# Temperature measurement

## Concept of Temperature

Temperature Measurement- If we rub a metal to a surface after some time it will become hot,when we rub hand it will be warm,if Press against a rapidly spinning wheel. The wheel slows down and becomes warm. When an airplane crashes, it becomes so hot that it catches fire. In each of these examples, mechanical energy is lost and the bodies become hot. Mechanical energy goes into the internal energy of the bodies. We conclude that the cold bodies absorb energy to become hot. In other words, a hot body has more internal energy than an otherwise identical cold body. When a hot body is kept in contact with a cold body, the cold body warms up and hot body cools down. Thus energy is transferred from the hot body to cold body when they are placed in contact. Notice that no mechanical work done during the transfer of energy (neglect any change in volume of the body).      The transfer of energy from a hot body to a cold body is a non-mechanical process. The energy that is transferred from one body to the other, without any mechanical work involved is called heat.

## Defining scale of temperature:

We are now in position to say whether two given bodies are at the same temperature or not. If they are not at same temp. we also know which is at higher temp. and which is at lower temp. Our next task is to define a scale of temp. So that we can give a numerical value to the temp. of body.

### 1) Mercury scale:

In this system the length of mercury in capillary tube is used as thermometric property and is directly proportional to the temp. If at the temp 0° C,100° C and t° C, their corresponding lengths of mercury in capillary tube are L0,L100 and Lt then

### 2)Constant- volume gas scale:

The pressure of any gas on constant volume is used as thermometric property and is directly proportional to the temp. If at the temp 0° C, 100 ° C and t° C, their corresponding pressure of the gas on constant volume are P0, P100 and Pt then

### 3)Platinum resistance scale:

The resistance of platinum wire is used as thermometric property and is directly proportional to the temp. If at the temp 0° C,100° C and t° C, their corresponding resistance platinum wire are R0 R100 and Rt then

## Absolute temperature scale:

Absolute temp. Scale is the scale, which zero point is -273° C and the degree division are equal to the degree division of Celsius scale. i.e.

t ° C = (273+ t )° K

### MECHANICAL TYPE MEASUREMENT OF TEMPERATURE:

Heat can be transferred from one place to another by three different methods, namely conduction, convection and radiation. Conduction usually takes place in solids, convection in liquids and gases, and no medium is required for radiation.

SOLID EXPANSION TYPE:

The solid expansion type is the bimetallic thermometer. The principle of operation is explained in fig.

Two strips A and B of dissimilar metals are bonded firmly together at a temp T(0) .The strips have thickness t(a) and t(b) and coefficients of expansion α(a) and α(b) respectively. One side of the bonded member is held rigidly as shown in fig. If now the temp. changes from that of the bonding temp. to T(1) ,because of unequal expansion in the two strips its free end will curve forming an arc, as it were, of      radius r

where E(a) and E(b) are the Young’s modules of the materials of the strips A and B.If thickness t(a) = t(b) = t and the materials are chosen such that E(a) ≈ E(b) then

Generally radius r is very large and movement of the free tip of the member is very small. However with a large {α(a)-α(b) }, this can be increased. Normally B is invar which has the lowest expansion coefficient and A is chosen to have large coefficient of expansion.

### FLUID EXPANSION TYPE

One of the early methods of measuring temp. was the use of pressure actuated.

thermometers which utilized “filled system”( enclosed systems filled with liquid, gas or vapor) respective to temperature variations. The liquid or gas expansion thermometers use the volumetric expansion unlike the solid expansion where normally the linear expansion principle is utilized. These types are quite rugged, cheap and need no maintenance. These have fairly good response, accuracy and sensitivity but less compared to electrical-types and with capillary lines remote indication up to about 250 to 300 ft is possible. These are also self-contained and self-operated. But ranges are quite limited and when they fail total replacement is necessary. The filled system thermometer consists of three fundamental elements i.e. the bourdon tube, capillary tube and the bulb are all interconnected as shown in fig. is sealed after filing with an appropriate liquid at a pressure at the normal ambient temperature.

The liquid is then incompressible and with change in temp. in the bulb a change in volume of the liquid due to expansion occurs which causes the Bourdon tube to expand.  The range is about -40ºF to 600 ºF with a vapor pressure change of 20 to 600 psig. Speed of response is dependent on the thermal system and the capillary length.

### Errors in filled-in system

The common sources of errors in –filled systems are:

1) Ambient temperature effect: The change of ambient temperatures causes volume changes in the capillary and the pressure spring, thereby causing error in measurement. As in the vapor pressure thermometer, the liquid surface temp. Is the only determining factor, it does not need correction for the ambient temp. effect. Compensation for the case or pressure spring temperature change is done either by using a bimetallic suitably adapted or by a compensating spring adapted with a differential link as shown in fig.

2) The head or elevation effect: If the thermometer bulb is placed at a different height with respect to the pressure spring, the elevation errors are produced. Fig The head of liquid ‘h’ will cause this error. If the filling is done at a high pressure compared with this head ‘h’, the error is negligible. The head of liquid ‘h’ will cause this error. If the filling is done at a high pressure compared with this head ‘h’, the error is negligible. ` The head of liquid ‘h’ will cause this error. If the filling is done at a high pressure compared with this head ‘h’, the error is negligible.

The head of liquid ‘h’ will cause this error. If the filling is done at a high pressure compared with this head ‘h’, the error is negligible.

3) The barometric effect: The effect dye to change in the atmospheric pressure is the barometric effect. This comes into being as the pressure spring works due to a differential pressure. If the filled system is at the high pressure sufficiently larger than the atmospheric pressure, the error due to this is negligible.

4) The immersion effect: If the bulb is not properly immersed or fully immersed and the head of the bulb is not properly insulated, heat from the bulb is lost due to conduction through the extension neck and thermal well.

5) The radiation effect: Radiation error occurs due to temperature difference between the bulb and other solid bodies around. A radiation shield around the bulb minimizes the error.

## Electrical type Temperature measurement

### Temperature Measurement by Resistance type:

Most metals have the property that change in electrical resistance is directly proportional to its change in temperature and is linear over a range of temperatures. RTD always works increase in resistance with increase temperature. RTD is the most widely used instrument for temperature measurement. The accuracy of RTD is very high.

### Temperature measurement by Thermocouple:

A thermocouple is a sensor that measures temperature. It is made up of two distinct metals that are attached at one end. A voltage is produced that is related to the temperature when the junction of the two metals is heated or cooled. Thermocouple is a widely used instrument for temperature measurement. Thermocouples are used for temperature measurement in almost all industries. The accuracy of thermocouple is less than RTD.