Two thermodynamical process are shown in the figure. The molar he… - Vidyadip

MCQ

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
$C_B=\infty, C_A=0$
B
$C_A=0$ and $C_B=\infty$
C
$C_P>C_B>C_A>C_V$
D
$C_A>C_P>C_V$

✓

Answer

For process $A$
$\log P=\gamma \log V \Rightarrow P=V^\gamma,(\gamma>1)$
$P V^{-\gamma}=\text { Constant }$
$C_A=C_V+\frac{R}{1+\gamma} \ldots . \text { (i) }$
Likewise for process $B \rightarrow P V^{-1}=\text { Constant }$
$C_B =C_v+\frac{R}{1+1}$
$C_B =C_v+\frac{R}{2} \ldots (ii)$
$C_P =C_v+R \ldots(iii)$
By $(i), (ii) \ (iii)$
$C_P>C_B>C_A>C_v$

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