Question

The value of the gas constant (R) calculated from the perfect gas equation is 8.32 joules/gm mole K, whereas its value calculated from the knowledge of $C_{P}$ and $C_{V}$ of the gas is 1.98 cal/gm mole K. From this data, the value of J is

• A. (a) $4.16\mspace{6mu} J/cal$
• B. $4.18\mspace{6mu} J/cal$
• C. $4.20\mspace{6mu} J/cal$
• D. $4.22\mspace{6mu} J/cal$

Answer 1

Answer: (C)

$4.20\mspace{6mu} J/cal$

Answer 2

We know that

$C_{P} - C_{V} = \frac{R}{J}$̃ $J = \frac{R}{C_{P} - C_{V}}$

$C_{P} - C_{V} = 1.98\mspace{6mu}\frac{cal}{gm - mol - K}$,$R = 8.32\frac{J}{gm - mol - K}$

$\therefore\mspace{6mu} J = \frac{8.32}{1.98} = 4.20 ⥂ \mspace{6mu} J/cal$