Q. The value of the gas constant $(R)$ calculated from the perfect gas equation is $8.32\ joules/g$ mole $K,$ whereas its value calculated from the knowledge of $C_{P}$ and $C_{V}$ of the gas is $1.98\ cal/g$ mole $K.$ From this data, the value of $J$ is
A) $4.16\ J/cal$
B) $4.18\ \ J/cal$
C) $4.20\ \ J/cal$
D) $4.22\ \ J/cal$
Explanation
(c) We know that $C_{P} - C_{V} = \frac{R}{J}$
$\Rightarrow J = \frac{R}{C_{P} - C_{V}}$
$C_{P} - C_{V} = 1.98\frac{cal}{g - mol - K}$
$R = 8.32\frac{J}{g - mol - K}$
$\therefore J = \frac{8.32}{1.98} = 4.20J/cal$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.