5 moles of $N_{2}$ at 5 atm pressure contained in a 100 L cylinder absorbed 30.26 kJ of heat when it expanded to 200 L at 2 atm. What is the change in internal energy of the gas?

10 kJ

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20 kJ

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40 kJ

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30 kJ

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Solution

The correct option is C 10 kJ
Temperature in both the states can be obtained using the ideal gas relation.

Temperature in the first state $= T_{1} = \frac{P_{1} V_{1}}{n R} = \frac{5 \times 100}{5 \times 0.082} = 1218 K$

Temperature in the second state state $= T_{2} = \frac{P_{2} V_{2}}{n R} = \frac{2 \times 200}{5 \times 0.082} = 974.42 K$

$Δ U = q - W = q - n R Δ T = 30.26 - 5 \times 0.0821 \times (1218 - 974.42) = 30.26 - 20.26 = 10 k J$

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