temperature - definition (long) - thermodynamics and thermal physics

Definition: The property of a body or region of space that determines whether or not there will be a net flow of heat into it or out of it from a neighboring body or region and in which direction (if any) the heat will flow. If there is no heat flow the bodies or regions are said to be in thermal equilibrium and at the same temperature. If there is a flow of heat, the direction of the flow is from the body or region of higher temperature. Broadly, there are two methods of quantifying this property. The empirical method is to take two or more reproducible temperature-dependent events and assign fixed points on a scale of values to these events. For example, the Celsius temperature scale uses the freezing point and boiling point of water as the two fixed points, assigns the values 0 and 100 to them, respectively, and divides the scale between them into 100 degrees. This method is serviceable for many practical purposes but lacking a theoretical basis it is awkward to use in many scientific contexts. In the 19th century, Lord Kelvin proposed a thermodynamic method to specify temperature, based on the measurement of the quantity of heat flowing between bodies at different temperatures. This concept relies on an absolute scale of temperature with an absolute zero of temperature, at which no body can give up heat. He also used Sadi Carnot's concept of an ideal frictionless perfectly efficient heat engine. This Carnot engine takes in a quantity of heat q₁ at a temperature T₁, and exhausts heat q₂ at T₂, so that T₁/T₂ = q₁/q₂. If T₂ has a value fixed by definition, a Carnot engine can be run between this fixed temperature and any unknown temperature T₁, enabling T₁ to be calculated by measuring the values of q₁ and q₂. This concept remains the basis for defining thermodynamic temperature, quite independently of the nature of the working substance. The unit in which thermodynamic temperature is expressed is the kelvin. In practice, thermodynamic temperatures cannot be measured directly; they are usually inferred from measurements with a gas thermometer containing a nearly ideal gas. This is possible because another aspect of thermodynamic temperature is its relationship to the internal energy of a given amount of substance. This can be shown most simply in the case of an ideal monatomic gas, in which the internal energy per mole (U) is equal to the total kinetic energy of translation of the atoms in one mole of the gas (a monatomic gas has no rotational or vibrational energy). According to the kinetic theory, the thermodynamic temperature of such a gas is given by T = 2U/3R, where R is the universal gas constant.