Thermodynamics

Thermodynamics applies to many different types of systems; gases, elastic solids (solids that can be stretched and return to their original form when the stretching force is removed), and mixtures of chemicals are all examples of such systems. Each system has its own equation of state, which depends upon the variables that need to be measured in order to describe its internal state. The relevant variables for a system can only be determined by experiment, but one of those variables will always be the temperature.

The system usually given as an example is a gas, where the relevant thermodynamic variables are the pressure of the gas (P), its volume (V), and, of course, the temperature. (These variables are the relevant ones for any simple chemical system, e.g., water, in any of its phases.) The amount of gas may be specified in grams or kilograms, but the usual way of measuring mass in thermodynamics (as well as in some other fields) is in terms of the number of moles. One kilomole (kmol) is defined as equal to M kilograms, where M is the molecular weight of the substance, with carbon-12 being taken as M = 12. (One mole of any substance contains 6.02 × 10²³ molecules, known as Avogadro's number.) Thus one kilomole of oxygen has a mass of 70.56 lb (32 kg); of nitrogen, 61.76 lb (28.01 kg); the molar mass of air (which is, of course, actually a mixture of gases) is commonly taken as 63.87 lb (28.97 kg). It is found, by experiment, that most gases at sufficiently low pressures have an equation of state of the form: PV = NRT, where P is in Newtons/m², V is in m³, N is the number of kilomoles of the gas, T is the temperature in K, and R = 8.31 kJ/kmol-K is known as the universal gas constant. The temperature is in degrees Kelvin (K), which is given in terms of the Celsius temperature as T(K) = T(°C)+273.15°C. It should be noted that real gases obey this ideal gas equation of state to within a few percent accuracy at atmospheric pressure and below.

The equation of state of substances other than gases is more complicated than the above ideal gas law. For example, an elastic solid has an equation of state which involves the length of the stretched material, the stretching force, and the temperature, in a relationship somewhat more complex than the ideal gas law.