Find the heat energy required to increase the temperature of $2$ moles of a monoatomic gas from $273 \ K$ to $373 \ K$. (No work is done in the process.) (in $R$)

$A$ cyclic process is shown in the figure. The work done during the isobaric expansion is ...... $J$.

For an isochoric process,if $T_1 = 27 \, ^\circ C$ and $T_2 = 127 \, ^\circ C$,then $P_1 / P_2 = \dots$

In a reversible isochoric change,

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

$A$ 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 $\text{ J}$)