Thermodynamics Question 128
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
[MP PMT 1995; DPMT 2001]
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:
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 $
