Final answer:
To raise the temperature of a gas by 10°C using the least amount of heat energy, it should be heated at constant volume. This is because the specific heat at constant volume is less than at constant pressure, resulting in less heat needed for the same temperature increase.
Step-by-step explanation:
To determine whether it is more efficient to raise the temperature of a gas by 10°C at constant pressure or at constant volume, we can look at the specific heat capacities at constant pressure (Cp) and constant volume (Cv). The specific heat capacity is the amount of heat required to raise the temperature of a given amount of substance by a certain temperature interval. For an ideal gas, Cp is always greater than Cv, because when the gas is heated at constant pressure, work is done to allow for the expansion of the gas.
The specific heats of gases are therefore central to this question. The values show that for a given amount of heat energy, the temperature of the gas will increase more if the process is done at constant volume due to the lower specific heat capacity. This means that at constant volume, less heat is required to raise the temperature of the gas by 10°C compared to at constant pressure.
When heating the gas at constant volume, no work is done on or by the surrounding environment, and all the heat energy goes into increasing the internal energy of the gas, which corresponds to an increase in temperature. On the other hand, at constant pressure, part of the heat energy is used to do work on the surroundings to allow for the expansion of the gas, according to the predictions of Charles's law. This implies that more heat will be required to achieve the same temperature increase at constant pressure.