Question

A closed hollow insulated cylinder is filled with gas at $0^{o}C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side is heated to ${100}^{o}C$. If the piston moves through 5 cm, the length of the hollow cylinder is

• A. 13.65 cm
• B. 27.3 cm
• C. 38.6 cm
• D. 64.6 cm

Answer 1

The correct option is D

64.6 cm

Let L be the length (in cm) of the follow cylinder and r its radius. Since the mass of the gas remains unchanged and the pressures of the gas in both sides are equal, we have, from Charles' law,
$\frac{V_1}{T_1}=\frac{V_2}{T_2}......\left(1\right)Given{V}_1=(\frac{L}{2}-5)\pi r^2,V_2=(\frac{L}{2}+5)\pi r^2,T_1=0^{o}C=273Kand{T}_2={100}^{o}C=373K.$ Using these values in (1), we get
$\frac{\frac{L}{2}-5}{273}=\frac{\frac{L}{2}+5}{373}$
which gives L = 64.6 cm.