Question

The air tight and smooth pistons of a cylindrical vessel are connected with a string, as shown. Initially, pressure and temperature are $P_0$ and $T_0$. The atmospheric pressure is also $P_0$. At a later time, tension in the string is $\frac{3}{8}{P}_{0}A$. where A is cross-sectional area of the cylinder. If the temperature of the gas has become $\frac{n}{8}{T}_0$
Then the value of $n$
is

Answer 1

Writing force equation for piston,

$T+P_{0}A=PA$
$T=(P-P_0)A=\frac{3}{8}{P}_{0}A$ (given)
$P=\frac{3}{8}{P}_0+P_0=\frac{11}{8}{P}_0$
The volume is constant because the pistons are connected by a string
So, $P\propto T$
$\Rightarrow \frac{P_i}{T_i}=\frac{P_i}{T_i}$ where i and f denote initial final
Intial temperature is $T_0$
When pressure is $\frac{3}{8}{P}_0$, final temperature $T_f=T_i\frac{P_f}{P_i}=\frac{3}{8}{T}_0$