Question

In an adiabatic change, the pressure P and temperature T of a monoatomic gas are related as $P\alpha T^c$ where c equals -

• A. $\frac{5}{3}$
• B. $\frac{2}{3}$
• C. $\frac{3}{5}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

In adiabatic process, relation between P and T :
$P^{1-\gamma }{T}^{\gamma }=constant$

so $P\alpha T^{\frac{\gamma }{\gamma -1}}$

$\gamma =\frac{5}{3}$ for monatomic gas
and $c=\frac{\gamma }{\gamma -1}$

so $c=\frac{\frac{5}{3}}{\frac{5}{3}-1}$
$C=\frac{5}{2}$.