# Thermodynamics

## Historical Background, Temperature, Expansion Coefficients, Thermostats, Water, Heat, The First Law Of ThermodynamicsConservation of energy

Thermodynamics is the science that deals with work and heat, and the transformation of one into the other. It is a macroscopic theory, dealing with matter in bulk, disregarding the molecular nature of materials. The corresponding microscopic theory, based on the fact that materials are made up of a vast number of molecules, is called statistical mechanics.

The conservation of energy is well known from mechanics, where energy does not disappear but only changes its form. For example, the potential energy of an object at some height is converted to the kinetic energy of its motion as it falls. Thermodynamics is concerned with the internal energy of an object and those things that affect it; conservation of energy applies in this case, as well.

### Clausius statement of the second law

The Clausius statement of the second law is: No process is possible whose only result is the transfer of heat from a cooler to a hotter object. The most common example of the transfer of heat from a cooler object to a hotter one is the refrigerator (air conditioners and heat pumps work the same way). When, for example, a bottle of milk is placed in a refrigerator, the refrigerator takes the heat from the bottle of milk and transfers it to the warmer kitchen. (Similarly, a heat pump takes heat from the cool ground and transfers it to the warmer interior of a house.) An idealized view of the refrigerator is as follows. The heat transfer is accomplished by having a motor, driven by an electrical current, run a compressor. A gas is compressed to a liquid, a phase change which generates heat (heat is taken from the gas to turn it into its liquid state). This heat is dissipated to the kitchen by passing through tubes (the condenser) in the back of (or underneath) the refrigerator. The liquid passes through a valve into a low pressure region, where it expands and becomes a gas, and flows through tubes inside the refrigerator. This change in phase from a liquid to a gas is a process which absorbs heat, thus cooling whatever is in the refrigerator. The gas then returns to the compressor where it is again turned into a liquid. The Clausius statement of the Second Law asserts that the process can only take place by doing work on the system; this work is provided by the motor which drives the compressor. However, the process can be quite efficient, and considerably more energy in the form of heat can be taken from the cold object than the work required to do it.

### Kelvin-Planck statement of the second law

Another statement of the second law is due to Lord Kelvin and Max Planck (1858-1947): No process is possible whose only result is the conversion of heat into an equivalent amount of work. Suppose that a cylinder of gas fitted with a piston had heat added, which caused the gas to expand. Such an expansion could, for example, raise a weight, resulting in work being done. However, at the end of that process the gas would be in a different state (expanded) than the one in which it started, so that this conversion of all the heat into work had the additional result of expanding the "working fluid" (in this case, the gas). If the gas were, on the other hand, then made to return to its original volume, it could do so in three possible ways: (a) the same amount of work could be used to compress the gas, and the same amount of heat as was originally added would then be released from the cylinder; (b) if the cylinder were insulated so that no heat could escape, then the end result would be that the gas is at a higher temperature than originally; (c) something in-between. In the first case, there is no net work output or heat input. In the second, all the work was used to increase the internal energy of the gas, so that there is no net work and the gas is in a different state from which it started. Finally, in the third case, the gas could be returned to its original state by allowing some heat to be transferred from the cylinder. In this case the amount of heat originally added to the gas would equal the work done by the gas plus the heat removed (the first law requires this). Thus, the only way in which heat could be (partially) turned into work and the working fluid returned to its original state is if some heat were rejected to an object having a temperature lower than the heating object (so that the change of heat into work is not the only result). This is the principle of the heat engine (an internal combustion engine or a steam engine are examples).