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Question

The heat capacity of a certain amount of a particular gas at constant pressure is greater than that at constant volume by 29.1 J/K. Match the items given in Column I with items given in Column II.

Column IColumn IIi. If the gas is monoatomic, heat capacity at constant volumea. 131 J/Kii. If the gas is monoatomic, heat capacity at constant pressureb. 43.7 J/Kiii. If the gas is rigid diatomic, heat capacity at constant pressurec. 72.7 J/Kiv. If the gas is vibrating diatomic, heat capacity at constant pressured. 102 J/K

A
i - b ii -a iii- b iv-c
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B
i - b ii- c iii- d iv- a
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C
i- a ii-d iii- b iv- a
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D
i- d ii-a iii- d iv- c
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Solution

The correct option is B i - b ii- c iii- d iv- a
ib; iic; iiid; ivaCpCv=29.1 J/K=nR
For molecular heat capacities
CpCv=R
Number of moles in the gas,
n=29.18.31=3.5 mol
For monoatomic gas,
CpCv=53
53CvCv=29.1 J/K
Cv=(32×29.1)J/K=43.7 J/K
Cp=72.7 J/K
For rigid diatomic gas the number of degree of freedom is 5.
CpCv=75
75CvCv=29.1
Solving this we get Cv and then further we get
Cp=102 J/K
For vibrating diatomic ideal gas, the total number of degrees of freedom is 7.

Internal energy,
U=72nRT
Cv=72nR and Cp=92nR
CpCv=nRCp=92×29.1=131 J/K

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