What is the molar heat capacity of water? ($R$ is the universal gas constant.)

The value of the gas constant $(R)$ calculated from the perfect gas equation is $8.32 \ J/mol \cdot K$,whereas its value calculated from the knowledge of $C_P$ and $C_V$ of the gas is $1.98 \ cal/mol \cdot K$. From this data,the value of $J$ is ......... $J/cal$.

Select the incorrect relation. (Where symbols have their usual meanings)

If the molar specific heat at constant volume is $\frac{3R}{2}$,then the adiabatic index $\gamma$ is:

$50 \, cal$ of heat is required to raise the temperature of $1 \, mol$ of an ideal gas from $20^{\circ} C$ to $25^{\circ} C$,while the pressure of the gas is kept constant. The amount of heat required to raise the temperature of the same gas through the same temperature range at constant volume is ........ $cal$ $(R = 2 \, cal / mol \cdot K)$.

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?