Q. 70 cal of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30$℃$ to 35$℃$. The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly (Gas coristant = 1.99 cal $K^{- 1} - mol^{- 1})$
A) 30 cal
B) 50 cal
C) 70 cal
D) 90 cal
Explanation
(b) As $dQ = C_{p}m\mathrm{\Delta}T$
$\therefore\ 70 = C_{p} \times 2(35 - 30)$
$C_{V} = C_{p} - R\ $
= $7 - 1.99 = 5.01\ calmol^{- 1}℃^{- 1}$
$\therefore\ dQ^{'} = \ C_{V}m\mathrm{\Delta}T\ $
= $5.01 \times 2 \times (35 - 30) = 50.1\ $cal
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.