Question

The molar heat capacity at a constant pressure for a diatomic molecule will be:
1. \(\frac{7}{2}R\)
2. \(\frac{5}{2}R\)
3. R
4. \(\frac{3}{2}R\)

Answer 1

Correct Answer - Option 1 : \(\frac{7}{2}R\)

EXPLANATION:

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.

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

• 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.

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

• The ratio of the two principal specific heat is represented by γ.

\(\therefore \gamma = \frac{{{C_p}}}{{{C_v}}}\)

• The value of γ depends on the atomicity of the gas.
• For monoatomic gas, 

​\(C_P = \frac{5}{2} R\) 

• For diatomic gas,

\(C_P = \frac{7}{2} R\)

• Therefore, option 1 is correct.

• Specific heat capacity at constant volume (CV): It is the amount of heat required to raise the temperature of 1 kg of gas maintained at constant volume by 1 degree Celcius.
• Specific heat capacity at constant volume (CV) for monoatomic gas is, 

​\(C_V = \frac{3}{2} R\) 

• Specific heat capacity at constant volume (CV) for for diatomic gas,

\(C_V = \frac{5}{2} R\)