Question

The relation between $P$ and $T$ for monoatomic gas during adiabatic process is $P\propto T$ ${}^c$. The value of c is

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

Answer 1

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

For an adiabatic process we have $P{T}^{\left(\frac{\gamma }{1-\gamma }\right)}=constant$
or, $P\propto \frac{1}{T^{\left(\frac{\gamma }{1-\gamma }\right)}}$

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

Now, $\frac{-\gamma }{1-\gamma }=c$

For a monoatomic gas we have $\gamma$ as $\frac{5}{3}$.

$\frac{\frac{-5}{3}}{1-\frac{5}{3}}=c$

Thus we get $c=\frac{5}{2}$