Work and Heat in Thermodynamic Processes As stated previously, pressure, temperature and volume are considered state variables and are used to define the particular state of the system. Work and Heat are called transfer variables. These describe changes in the state. They do not describe the state. We know how to describe the work done on a system. For example let us look at applying a force to a piston in order to compress the gas inside a container. We will compress the gas slowly enough for all of the system to remain in thermal equilibrium. This is a quasi-static process. External force is equal and opposite to force gas exerts on piston. Work done on gas! -F is parallel to y Work done to change the volume of a gas

The work done on a system is typically determined by looking at a PV-Diagram. A PV-Diagram is a plot of pressure vs. volume. The work done during the process shown by the PV-diagram can be determined by looking at the area under the curve. Remember this is the same as the integral expression for the work. In the three figures shown (a), (b) and (c), rank the amount of work done by each of the processes shown from largest to smallest. (b) > (c) > (a) How much work is done in each case? (a) W=-Pi(Vf-Vi) (c) (b) W=-Pf(Vf-Vi) The amount of work done during a process depends on the path you take from your initial point to your final point. In other words it depends on how you change your pressure and volume!

First Law of Thermodynamics The first law of thermodynamics looks at how transfer variables affect the internal energy of a system. We know that when a frictional force does work on a system to change its velocity, the work done increases the internal energy. This is an example of an application of the first law of thermodynamics. DEint – Change in internal energy [J] Q – Heat added or lost by the system [J] W – Work done on or by the system [J] 1st Law of Thermodynamics The signs on Q and W depend on the way the internal energy is changed. If Q and W are positive the internal energy increases, but if Q and W are negative the internal energy decreases. The first law of thermodynamics tells us that in order to change the internal energy of a system we must add (or remove) heat and/or do work on (or have work done by) the system. The internal energy is also a state variable. It is at times more useful to look at infinitesimal changes to the internal energy. dEint – Change in internal energy [J] dQ – small amount of heat added or lost by the system [J] dW – small amount of work done on or by the system [J]

Special Cases of the 1st Law of Thermodynamics Isolated System The system doesn’t interact with the environment. What does this mean in terms of the 1st law of thermodynamics? Q = 0 – No heat is transferred into or out of the system. W = 0 – No work is done on the system. Cyclic Process The system starts and ends in the same state (same internal energy). The system is not necessarily isolated. The function that describes the changes in the state on a PV - diagram would be a closed curve. What does this mean in terms of the 1st law of thermodynamics? DEint = 0 – No net change in the internal energy.

Applications of the 1st Law of Thermodynamics Adiabatic Process This process considers a system where there is no loss or gain through heat. This can be accomplished by: Thermally insulating the chamber Performing the process very rapidly – no time for heat to be transferred. W Therefore if we do work to compress the gas the temperature of the gas should increase. The increase in the temperature of the gas corresponds to an increase in the internal energy of the system. Examples: Expansion of hot gases in an internal combustion engine Liquefaction of gases in a cooling system Adiabatic Free Expansion This is a special case of an adiabatic process, where the gas expands into free space.