A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy?

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the gas in the cylinder, the energy added by the heater (100 J) will either increase the internal energy of the gas or do work on the piston, depending on whether the piston is allowed to move or is fixed.

Work Done by a Gas

When a gas expands against a piston, it does work on the piston, which can affect its temperature. In case (1), where the piston can move, some of the energy added will be used to do work, resulting in a lower temperature increase compared to case (2), where the piston is fixed and all the energy contributes to increasing the internal energy and temperature of the gas.

Temperature and Internal Energy

Temperature is a measure of the average kinetic energy of the particles in a substance. In thermodynamics, when energy is added to a gas, its internal energy increases, which typically raises its temperature. In the fixed piston scenario, all the added energy increases the internal energy, leading to a higher temperature than in the moving piston scenario, where some energy is used for work.