Physics
Physics
Problem
Two ideal gases, X and Y, have the same pressure, volume and temperature. Thermal energy is supplied to both gases. Gas X absorbs the thermal energy at constant volume whereas gas Y absorbs the thermal energy at constant pressure. The increase in temperature of both gases is the same. State and explain which of the two gases received the largest quantity of energy.Intuitive explanation
The key is understanding how heat capacity depends on whether volume or pressure stays fixed. When you heat a gas at constant volume, all the energy goes into raising temperature; at constant pressure, some energy must go into doing expansion work against the surroundings. Since both gases experience the same temperature rise, gas Y must absorb more total thermal energy to account for both the internal energy increase and the work it performs during expansion. The constant-pressure process is less efficient at converting supplied heat into temperature change.
Intuitive explanation
The key is understanding how heat capacity depends on whether volume or pressure stays fixed. When you heat a gas at constant volume, all the energy goes into raising temperature; at constant pressure, some energy must go into doing expansion work against the surroundings. Since both gases experience the same temperature rise, gas Y must absorb more total thermal energy to account for both the internal energy increase and the work it performs during expansion. The constant-pressure process is less efficient at converting supplied heat into temperature change.