Temperature

  In everyday terms, the temperature is an indication of how “hot” or “cold” a body is. In science, temperature, T, is the property of an object that determines in which direction energy will flow when it is in contact with another object: energy flows from higher temperature to lower temperature. When the two bodies have the same temperature, there is no net flow of energy between them. In that case we say that the bodies are in thermal equilibrium (Fig.1).

Fig. 1 The temperatures of two objects act as a signpost showing the direction in which energy will flow as heat through a thermally conducting wall: (a) heat always flows from high temperature to low temperature. (b) When the two objects have the same temperature, although there is still energy transfer in both directions, there is no net flow of energy.

  Temperature in science is measured on either the Celsius scale or the Kelvin scale. On the Celsius scale, in which the temperature is expressed in degrees Celsius (°C), the freezing point of water at 1 atm corresponds to 0°C and the boiling point at 1 atm corresponds to 100°C. This scale is in widespread everyday use. Temperatures on the Celsius scale are denoted by the Greek letter ɵ (theta) throughout this text. However, it turns out to be much more convenient in many scientific applications to adopt the Kelvin scale and to express the temperature in kelvin (K; note that the degree sign is not used for this unit). Whenever we use T to denote a temperature, we mean a temperature on the Kelvin scale. The Celsius and Kelvin scales are related by

That is, to obtain the temperature in kelvins, add 273.15 to the temperature in d grees Celsius. Thus, water at 1 atm freezes at 273 K and boils at 373 K; a warm day (25°C) corresponds to 298 K.

  A more sophisticated way of expressing the relation between T and ɵ, and one that we shall use in other contexts, is to regard the value of T as the product of a number (such as 298) and a unit (K), so that T/K (that is, the temperature divided by K) is a pure number. For example, if T = 298 K, then T/K = 298. Likewise, ɵ/°C is a pure number. For example, if ɵ = 25°C, then ɵ/°C =25. With this convention, we can write the relation between the two scales as

T/K = ɵ/°C = 273.15

This expression is a relation between pure numbers.