Previous Year NEET Question- Kinetic Theory L-5

Question: The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is [CBSE AIPMT 2006]#

A) $7 / 5$

B) $8 / 7$

C) $5 / 7$

D) $9 / 7$

Answer: $7 / 5$#

Solution:#

We have given molar specific heat at instant pressure $$ C_p=\frac{7}{2} R $$

Mayer’s relation can be written as : Molar specific heat at constant pressure - Molar specific heat at constant volume $=$ Gas constant, $$ \text { i.e. } \begin{aligned} C_p-C_V & =R \Rightarrow C_V=C_p-R \ & =\frac{7}{2} R-R=\frac{5}{2} R\left[\because C_p=\frac{7}{2} R\right] \end{aligned} $$

Hence, required ratio is $$ \gamma=\frac{C_p}{C_v}=\frac{\left(\frac{7}{2}\right) R}{\left(\frac{5}{2}\right) R}=\frac{7}{5} $$