Question

The ratio of specific heat at constant pressure to the specific heat at constant volume for argon and helium is-
1. 1.11
2. 1.3
3. 1.4
4. 1.667

Answer 1

Correct Answer - Option 4 : 1.667

Concept:

• The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.

\({C_v} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;volume}}\)

• The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

\({C_p} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;pressure}}\)

• The relation between the ratio of Cp and Cv with a degree of freedom is given by

\(\gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

Where f = degree of freedom

EXPLANATION:

• The relation between the ratio of Cp and Cv with a degree of freedom is given by

\(\Rightarrow \gamma = \frac{{{C_p}}}{{{C_v}}} = 1 + \frac{2}{f}\)

Monoatomic gas has 3 degrees of freedom

\(\Rightarrow \gamma = 1 + \frac{2}{3} = \frac{3 +2}{3} = \frac{5}{3} =1.67\)