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JEE Advanced levelSingle correct optionDifficulty 3 of 3td204

For a monatomic ideal gas the pressure is proportional to the volume ( $P \propto V$ ) during a reversible process. Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ , the molar heat capacity along this path is nearest to

A $16.63 J mo l^{- 1} K^{- 1}$
B $24.94 J mo l^{- 1} K^{- 1}$
C $20.79 J mo l^{- 1} K^{- 1}$
D $12.47 J mo l^{- 1} K^{- 1}$

Answer: A

Let

P = kV

. Then

P V = k V^{2} = RT

, so

2 kV d V = R d T

and

P d V = kV d V = R d T /2

. Per mole,

d q = C_{V} d T + P d V = (1.5 R + 0.5 R) d T

, so

C = 2 R = 16.63 J mo l^{- 1} K^{- 1}

.

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