Q. If 70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from $30℃$ to $35℃$, then the amount of heat required to raise the temperature of same gas through same range at constant volume is
A) 50 cal
B) 70 cal
C) 60 cal
D) 65 cal
Explanation
(a) From $\mathrm{\Delta}Q = m\ C_{p}(\mathrm{\Delta}T)$
$70 = 2 \times C_{p} \times (35 - 30),$
$\therefore\ C_{p} = 70/10 = 7\ cal\ (mol{^\circ}C)^{- 1}$
$C_{v} = C_{p} - R = 7 - 2 = cal/mol℃$
$\mathrm{\Delta}Q^{'} = n\ C_{v}(\mathrm{\Delta}T) = 2 \times 5 \times 5 = 50$ cal
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.