Discussion
If 300 J of heat energy is used to raise the temperature of one mole of an ideal gas by 10 K at constant pressure, then heat energy required to raise its temperature by 10 K at constant volume is (R = 8.3 J mol-1K-1)
Answer: D
The heat required at constant volume is 217 J.
For one mole, \(C_p - C_v = R\). The extra heat at constant pressure is the work done in expansion, \(nR\Delta T\).
\[ \begin{aligned} Q_v &= Q_p - nR\Delta T \\ &= 300 - 1 \times 8.3 \times 10 = 217\ \text{J} \end{aligned} \]
83 J is the work done at constant pressure, and 300 J is the heat at constant pressure itself. 383 J would add the work instead of subtracting it.
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