Temperature and Measurement
There are several equivalent definitions of temperature. In thermodynamics, temperature is defined as a property of an object that determines the direction of heat flow. Heat always flows from a higher temperature region to a lower temperature region. Heat flow stops when the two regions reach an equilibrium state, called thermal equilibrium. Two objects are said to be of the same temperature if they are in thermal equilibrium. This is also called the 0th law of thermodynamics. This definition only gives a comparison between the temperatures of two objects. In statistical physics, the temperature can be defined without using comparison between two objects. Simply speaking, the temperature is a quantity proportional to the internal energy of an object. Internal energy is defined to be the sum of the kinetic and potential energy of all the molecules inside the object. Internal energy is difficult to measure so this definition is mainly a theoretical one.
There are two approaches to quantify temperature according to the first definition. The first is to choose a material, often water, and define its temperature arbitrarily in two states, often at melting and boiling points. Two temperature scales were originally defined this way, the Fahrenheit scale and the Celsius scale. The Fahrenheit scale defines the melting point of water to be 32°F and its boiling point to be 212°F. This scale is familiar to people in the United States. The Celsius scale defines the melting point of water to be 0°C and its boiling point to be 100°C. The Celsius scale is used throughout the world and in scientific research and reporting. Once two temperatures are specified, temperatures at any other state can be determined. Another way to define temperature is to use the Carnot engine. Kelvin temperature is defined this way, and is used in scientific research. 0K is defined as the point at which no body can emit heat, and 1K equals 1/273.16 of the temperature of the triple point of water. The triple point is a unique state where water, steam, and ice can exist together. Today the Celsius and Fahrenheit scale are both defined through the Kelvin scale. °C = K - 273.15 and °F = °C(9/5)+32. Kelvin temperature can be quantified through a Carnot engine.
A Carnot engine is a ideal engine. It absorbs a certain amount of heat (Q1) at a hot source (temperature T2), then release a certain amount of heat (Q2) at a cold source(temperature T1) and does some work. The process is carried slowly so the thermal equilibrium is always kept. Then we have Q1/T1 = Q2/T2. Kelvin temperature can be determined through this equation. The lowest temperature is 0K. Nothing can reach this temperature in a finite number of steps. This is also called the fourth law of thermodynamics. The third law of thermodynamics is about entropy.
There are numerous ways to measure temperature. They can be put into two classes: contact method and non-contact method. The contact method is easier to use. Measuring body temperature in a hospital, for example, is a contact method. Contact methods are based on the 0th law of thermal physics. A thermometer is put in contact with an object, and time passes until they reach thermal equilibrium. The temperature of the object can be read from the thermometer because they have equal temperature in thermal equilibrium. Sometimes a contact method is not feasible or not accurate enough. A non-contact method can be used when we cannot or do not want to touch the object we want to measure or when we want high accuracy. These methods are based on physical laws. An example is the pyrometer. It measures temperature through the radiation from an object. Compared with contact methods, it can be used in many more cases. Say, if we want to measure the temperature of a star, a contact thermometer certainly won't do. We can only use a non-contact thermometer. A total-radiation pyrometer is often used in this case. The radiation of the star can be focused by a telescope to a blackened foil to which a thermopile is connected. From the E.M.F. (electric potential difference) produced by the thermopile, the total radiation energy and thus the temperature of the star can be calculated.
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