The heat capacity of a certain amount of a particular gas at constant pressure is greater than that at constant volume by $29.1 J / K$ . Match the items given in Column I with the items given in Column II.

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Solution

Heat capacity at constant volume for an ideal gas is given by the formula

$C_{V} = \frac{f}{2} R$ where f is total degrees of freedom.

Heat capacity at constant pressure for an ideal gas is given by the formula

$C_{P} = \frac{f + 2}{2} R$

For monoatomic gas, no rotational degrees of freedom. Hence $f = 3$

$C_{V} = \frac{3}{2} (29.1) = 43.7 J / K$

$C_{P} = \frac{5}{2} (29.1) = 72.7 J / K$

For diatomic gas, $f = 3 + 2 = 5$

$C_{P} = \frac{7}{2} (29.1) = 102 J / K$

For vibrating gas, $f = 3 + 2 + 2 = 7$

$C_{P} = \frac{9}{2} (29.1) = 131 J / K$

Answer is A- 2, B- 3, C- 4, D- 1

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29.1 J/K

\begin{matrix} Column I & Column II i. If the gas is monoatomic, heat capacity at constant volume & a. 131 J/K ii. If the gas is monoatomic, heat capacity at constant pressure & b. 43.7 J/K iii. If the gas is rigid diatomic, heat capacity at constant pressure & c. 72.7 J/K iv. If the gas is vibrating diatomic, heat capacity at constant pressure & d. 102 J/K \end{matrix}

29.1 J/K

\begin{matrix} Column I & Column II i. If the gas is monoatomic, heat capacity at constant volume & a. 131 J/K ii. If the gas is monoatomic, heat capacity at constant pressure & b. 43.7 J/K iii. If the gas is rigid diatomic, heat capacity at constant pressure & c. 72.7 J/K iv. If the gas is vibrating diatomic, heat capacity at constant pressure & d. 102 J/K \end{matrix}

List 1	List 2
If the gas is monatomic, heat capacity at constant volume	131 J/K
If the gas monatomic, heat capacity at constant pressure	43.7 J/K
If the gas is rigid diatomic, heat capacity at constant pressure	72.7 J/K
If the gas is vibrating diatomic, heat capacity at constant pressure	102 J/K

29.1 J / K

29.1 J / K

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