Correct Answer - Option 3 : 5RT/2
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 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.
EXPLANATION:
- The total internal energy of a mole of a rigid diatomic gas is
\(⇒ U=\frac{5}{2}RT\)
NOTE:
As we know,
\(\Rightarrow C_v=\frac{dU}{dt}\)
\(\Rightarrow C_v=\frac{d}{dT}(\frac{5}{2}RT)=\frac{5}{2}R\)
- The molar specific heat capacity of a gas at constant volume is \(C_v=\frac{7}{2}R\).
As we know,
⇒ Cp - Cv = R
- Therefore, the molar specific heat of a gas at constant pressure is
\(\Rightarrow {C_p} = R+ {C_v}=R+\frac{5}{2}R=\frac{7}{2}R\)
