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Two moles of an ideal monoatomic gas occupies a volume V at 27°C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in internal energy.

1. (a) 189 K (b) 2.7 kJ
2. (a) 195 K (b) -2.7 kJ
3. (a) 189 K (b) -2.7 kJ
4. (a) 195 K (b) 2.7 kJ

Correct answer: (a) 189 K (b) -2.7 kJ

Solution

The final temperature of the gas after adiabatic expansion can be calculated using the adiabatic relation, which shows that the temperature decreases as the volume increases for an ideal monoatomic gas. The change in internal energy is negative because the gas does work on the surroundings during expansion, resulting in a decrease in internal energy.

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