Q. The specific heat of hydrogen gas at constant pressure is $C_{P} = 3.4 \times 10^{3}cal/kg\ ℃$ and at constant volume is $C_{V} = 2.4 \times 10^{3}cal/kg\ ℃$. If one kilogram hydrogen gas is heated from $10℃$ to $20℃$ at constant pressure, the external work done on the gas to maintain it at constant pressure is
A) $10^{5}cal$
B) $10^{4}cal$
C) $10^{3}cal$
D) $5 \times 10^{3}cal$
Explanation
(b) From FLOT $\mathrm{\Delta}Q = \mathrm{\Delta}U + \mathrm{\Delta}W$
Work done at constant pressure $(\mathrm{\Delta}W)_{P} = (\mathrm{\Delta}Q)_{P} - \mathrm{\Delta}U$
$= (\mathrm{\Delta}Q)_{P} - (\mathrm{\Delta}Q)_{V}$ [As we know $(\mathrm{\Delta}Q)_{V} = \mathrm{\Delta}U$]
Also $(\mathrm{\Delta}Q)_{P} = mc_{P}\mathrm{\Delta}T$ and $(\mathrm{\Delta}Q)_{V} = mc_{V}\mathrm{\Delta}T$
$\Rightarrow (\mathrm{\Delta}W)_{P} = m(c_{P} - c_{V})\mathrm{\Delta}T$
$\Rightarrow (\mathrm{\Delta}W)_{P} = 1 \times \left( 3.4 \times 10^{3} - 2.4 \times 10^{3} \right) \times 10 = 10^{4}cal$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.