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Question

A certain gas is expanded from (1 L, 10 atm) to (4 L, 5 atm) against a constant external pressure of 1 atm. If the initial temperature of the gas is 300 K and the heat capacity for the process is 50 J/C0, the enthalpy change during the process is :

A
15 kJ
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B
15.7 kJ
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C
14.3 kJ
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D
14.7 kJ
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Solution

The correct option is B 15.7 kJ
The amount of gas expanded using the ideal gas equation:
P1V1=nRT1
10×1=n×0.0821×300
n = 0.4 mole
Final temperature obtained:
P2V2=nRT2
5×4=0.4×0.0821×T2
T2 = 600 K
Work done during expansion = Pext(V2V1)
= -1(4-1) atm L = 300 J
and heat involved = Q=CpdT
= 50×(600300) = 15000 J
Using equation δU=δQ+δW
= 15000-300 = 14700 J
and δH=δU+δ(PV)
= 14700 + (4×510×1)×100 J
=15700J = 15.7 kJ



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