Question

In an adiabatic change, the pressure $P$ and temperature $T$ of a diatomic gas are realtion $P\propto T^{\alpha }$ where $\alpha$ equals

• A. $1.67$
• B. $0.4$
• C. $0.6$
• D. $3.5$

Answer 1

The correct option is D $3.5$

The equation of state is given by:
$T^{\gamma }{P}^{\gamma -1}=constant$
$P^{\gamma -1}=\left(constant\right)T^{-\gamma }$

$P=\left(constant\right)T^{\left(\frac{-\gamma }{\gamma -1}\right)}$
$\alpha =\frac{-\gamma }{\gamma -1}$
for a diatomic gas: $\gamma =\frac{7}{5}$
i.e. $\alpha =-3.5$
Hence option D is correct.