An ideal gas is expanding such that $P T^{3} = c o n s t a n t$ . The Molar Specific heat capacity of the gas is

\frac{11 R}{2}

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\frac{7 R}{2}

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\frac{5 R}{2}

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\frac{9 R}{2}

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Solution

The correct option is A $\frac{11 R}{2}$
Given $P T^{3} = c o n s t a n t$
From ideal gas equation, $\frac{P V}{T} = c o n s t a n t$
Hence for given ideal gas, $P^{4} V^{3} = c o n s t a n t \Rightarrow P V^{3 / 4} = c o n s t a n t$
For polytropic process $P V^{x} = c o n s t a n t$ ,
heat capacity $C = \frac{R}{1 - x} + \frac{R}{γ - 1}$
Here $x = \frac{3}{4}, γ = \frac{5}{3} \Rightarrow C = 4 R + \frac{3 R}{2} = \frac{11 R}{2}$

Suggest Corrections

Similar questions

\frac{V}{T^{2}} = c o n s t a n t

P T^{2} = c o n s t a n t

\frac{V}{T^{3}} = c o n s t a n t

P T^{3 / 2} = c o n s t a n t

(R

\frac{3}{2}

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