Thermodynamics Question 371

Question: The specific heat of hydrogen gas at constant pressure is $ C _{P}=3.4\times 10^{3}cal/kg{{}^{o}}C $ and at constant volume is $ C _{V}=2.4\times 10^{3}cal/kg{{}^{o}}C. $ If one kilogram hydrogen gas is heated from $ 10^{o}C $ to $ 20^{o}C $ at constant pressure, the external work done on the gas to maintain it at constant pressure is

Options:

A) $ 10^{5} $ cal

B) $ 10^{4} $ cal

C) $ 10^{3} $ cal

D) $ 5\times 10^{3} $ cal

Show Answer

Answer:

Correct Answer: B

Solution:

[b] From FLOT DQ = DU + DW Work done at constant pressure $ \Delta W _{P}=\Delta Q _{P}-\Delta U $ $ \Delta Q _{P}-\Delta Q _{V} $

(As we know $ \Delta Q _{V}=\Delta U $ )

Also $ \Delta Q _{P}=mc _{P}\Delta T $

and $ \Delta Q _{V}=mc _{V}\Delta T $

Therefore $ \Delta W _{P}=m(c _{P}-c _{V})\Delta T $

Therefore $ \Delta W _{P}=1\times (3.4\times 10^{3}-2.4\times 10^{3})\times 10=10^{4}cal $



NCERT Chapter Video Solution

Dual Pane