The heat required to raise the temperature of $5$ moles of $O_2$ from $10\,^{\circ}C$ to $20\,^{\circ}C$ at constant volume is ....... $cal$. Given: $C_p = 7.2\,cal/mol/^{\circ}C$ and $R = 2\,cal/mol/^{\circ}C$.

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 $N_{2} = 28; R = 8.3 \; J \; mol^{-1} K^{-1}$.)

What is the relationship between the internal energy $U$ of an ideal gas and its pressure $P$ and volume $V$?

If $\Delta Q$ is the amount of heat supplied to $n$ moles of a diatomic gas at constant pressure,$\Delta U$ is the change in internal energy,and $\Delta W$ is the work done,then the ratio $\Delta W : \Delta U : \Delta Q$ is

Given below are observations on molar specific heats at room temperature of some common gases.

Gas	Molar specific heat $(C_v)$ $(cal\, mol^{-1}\, K^{-1})$
Hydrogen	$4.87$
Nitrogen	$4.97$
Oxygen	$5.02$
Nitric oxide	$4.99$
Carbon monoxide	$5.01$
Chlorine	$6.17$

The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically,molar specific heat of a monatomic gas is $2.92 \; cal/mol\; K$. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?

For a gas,$\frac{R}{C_{v}} = 0.67$. This gas is made up of molecules which are