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<x≤1.4Molar Specific heat of a gas during a polytropic process is given by (C)=CV+R1−x ..........(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, 5R2≤Rx−1 ⇒52≤1x−1For x>1 ⇒x−1≤25⇒x≤1.4 ∴ For values of x between 1<x≤1.4 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<x≤γ For CO2 we know that, γ=75=1.4 ∴ we can conclude that 1<x≤1.4 Hence, option (c) is the correct answer.

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