γ} =$ constant
Hence, $γ = \frac{3}{2}$ .

PHXI12:THERMODYNAMICS

371468 Assertion :
Air quickly leaking out of a balloon becomes cooler.
Reason :
The leaking air undergoes adiabatic expansion

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Both Assertion and Reason are incorrect.

4 Assertion is incorrect but Reason is correct.

AIIMS - 2005

PHXI12:THERMODYNAMICS

371469 A monoatomic gas $(γ = \frac{5}{3})$ is suddenly compressed to $1 / 8$ of its volume adiabatically. If the initial pressure is $P$ , then the final pressure of the gas is

1

\frac{24}{5} P

2

8 P

3

\frac{40}{3} P

4

32 P

Explanation:

For adiabatic process, $P V^{γ} = constant ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P V^{γ} = P_{2} {(\frac{V}{8})}^{γ},$ $(∵ V_{2} = \frac{V}{8})$
$P = \frac{P_{2}}{8^{γ}}$ or $P_{2} = 8^{γ} P$
$∴ P_{2} = 8^{5 / 3} P$ $(∵ γ = \frac{5}{3})$
$\Rightarrow P_{2} = 32 P$ .
So correct option is (4)

PHXI12:THERMODYNAMICS

371465 During an adiabatic expansion, the increase in volume is associated with which of the following possibilities regarding pressure and temperature ?
$P r e s s u r e T e m p e r a t u r e$

1

\begin{matrix} I n c r e a s e & I n c r e a s e \end{matrix}

2

\begin{matrix} D e c r e a s e & D e c r e a s e \end{matrix}

3

\begin{matrix} I n c r e a s e & D e c r e a s e \end{matrix}

4

\begin{matrix} D e c r e a s e & I n c r e a s e \end{matrix}

Explanation:

$P V^{γ} =$ const $\Rightarrow V^{γ} \propto \frac{1}{P}$
$T V^{γ - 1} =$ const $\Rightarrow V^{γ - 1} \propto \frac{1}{T}$

PHXI12:THERMODYNAMICS

371466 In a thermodynamic system, ' $W$ ' represents the work done by the system and ' $Δ U$ ' is the increase in internal energy. Which of the following statements is true?

1 In an isothermal process,

Δ U = W

2 In an adiabatic process,

Δ U = - W

3 In an isothermal process,

Δ U = - W

4 In an adiabatic process,

Δ U = W

.

Explanation:

According to the first law of thermodynamics
$Δ Q = Δ U + Δ W$
In adiabatic process
$Δ U = - Δ W$

MHTCET - 2022

PHXI12:THERMODYNAMICS

371467 During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{P}}{C_{V}}$ for the gas is

1

\frac{4}{3}

2

2

3

\frac{5}{3}

4

\frac{3}{2}

Explanation:

Given adiabatic process $P \propto T^{3}$ .
Ideal gas equation $\Rightarrow T = \frac{P V}{n R}$
$P \propto T^{3}$
$P \propto (P V)^{3} \Rightarrow P^{2} V^{3} = P V^{\frac{3}{2}} =$ constant
Comparing with $P V^{γ} =$ constant
Hence, $γ = \frac{3}{2}$ .

PHXI12:THERMODYNAMICS

371468 Assertion :
Air quickly leaking out of a balloon becomes cooler.
Reason :
The leaking air undergoes adiabatic expansion

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Both Assertion and Reason are incorrect.

4 Assertion is incorrect but Reason is correct.

AIIMS - 2005

PHXI12:THERMODYNAMICS

371469 A monoatomic gas $(γ = \frac{5}{3})$ is suddenly compressed to $1 / 8$ of its volume adiabatically. If the initial pressure is $P$ , then the final pressure of the gas is

1

\frac{24}{5} P

2

8 P

3

\frac{40}{3} P

4

32 P

Explanation:

For adiabatic process, $P V^{γ} = constant ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P V^{γ} = P_{2} {(\frac{V}{8})}^{γ},$ $(∵ V_{2} = \frac{V}{8})$
$P = \frac{P_{2}}{8^{γ}}$ or $P_{2} = 8^{γ} P$
$∴ P_{2} = 8^{5 / 3} P$ $(∵ γ = \frac{5}{3})$
$\Rightarrow P_{2} = 32 P$ .
So correct option is (4)