Question

In an adiabatic process, $R=\frac{2}{3}{C}_v$. The pressure of the gas will be proportional to:

• A. $T^{5/3}$
• B. $T^{5/2}$
• C. $T^{5/4}$
• D. $T^{5/6}$

Answer 1

Answer: (B)

$T^{5/2}$

It is given that, $C_v=1.5R$
Using, $C_p=C_v+R$,
$C_p=2.5R$
Thus, $\gamma =\frac{2.5}{1.5}=5/3$

Now,
Using the condition of adiabaticity,
$P^{1-\gamma }{T}^{\gamma }=constant$
Substituting the value of $\gamma$ ,
Pressure is directly proportional to $T^{5/2}$