Question

An ideal monoatomic gas undergoes a process in which the gas volume relates to temperature as $VT=constant$. Then molar specific heat of gas in this process is:

• A. $R/2$
• B. $R$
• C. $4R/2$
• D. $4R$

Answer 1

Answer: (C)

$4R/2$

$P_1{V}_1=RT$

$C_v=\frac{3}{2}R$

$\frac{P}{V}=1$

$\therefore P=V$

$dq=C_{v}dt+pdV$

For $1$ mole of gas

$PV=RT$

On differentiating$,$

$PdV+VdP=RdT$

$\therefore 2PdV=RdT$

$PdV=\frac{RdT}{2}$

$\therefore dq=C_{v}dT+\frac{RdT}{2}$

$=\frac{4R}{2}$

Hence,

option $\left(C\right)$ is correct answer.