Thermodynamics

Thermodynamics is the study of systems involving energy in the form of heat and work. A good example of a thermodynamic system is gas confined by a piston in a cylinder. If the gas is heated, it will expand, doing work on the piston; this is one example of how a thermodynamic system can do work.
Thermal equilibrium is an important concept in thermodynamics. When two systems are in thermal equilibrium, there is no net heat transfer between them. This occurs when the systems are at the same temperature. In other words, systems at the same temperature will be in thermal equilibrium with each other.
The first law of thermodynamics relates changes in internal energy to heat added to a system and the work done by a system. The first law is simply a conservation of energy equation:
 

The internal energy has the symbol U. Q is positive if heat is added to the system, and negative if heat is removed; W is positive if work is done by the system, and negative if work is done on the system.
We've talked about how heat can be transferred, so you probably have a good idea about what Q means in the first law. What does it mean for the system to do work? Work is simply a force multiplied by the distance moved in the direction of the force. A good example of a thermodynamic system that can do work is the gas confined by a piston in a cylinder, as shown in the diagram.

 
If the gas is heated, it will expand and push the piston up, thereby doing work on the piston. If the piston is pushed down, on the other hand, the piston does work on the gas and the gas does negative work on the piston. This is an example of how work is done by a thermodynamic system. An example with numbers might make this clearer.

An example of work done

Consider a gas in a cylinder at room temperature (T = 293 K), with a volume of 0.065 m3. The gas is confined by a piston with a weight of 100 N and an area of 0.65 m2. The pressure above the piston is atmospheric pressure.

(a) What is the pressure of the gas?
This can be determined from a free-body diagram of the piston. The weight of the piston acts down, and the atmosphere exerts a downward force as well, coming from force = pressure x area. These two forces are balanced by the upward force coming from the gas pressure. The piston is in equilibrium, so the forces balance. Therefore:

 
Solving for the pressure of the gas gives:

 
The pressure in the gas isn't much bigger than atmospheric pressure, just enough to support the weight of the piston.

(b) The gas is heated, expanding it and moving the piston up. If the volume occupied by the gas doubles, how much work has the gas done?
An assumption to make here is that the pressure is constant. Once the gas has expanded, the pressure will certainly be the same as before because the same free-body diagram applies. As long as the expansion takes place slowly, it is reasonable to assume that the pressure is constant.
If the volume has doubled, then, and the pressure has remained the same, the ideal gas law tells us that the temperature must have doubled too.
The work done by the gas can be determined by working out the force applied by the gas and calculating the distance. However, the force applied by the gas is the pressure times the area, so:

W = F s = P A s

and the area multiplied by the distance is a volume, specifically the change in volume of the gas. So, at constant pressure, work is just the pressure multiplied by the change in volume:

 
This is positive because the force and the distance moved are in the same direction, so this is work done by the gas.