Question

An insulated cylindrical vessel is filled with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel. The cylinder contains a gas at $0^{\circ }C$. When the gas is heated to ${100}^{\circ }C$, the piston moves through a length of $5cm$. Length of the cylindrical vessel in $cm$ is:

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

Answer 1

The correct option is A $13.65$

The given process is isobaric.

So, $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

$⟹$ $\frac{AL}{273}=\frac{A(L+5)}{373}$, where $A$ and $L$ are corss-section area of the piston and the initial length of the gas column respectively.

Solving, we get: $L=13.65cm$