# Temperature Measurement - General Instructions

1. Temperature as Measured Variable

For nearly all procedures in research and production, temperature is a factor to be considered. It is of considerable importance as measured variable. For temperature measurements, temperature dependent characteristics of materials can be used, as, for example, the changing electrical resistance (resistance thermometer), the electromagnetic radiation of hot bodies (radiation pyrometer), and resulting thermoelectric voltage (thermocouple). The different electric contact thermometers are frequently used in the field of temperature measurement.

2. Physical Basis

2.1. Resistance Thermometer
Temperature measurement with the help of resistance thermometers base on the special characteristic of conducting materials to change their resistance dependent on temperature. For metals, the resistance increases with rising temperature. In case that the correlation between temperature and resistance is known, the temperature can be determined by resistance measurement. The suggestion to use the temperature dependent resistance of metal conductors for temperature measurement was first made by Wilhelm von Siemens, the brother of Werner von Siemens in 1861. It was realized in the development of a thermometer for the measurement of deep sea temperatures. The works of H.L. Callendar made the resistance thermometer a precision device in 1886.

2.2. Thermocouples
The first basis of the thermovoltage effect was discovered by Seebeck in 1821. Thirty years later, the exact correlations were found out by Thompson. The thermovoltage between two different metals depend on the thermal motion of electrons. It is not dependent on the absolute temperature values but on temperature differences. The higher the temperature difference between ”hot” and ”cold”, the higher the thermovoltage. The voltage at one degree Celsius is called the thermoelectric force of the thermocouple. It depends on the nature of the two materials whose connection point is heated.

3. The Response

Time of Contact Thermometers The temperature measurement with the help of contact thermometers is generally afflicted with a delayed indication. The result is that a changing temperature is not immediately indicated correctly but only after a certain time when the heat exchange between the measured medium and the temperature probe has been fully realized. This inertia of thermometers shall be as small as possible for certain measuring tasks. This is called the response time of a thermometer which means the time constant. Generally spoken: the time constant corresponds to the relation of the capacity of heat absorption and heat release of the thermometer. Both characterisitics are mainly determined by:

• heat capacity
• transversal thermal conductivity of the thermometer
• relation of surface to volume of the thermometer
• coefficient of thermal conductivitiy between medium and surface of the thermometer as well as of the medium velocity, its thermal conductivity and its specific heat.

If a thermometer is suddenly exposed to another temperature as, for example, by taking it out of water with a temperature of 20°C and putting it into water of 40°C, the indicated temperature rises almost according to the exponential function. The usual quantity for the changing velocity of such exponential procedures is the time constant. The time constant is equal to the time that passes until 63,2% of the temperature leap is indicated. In many cases, the temperature indication does not change according to the exponential function. For those cases, the time constant is not sufficient to characterize the time response. Therefore, it is useful to indicate the half-time z 0.5 and the 9/10 time value z 0.9. This is the definition of time from the sudden change of temperature to the reach of 50% either 90% of this temperature change. The exponential course shows z 0.5 =0.693 (time constant) resp. z 0.9 = 2.303 (time constant) and the ratio z 0.9/z 0.5 has to be equal to 3.32

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