Heat and Thermodynamics 4 Question 2

2. Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume?

[Take, R=8.3J/molK ]

(2019 Main, 12 April I)

(a) 19.7J/molK

(b) 15.7J/molK

(c) 17.4J/molK

(d) 21.6J/molK

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Solution:

  1. Let molar specific heat of the mixture is CV.

Total number of molecules in the mixture

=3+2=5

CV can be determined using

nCVdT=n1CV1dT+n2CV2dT or (n1+n2)(CV)mix =n1CV1+n2CV2[ here, n=n1+n2]

Here, CV1=3R2 (for helium); n1=2

CV2=5R2 (for hydrogen); n2=3

[For monoatomic gases, CV=32R and for diatomic gases, CV=52R]

5×CV=(2×3R2)+(3×5R2)5CV=21R2 or CV=21R10=21×8.310=174.310

or

CV=17.4J/molK



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