Answer
(a) $23cm$
(b) $7.5cm$
Work Step by Step
(a) We can find the piston height as follows:
$h=\frac{4nRT}{p_{\circ}\pi d^2+4mg}$
We plug in the known values to obtain:
$h=\frac{4(0.12)(8.31)(303)}{101300\pi+(0.1)^2+4(50)(9.8)}$
$\implies h=23cm$
(b) We know that
$h=\frac{4nRT}{p_{\circ}\pi d^2+4mg}$
We plug in the known values to obtain:
$h=\frac{4(0.12)(8.31)(403)}{101300\pi(0.1)^2+4(50)(9.8)}$
This simplifies to:
$h=31.3cm$
Now $\Delta h=h^{\prime}-h$
$\implies \Delta h=31.3-23.5=7.5cm$
