Question

An ideal $C{O}_2$ gas obey the law $P{V}^x=constant$. The value of x for which it has non positive molar specific heat at normal temperature, is

• A. $-0.5$
• B. $1.45$
• C. $1.4$
• D. $-1.4$

Answer 1

The correct option is C $1.4$

$Molar$ $Specific$ $heat\left(C\right)=C_v+\frac{R}{1-x}$

As negative value is not possible the only non-positive case is $C=0$

$C_v=\frac{5R}{2}$

$\Rightarrow \frac{5R}{2}=\frac{R}{x-1}$

$\Rightarrow x=1.4$