Question

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

Using Boyle's law, we have $\frac{V}{T}=$ constant

$\Rightarrow \frac{\frac{l}{2}+5}{373}=\frac{\frac{l}{2}-5}{273}$
As the piston moves 5 cm, the length of one side will be $(\frac{l}{2}+5)$ and other side $(\frac{l}{2}-5)$. On solving this equation, we get $I=64.6cm.$