Answer
Constant volume.
Work Step by Step
At constant volume, when heat is added at constant volume, all the heat energy is used to increase the internal energy of the gas molecules, leading to an increase in its temperature.
At constant pressure, when heat is added at constant pressure, some of the heat energy is used to do work on the gas to increase its volume, and the rest is used to increase the internal energy of the gas molecules. This means that the increase in temperature, in this case, will be less than the increase in temperature in the constant-volume case because some of the added heat energy is used to do work instead of increasing the internal energy of the gas molecules.
We can easily prove that by assuming we need the temperature difference in both cases is the same.
- The heat added at constant volume:
$$Q_1=nC_{\rm v}\Delta T $$
- The heat added at constant pressure:
$$Q_2=nC_{\rm p}\Delta T $$
$$\dfrac{Q_2}{Q_1}=\dfrac{ \color{red}{\bf\not} nC_{\rm p} \color{red}{\bf\not} \Delta T }{ \color{red}{\bf\not} nC_{\rm v} \color{red}{\bf\not} \Delta T }$$
Recall that $C_{\rm p}\gt C_{\rm v}$
Thus,
$$\dfrac{Q_2}{Q_1}\gt 1$$
$$\boxed{Q_2\gt Q_1}$$
Therefore, heating the gas at constant volume is more efficient and requires less heat energy to achieve the same temperature increase compared to heating the gas at constant pressure.
