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NEET levelSingle correct optionDifficulty 1 of 3td056

One mole of an ideal gas undergoes free expansion (against zero external pressure) isothermally into an evacuated vessel so that its volume doubles. Which statement is correct?

A $w = 0$ , $q = 0$ and $Δ U = 0$
B $w = - RT ln 2$ and $q = + RT ln 2$
C $w = 0$ but $q = + RT ln 2$
D $Δ U < 0$ because the gas does work while expanding

Answer: A

In free expansion the external pressure is zero, so

w = - P_{e x t} Δ V = 0

. For an ideal gas at constant temperature

Δ U = 0

, hence

q = Δ U - w = 0

. The expression

RT ln 2

applies only to reversible isothermal expansion.

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