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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Specific Heat Capacities of Gases

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Specific Heat Capacities of Gases

Two samples A and B are initially maintained in identical states....

Two samples

A

and

B

are initially maintained in identical states. Sample

A

undergoes expansion via an adiabatic process, whereas sample

B

expands via an isothermal process. Both samples reach the same final volume. If the final pressures for

A

and

B

are denoted by

p_A

and

p_B

respectively, then:

Options

A $p_A > p_B$
B $p_A < p_B$
CThe relationship between $p_A$ and $p_B$ cannot be determined
D $p_A = p_B$

Correct answer

B. $p_A < p_B$

Step-by-step solution

Let the initial pressure and volume of both samples be

p_0

and

V_0

respectively.

Let the final volume be

V

, where

V > V_0

since the gas undergoes expansion.

For sample

A

(adiabatic process):

p_A V^{\gamma} = p_0 V_0^{\gamma} \Rightarrow p_A = p_0 \left(\dfrac{V_0}{V}\right)^{\gamma}

For sample

B

(isothermal process):

p_B V = p_0 V_0 \Rightarrow p_B = p_0 \left(\dfrac{V_0}{V}\right)<br><br>Since

V > V_0

, the ratio \dfrac{V_0}{V}

< 1

.<br><br>As the ratio of specific heats

\gamma > 1

, we have \left(\dfrac{V_0}{V}\right)^{\gamma} < \left(\dfrac{V_0}{V}\right).<br><br>Therefore,

p_A < p_B

.

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