MCQ
A gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{{\sqrt V }}$, the value of ${C_P}/{C_V}$ of gas is
- A$1.3$
- ✓$1.5$
- C$1.67$
- D$2$
✓
Answer
Correct option: B.
$1.5$
b
(b) $T{V^{\gamma - 1}} = $ constant ==> $T \propto {V^{1 - \gamma }}$
(b) $T{V^{\gamma - 1}} = $ constant ==> $T \propto {V^{1 - \gamma }}$
According to question $T \propto {V^{ - \frac{1}{2}}}$
Hence $1 - \gamma = - \frac{1}{2} \Rightarrow \gamma \frac{3}{2} = 1.5$
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