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

A gas expands isthermally an reversibly.The work done by the gas is ______.

Two spheres $A$ and $B$ with masses in the ratio $2 : 3$ and specific heat $2 : 3$ fall freely rest. If the rest in their temperatures on reaching the ground in the ratio $1 : 2$ the ratio of their heights of fall is:-

An ideal gas $A$ and a real gas $B$ have their volumes increased from $V$ to $2V$ under isothermal conditions.The increase in internal energy

An ideal monoatomic gas undergoes expansion according to $P=bV$,Where 'b' is a constant.Molar heat capacity of gas in the process is