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Question

An ideal CO2 gas obeys the law PVx= constant. The range of x for which the gas has non-positive molar specific heat at normal temperature is

A
x0.5
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B
x1.7
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C
1<x1.4
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D
x1.4
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Solution

The correct option is C 1<x1.4
Molar Specific heat of a gas during a polytropic process is given by (C)=CV+R1x ..........(1)
Where x is the exponent of polytropic process which can take values in the range of (<x<+)

Since, CO2 is a linear triatomic molecule, at normal temperatures we can say that CV=5R2
Thus, from (1) we get,
5R2Rx1 521x1For x>1 x125x1.4
For values of x between 1<x1.4 heat capacity of gas becomes non-positive.
Thus, option (c) is the correct answer.

Alternate solution:
we know that,
Heat capacity of a gas can be negative if 1<x<γ
we can say that, Heat capacity of a gas can be non-positive iff 1<xγ
For CO2 we know that, γ=75=1.4
we can conclude that 1<x1.4
Hence, option (c) is the correct answer.

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