An enclosed one mole of a monoatomic gas is taken through a process $A$ to $B$ as shown in the figure. The molar heat capacity of the gas for this process is

One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

One mole of an ideal monoatomic gas expands along the polytropic process $PV^3 = \text{constant}$ from volume $V_1$ to $V_2$. The molar specific heat capacity for this process is given by $C = C_V + \frac{R}{1-n}$. The total heat absorbed during the process can be expressed as:

$A$ diatomic gas undergoes a process represented by $PV^{1.3} = \text{constant}$. Choose the incorrect statement.

$A$ gas is found to obey the law $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$,its final temperature becomes

Consider a $P - V$ diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in the figure.
$(a)$ Find the work done when the gas is taken from state $1$ to state $2$.
$(b)$ What is the ratio of temperature $\frac{T_1}{T_2}$ if $V_2 = 2V_1$?
$(c)$ Given the internal energy for one mole of gas at temperature $T$ is $\frac{3}{2}RT$,find the heat supplied to the gas when it is taken from state $1$ to $2$,with $V_2 = 2V_1$.