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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3td209

For one mole of a monatomic ideal gas, the molar heat capacity $C$ along a reversible path $P V^{n} = constant$ is $C = C_{V} + R / (1 - n)$ . Select all correct statements.

A $C \to \infty$ for the isothermal path
B $C = 0$ for the reversible adiabatic path
C $C = \frac{11}{6} R$ along the path $P \propto V^{2}$
D $C$ is negative along the path $P V^{2} = constant$

Answer: A, B, C

Isothermal corresponds to

n = 1

, so

R / (1 - n)

diverges. Adiabatic has

n = 5/3

:

C = 1.5 R + R / (1 - 5/3) = 1.5 R - 1.5 R = 0

. For

P \propto V^{2}

,

n = - 2

and

C = 1.5 R + R /3 = 11 R /6

. For

n = 2

,

C = 1.5 R - R = 0.5 R > 0

, so the last statement is false.

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