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BITSAT 2024

Exam: BITSAT
Year: 2024
Subject: Physics
Chapter: Thermodynamics

BITSAT 2024 · Physics · Thermodynamics

In the given cycle A B C D A , the heat required for an ideal...

In the given cycle

A B C D A

, the heat required for an ideal monoatomic gas will be In the given cycle A B C D A , the heat required for an ideal monoatomic gas will be

In the given cycle A B C D A , the heat required for an ideal monoatomic gas will be

Options

A $p_0 V_0$
B $\frac{13}{2} p_0 V_0$
C $\frac{11}{2} p_0 V_0$
D $4 p_0 V_0$

Correct answer

B. $\frac{13}{2} p_0 V_0$

Step-by-step solution

In the given cycle, heat is supplied in process

D

to A

at constant volume and in process A to B

at constant pressure.

\therefore

Heat supplied,

Q=n C_V(\Delta T)_{D A}+n C_p(\Delta T)_{A B}

For an ideal monoatomic gas,

\begin{aligned} C_V & =\frac{3}{2} R \text{ and } C_p=\frac{5}{2} R \\ \Rightarrow \quad Q & =\frac{3}{2} n R \Delta T+\frac{5}{2} n R \Delta T \quad[\because n R \Delta T=p \Delta V] \\ & =\frac{3}{2}\left(p_0 V_0\right)+5\left(p_0 V_0\right) \\ & =\frac{13}{2} p_0 V_0 \end{aligned}

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