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JEE Main levelSingle correct optionDifficulty 2 of 3td028

Two moles of a diatomic ideal gas (vibrations ignored) cool from $400 K$ to $300 K$ by a reversible adiabatic expansion. With $R = 8.314 J mo l^{- 1} K^{- 1}$ , the work done by the gas is

A $4157 J$
B $5820 J$
C $2494 J$
D $1663 J$

Answer: A

Adiabatic:

q = 0

, so

w_{o n} = Δ U = n C_{V} Δ T = 2 (\frac{5}{2}) (8.314) (- 100) = - 4157 J

. The gas therefore does

4157 J

of work. Using

C_{P}

or

\frac{3}{2} R

gives the wrong magnitudes.

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