$dQ$ is the heat energy supplied to an ideal gas under isochoric conditions. If $dU$ and $dW$ denote the change in internal energy and the work done respectively,then:

Given the relation $V = K \left( \frac{P}{T} \right)^{0.33}$,where $K$ is a constant. Identify the type of thermodynamic process.

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 $J$)

The equation of state for a gas is given by $PV = nRT + \alpha V$,where $n$ is the number of moles and $\alpha$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_0$ and $P_0$ respectively. The work done by the gas when its temperature doubles isobarically will be

Two cylinders contain the same amount of an ideal monatomic gas. The same amount of heat is given to both cylinders. If the temperature rise in cylinder $A$ is $T_0$,then the temperature rise in cylinder $B$ will be:

The heat energy supplied to a diatomic gas at constant pressure is $210 \,J$. Then, the work done by the gas is: (in $\,J$)