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An ideal monoatomic gas is expanding such that PT^2= constant.

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An ideal monoatomic gas is expanding such that $P T^{2} = co n s t an t$ . The molar specific heat of the gas is :

\frac{11 R}{2}

\frac{7 R}{2}

\frac{5 R}{2}

\frac{9 R}{2}

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An ideal monoatomic gas is expanding such that

P T^{2} = co n s t an t

. The molar specific heat of the gas is :

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Text solutionVerified

The given relation is

P T^{2} = co n s t an t

Substituting

T = \frac{P V}{R}

in the above relation,

we get

P \times (\frac{P V}{R})^{2} = co n s t an t

⟹ P V^{2/3} = co n s t an t

Comparing this with

P V^{η} = co n s t an t

Hence, we get polytropic exponent

η = \frac{2}{3}

Also, for monoatomic gas

γ = \frac{5}{3}

∴

Molar specific heat

C = \frac{R}{γ - 1} - \frac{R}{η - 1}

= \frac{R}{\frac{5}{3} - 1} - \frac{R}{\frac{2}{3} - 1}

⟹ C = \frac{3}{2} R + 3 R = \frac{9}{2} R

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Question Text	An ideal monoatomic gas is expanding such that $P T^{2} = co n s t an t$ . The molar specific heat of the gas is :
Answer Type	Text solution:1
Upvotes	150