Special Cases of 1st Law of Thermodynamics

1. Adiabatic Processes

Adiabatic processes are those that occur so rapidly that there is no transfer of heat between the system and its environment. Thus Q = 0 and

For example if we push in the piston very quickly then our work will increase the internal energy of the gas. It will store potential energy (ΔU = ΔE_int) like a spring and make the piston bounce back when we let it go.

2. Constant-volume Processes

If we glue the piston so that it won't move then obviously the volume is constant, and , because the piston can't move. Thus

which means the only way to increase the internal energy of the gas is by adding heat Q.

3. Cyclical Processes

Recall the motion of a spring. It is a cyclical process in which the spring oscillates back and forth. After one complete cycle the potential energy U of the spring has not changed, thus ¢U = 0. Similarly we can push in the piston, then let it go and it will push back to where it started, similar to the spring. Thus ΔE_int = 0 and

meaning that work done equals heat gained.

4. Free Expansion

Another way to get ΔE_int = 0 is for