I. Work
Remember earlier that we said the work done by a force F upon an object as the object was displaced over some path was equal to the area under the Force-Position graph.
Positive work in going from point A to point B where force is in the same direction as the displacement and negative work when going from point B to point A.
Let us now consider the work done by a gas of pressure P upon a piston of cross sectional area A as the piston is displace a distance x as shown below:
The force is found from the pressure by:
The amount of work for a small displacement is therefore given by
Thus, the area under a pressure-volume graph gives us the work done by the gas upon the piston.
These pressure-volume graphs are called P-V diagrams.
II. First Law of Thermodynamics
The change in the internal energy of a system is equal to heat transferred to the system minus the work done by the system.
The first law of thermodynamics is simply a statement of the law of the conservation of energy.
III. Thermodynamics Processes
1. Isobaric Process – A process performed under constant pressure.
Work = 2. Isovolumetric Process – A process performed under constant volume
Work =
3. Isothermal Process – A process where the system’s temperature (internal energy) is constant.
4. Adiabatic Process – A process in which no thermal energy (Q) is transferred.
5. Cyclic Process – A process or combination of processes that returns the system to its initial state.
Work is the area bounded by the curve on the P-V diagram.
IV. Heat Engine
An engine is a cyclic device which transfers energy as work. An important type of engine is the heat engine which absorbs thermal energy from the environment (outside the engine) and converts a portion of that energy to work.
Consider the heat engine below consisting of two isothermal processes and two isovolumetric processes:
During the first isothermal process (State A to State B), the engine takes in heat at a higher temperature and converts it to work. During the second isothermal process (State C to State D), the engine does negative work that is released as heat at a lower temperature.
During the two isovolumetric processes, heat is absorbed to increase the internal energy of the system (raise the temperature) or released to decrease the internal energy of the system (lower the temperature). These two processes are done across the same temperature difference and cancel each other.
The bounded area gives the net heat that was converted to work.
Efficiency - The efficiency of an engine is the ratio of the work obtained to the thermal energy absorbed by the engine.
Efficiency =
V. Entropy
Entropy is a state variable that measure the number of ways that a microscopic system can be arranged.
For instance, if you drop three identical coins there are only a few ways (arrangements) that they can fall in a stack while many ways they can fall into a disorganized pattern.
Because each arrangement is equally probable, nature will select the state with the greatest number of arrangements (i.e. the coils will land in a random pattern). This why gas molecules spread out rather than all going to one corner of the room.
A change in entropy occurs whenever heat is added to a system.
VI. Second Law of Thermodynamics
The change in the total entropy of a system and its environment will change is such a way that it is greater or equal to zero.
The most efficient heat engine is an engine with no change in entropy of the system. Using our relationship between entropy and heat, we get the following relationship for this engine: