One mole of an ideal monoatomic gas is heated at a constant pressure from $0^{\circ} C$ to $100^{\circ} C$. The change in the internal energy of the gas is (Given, $R = 8.32 \text{ J mol}^{-1} \text{ K}^{-1}$):

The figure shows the variation in heat supplied $(Q)$ with the change in temperature $(\Delta T)$ in an isobaric process for a monoatomic $(M)$,diatomic $(D)$,and a polyatomic $(P)$ gas. The initial state of all the gases is the same,and the scales for the two axes coincide. Ignoring vibrational degrees of freedom,the lines $a, b,$ and $c$ respectively correspond to

The difference between the two specific heats of $1\, g$ of helium gas at $NTP$ is .... $cal\, g^{-1} K^{-1}$. (Atomic weight of helium $= 4$ and $J = 4.186 \times 10^7\, erg\, cal^{-1}$)

One mole of an ideal gas $\left( \frac{C_P}{C_V} = \gamma \right)$ is heated according to the law $P = \alpha V$,where $P$ is the pressure of the gas,$V$ is the volume,and $\alpha$ is a constant. What is the molar heat capacity of the gas in this process?

In the case of a diatomic gas,the fraction of heat supplied at constant pressure that is used for the expansion of the gas is:

What amount of heat (in $J$) must be supplied to $2.0 \times 10^{-2} \; kg$ of nitrogen (at room temperature) to raise its temperature by $45 \; ^{\circ}C$ at constant pressure? (Molecular mass of $N_{2} = 28; R = 8.3 \; J \; mol^{-1} K^{-1}$.)