# 5.6 litre of an unknown gas at NTP requires 12.5 calorie to raise its temperature by $10^{\large\circ}C$ at constant volume. Calculate the $C_v$ of the gas.

$(a)\;3\;calorie\qquad(b)\;5\;calorie\qquad(c)\;7\;calorie\qquad(d)\;9\;calorie$

Given
Volume = 5.6 litre
R = 0.0821
T = 273K
We have $n = \large\frac{PV}{RT}$
$=\large\frac{1\times5.6}{0.0821\times273}$
= 0.25
Also $q = mS\bigtriangleup T$
$12.5 = 0.25\times C_v\times10$
$C_v = 5\;calorie$