Question 77 of 168

Two thermodynamical process are shown in the figure. The molar heat capacity for process $A$ and $B$ are ${C}_{A}$ and ${C}_{B}$. The molar heat capacity at constant pressure and constant volume are represented by ${C}_{P}$ and ${C}_{V}$, respectively. Choose the correct statement.

A${C}_{P}\gt {C}_{B}\gt {C}_{V}$B${C}_{A}=0$ and ${C}_{B}=\infty$C${C}_{P}\gt {C}_{V}\gt {C}_{A}={C}_{B}$D${C}_{A}\gt {C}_{P}\gt {C}_{V}$

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Answer: (A) ${C}_{P}\gt {C}_{B}\gt {C}_{V}$

For process $A$:
$\log P=\gamma \log V\Rightarrow P={V}^{\gamma },(\gamma \gt 1)$
$P{V}^{-\gamma }=$ Constant
${C}_{A}={C}_{V}+\dfrac{R}{1+\gamma }\ldots \left(i\right)$
Likewise, for process $B\rightarrow P{V}^{-1}=$ Constant
${C}_{B}={C}_{v}+\dfrac{R}{1+1}$
${C}_{B}={C}_{v}+\dfrac{R}{2}\ldots \left(ii\right)$
Also, ${C}_{P}={C}_{v}+R\ldots \left(iii\right)$
By $\left(ii\right)$ and $\left(iii\right)$, we get
${C}_{P}\gt {C}_{B}\gt {C}_{v}$