$A$ diatomic gas $(\gamma = 1.4)$ does $300 \ J$ of work when expanded isobarically. The heat given to the gas in this process is: (in $J$)

$A$ graph is drawn between absolute temperature and volume of $3$ moles of helium gas as shown in the figure. If $5 \text{ cal}$ of heat is used in the process, then the work done is (in $\text{ J}$)

The condition $dQ = dU$ (heat supplied equals the increase in internal energy) is true for which of the following processes?

In a reversible isochoric change,

Work done by $0.1$ mole of a gas at $27^{\circ}C$ to double its volume at constant pressure is ....... $cal$ $(R = 2 \, cal \, mol^{-1} \, K^{-1})$.

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