Question

In an adiabatic change, the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P\propto T^c$, where $C$ equals to:

• A. $1.6$
• B. $0.4$
• C. $0.6$
• D. $2.5$

Answer 1

Answer: (D)

$2.5$

$\text{Explanation:-}$

For adiabatic change, $P{V}^{\gamma }=constant$

$\Rightarrow P\left(\frac{RT}{\rho }\right)=constant$

$\Rightarrow P^{1-\gamma }{T}^{\gamma }=constant$

$\Rightarrow P\propto T^{\frac{-\gamma }{1-\gamma }}$

Therefore, the value of constant

$C=\frac{\gamma }{(\gamma -1)}$For

$monoatomicgas,\gamma =\frac{5}{3}$

Therefore, $C=\frac{5/3}{\left(5/3\right)-1}$

$C=\frac{5/3}{2/3}$

$C=\frac{5}{2}=2.5$

$\text{Hence the correct option is D}$