A gas expands adiabatically at constant pressure such that its te… - Vidyadip

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 ==> $T \propto {V^{1 - \gamma }}$

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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