0th Law of Thermodynamics Summary

• Thermal Equilibrium

  A system with many microscopic components (for example, a gas, a liquid, a solid with many molecules) that is isolated from all forms of energy exchange and left alone for a ``long time'' moves toward a state of thermal equilibrium. A system in thermal equilibrium is characterized by a set of macroscopic quantities that depend on the system in question and characterize its ``state'' (such as pressure, volume, density) that do not change in time.

  Two systems are said to be in (mutual) thermal equilibrium if, when they are placed in ``thermal contact'' (basically, contact that permits the exchange of energy between them), their state variables do not change.

• Zeroth Law of Thermodynamics

  If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then system A is in thermal equilibrium with system B.

• Temperature and Thermometers

  The point of the Zeroth Law is that it is the basis of the thermometer. A thermometer is a portable device whose thermal state is related linearly to some simple property, for example its density or pressure. Once a suitable temperature scale is defined for the device, one can use it to measure the temperature of a variety of disparate systems in thermal equilibrium. Temperature thus characterizes thermal equilibrium.

• Temperature Scales
  1. Fahrenheit: This is one of the oldest scales, and is based on the coldest temperature that could be achieved with a mix of ice and alcohol. In it the freezing point of water is at 32$^\circ$ F, the boiling point of water is at 212$^\circ$ F.
  2. Celsius or Centigrade: This is a very sane system, where the freezing point of water is at 0$^\circ$ C and the boiling point is at 100$^\circ$ C. The degree size is thus $9/5$ as big as the Fahrenheit degree.
  3. Kelvin or Absolute: 0$^\circ$ K is the lowest possible temperature, where the internal energy of a system is at its absolute minimum. The degree size is the same as that of the Centigrade or Celsius scale. This makes the freezing point of water at atmospheric pressure 273.16$^\circ$ K, the boiling point at 373.16$^\circ$ K.

• Thermal Expansion
  

  $$\Delta L = \alpha L \Delta T$$ (216)

  
  
  where $\alpha$ is the coefficient of linear expansion. If one applies this in three dimensions:
  

  $$\Delta V = \beta V \Delta T$$ (217)

  
  
  where $\beta = 3\alpha$.

• Ideal Gas Law
  

  $$PV = nRT = NkT$$ (218)

  
  
  where $R = 8.315$ J/mol-K, and $k = R/N_A$ = 1.38 $\times 10^{-23}$ J/K.