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JEE Main levelSingle correct optionDifficulty 2 of 3td181

One mole of a monatomic ideal gas at $300 K$ doubles its volume, once by a reversible isothermal path and once by a reversible adiabatic path. The ratio $∣ w_{adiabatic} ∣/∣ w_{isothermal} ∣$ is nearest to

A0.80
B1.25
C0.50
D1.00

Answer: A

Isothermal:

∣ w ∣ = RT ln 2 = 1729 J

. Adiabatic:

T_{2} = 300 \times 2^{- 2/3} = 189.0 K

and

∣ w ∣ = 1.5 R (300 - T_{2}) = 1384 J

. The ratio is

0.80

; the adiabatic work is smaller because the gas cools as it expands.

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