Question

Heat capacity of a diatomic gas is smaller than that of a monatomic gas.
A. True
B. False

Answer 1

$\left( {{{\text{C}}_{\text{v}}}} \right)$ is the molar specific heat capacity of a gas at constant volume It is defined as the amount of heat that is needed to raise the temperature of one mol of the gas by ${{1 ^\circ C}}$at the constant volume. $\left( {{{\text{C}}_{\text{p}}}} \right)$ is the molar specific heat of a gas at constant pressure. It is defined as the amount of heat required to raise the temperature of one mol of the gas by ${{1 ^\circ C}}$ at a constant pressure.

Complete step by step answer:
For monatomic ideal gas $\left( {{{\text{C}}_{\text{v}}}} \right)$ is ${\dfrac{3R}{2}}$ and the value for diatomic ideal gas it is ${\dfrac{5R}{2}}$. $\left( {{{\text{C}}_{\text{p}}}} \right)$ for monatomic ideal gas is ${\dfrac{5R}{2}}$ and the value for diatomic ideal gas is ${\dfrac{7R}{2}}$.
On the basis of degrees of freedom, a gas molecule will move when we give a certain amount of energy (form of electromagnetic or thermal) to the molecule. This resulting movement can be translational (moving straight line along the 3 axes, i.e., 3 degrees of freedom), rotational (can be clockwise and anti-clockwise i.e.’ 2 degrees of freedom) or vibrational (1 degree of freedom).Thus, for mono-atomic and di-atomic gas molecules the total possible degrees of freedom are 6.
But at room temperature, the monatomic gases can have only three degrees of freedom (because an atom cannot rotate around its own or vibrate), whereas diatomic molecules have five degrees of freedom (3 translational and 2 rotational).
Therefore, heat capacity of diatomic atomic gases is higher than that of monoatomic gases and heat capacity of polyatomic atomic gases is less than that of monoatomic gases
Hence, the answer to the above question is option B, False.

Note: Specific Heat of Water: For liquid at room temperature and pressure, the value of specific heat capacity ($C_p$) is approximately 4.187 kJ/kgK
The heat capacity of a substance is the amount of heat required to change its temperature by one degree. It is the measure of the total internal energy of a system. For quantifying the heat energy associated with matter and the dependence on temperature, two properties are put forward. These properties are specific heat capacity and heat capacity of the system.