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A single mole of an ideal monoatomic gas absorbs 207 J of heat to increase its temperature by 10 K under constant pressure. How much heat is needed to achieve the same temperature increase under constant volume? [Gas constant R = 8.3 J / mol·K]

1. 198.7 J
2. 29 J
3. 215.3 J
4. 124 J

Correct answer: 198.7 J

Solution

For a monoatomic ideal gas, the molar specific heat at constant pressure is Cp = (5/2)R. Given CpΔT = 207 J, we calculate R = 207 / (5/2 × 10) = 8.3 J/mol·K. At constant volume, Cv = (3/2)R, so heat required is CvΔT = (3/2) × 8.3 × 10 = 198.7 J.

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