Q. $310\ J$ of heat is required to raise the temperature of 2 mole of an ideal gas at constant pressure from $25℃$ to $35℃.$ The amount of heat required to raise the temperature of the gas through the same range at constant volume is
A) $384\ J$
B) $144\ J$
C) $276\ J$
D) $452\ J$
Explanation
(b) $C_{P} - C_{V} = R$
At constant pressure, Heat $= nC_{P}\theta$
$\Rightarrow 310 = 2 \times C_{P} \times (35 - 25) = 20C_{P}$
$\Rightarrow C_{P} = \frac{310}{20} = 15.5$
At constant volume, Heat required $= nC_{V}\theta$
$\Rightarrow Q = 2 \times (C_{P} - R) \times (32 - 25)$
$= 2 \times (15.5 - 8.3) \times 10 = 2 \times 7.2 \times 10 = 144J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.