The change in the internal energy of $3$ moles of a gas heated at constant volume from $20^{\circ}C$ to $40^{\circ}C$ is $1080 \ J$. The molar specific heat of the gas at constant volume in $J \ mol^{-1} \ K^{-1}$ is:

Two moles of ideal helium gas are in a rubber balloon at $30^{\circ} C$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^{\circ} C$. The amount of heat required in raising the temperature is nearly (take $R = 8.31 \ J / mol \cdot K$) (in $J$)

Which of the following graphs between pressure $(P)$ and volume $(V)$ of a gas correctly shows an isochoric process in thermodynamics?

The percentage of heat supplied to a diatomic ideal gas that is converted into work in an isobaric process is

Which of the following relations is correct for an isochoric process?

Volume versus temperature graph of two moles of helium gas is as shown in figure. The ratio of heat absorbed and the work done by the gas in process $1-2$ is