# The ratio of specific heat at constant pressure to the specific heat at constant volume for a monoatomic gas, is:

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## Options:

1. 1.6

2. 1.2

3. 1.4

4. 1.8

### Correct Answer: Option 1 (Solution Below)

This question was previously asked in

SSC JE ME Previous Paper 7 (Held on: 27 October 2020 Morning)

SSC JE ME Previous Paper (Held on: 27 October 2020 Morning)

## Solution:

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

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