Question
For a certain gas the ratio of specific heats is given to be $$\gamma = 1.5,$$ for this gas
A.
$${C_V} = \frac{{3R}}{J}$$
B.
$${C_p} = \frac{{3R}}{J}$$
C.
$${C_p} = \frac{{5R}}{J}$$
D.
$${C_v} = \frac{{5R}}{J}$$
Answer :
$${C_p} = \frac{{3R}}{J}$$
Solution :
Given, $$\gamma = \frac{{{C_p}}}{{{C_V}}} = 1.5 = \frac{3}{2}$$
$$\therefore {C_V} = \frac{2}{3}{C_p}$$
Again from Mayer's formula
$$\eqalign{
& {C_p} - {C_V} = \frac{R}{J} \cr
& \therefore {C_p} - \frac{2}{3}{C_p} = \frac{R}{J} \cr
& \Rightarrow \frac{{{C_p}}}{3} = \frac{R}{J} \cr
& \Rightarrow {C_p} = \frac{{3R}}{J} \cr} $$