Problem 2.10

A smooth vertical tube having two different sections is open from both ends and equipped with two pistons of different areas (Fig. 2.1). Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a non-stretchable thread. The crosssectional area of the upper piston is $\Delta S=10 \mathrm{~cm}^{2}$ greater than that of the lower one. The combined mass of the two pistons is equal to $m=5.0 \mathrm{~kg}$. The outside air pressure is $p_{0}=1.0$ atm. By how many kelvins must the gas between the pistons be heated to shift the pistons through $l=5.0 \mathrm{~cm} ?$