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The molar specific heat at constant pressure of an ideal gas is $\left(\dfrac{7}{2}\right)R$. The ratio of specific heat at constant pressure to that at constant volume is :-
A
$\dfrac{7}{5}$
B
$\dfrac{8}{7}$
C
$\dfrac{5}{7}$
D
$\dfrac{9}{7}$
Detailed Solution
Given $C_P = \dfrac{7}{2}R$
By Mayer's relation, $C_P - C_V = R$
$\Rightarrow C_V = C_P - R = \dfrac{7}{2}R - R = \dfrac{5}{2}R$
$\gamma = \dfrac{C_P}{C_V} = \dfrac{\frac{7}{2}R}{\frac{5}{2}R}$
$\gamma = \dfrac{7}{5}$
(This is the value for a diatomic gas.)
By Mayer's relation, $C_P - C_V = R$
$\Rightarrow C_V = C_P - R = \dfrac{7}{2}R - R = \dfrac{5}{2}R$
$\gamma = \dfrac{C_P}{C_V} = \dfrac{\frac{7}{2}R}{\frac{5}{2}R}$
$\gamma = \dfrac{7}{5}$
(This is the value for a diatomic gas.)