The zeroth law of thermodynCimics is the basis of temperature measurement. In order to obtain a quantitative measure of temperature, a reference body of known physical characteristic which changes with temperature is choosen. the choosen characteristic is called thermometric property and the reference body is called thermometer. In common thermometer, expansion of mercury is used as thermometric property. Table 2.1 shows the types of thermometer with its thermometric property.

** Table 2.1**

S. No Thermometer Thermometric property Symbol

1. Mercury-in-glass Length L

2. Constant volume gas Pressure p

3 . Electrical resistance Resistance R

4. Constant pressure gas Volume V

5. Thermocouple Thermal Electromotiveforce E

6. Pyrometer (Radiation) Intensity of radiation I or J.

**2.2.1 Empirical Relations between Temperature and Thermometric Property**

** **

If xis the thermometric property and temperature is the linear fw1Ction (direct proportionality) of x. So, mathematically

f(x) = nx

where a is an arbitrary constant.

If x_{1} corresponds to f (x_{1}), then x_{2} can be calculated as follows.

f(x_{1}) = ax_{1}

_{ }a = f (x) / x_{1} inserting this in equation (2 .1 ) we get

f (x) = f (x) / x_{1} .x

x = x_{2} we get from (2.2)

f (x_{2}) = f (x_{1}) / x_{1} . x_{2}

f (x_{2}) / f (x_{1}) = x_{2} / x_{1}

_{ }

Equation (2.3) shows that two temperatures on the linear x scale are to each other as the ratio of the corresponding readings i.e., x_{2} and x_{1}.

**2.2.2 Method Used Before 1954**

Let f(x) = ax + b … (2.4)

The thermometer is first placed in contact with a standard system and measures the temperature of it. Let x1 is the reCiding, so,

f (x_{1}) = ax_{1} + b

Then the thermometer is placed with an another standard system and measures the temperature of it and let x_{2} is the reading , so,

f (x_{2}) = ax_{2} +b

Solving (2.5) and (2.6) for a and b,

F(x_{1}) – (x_{2}) = a (x_{1} –x_{2})

A = f (x_{1}) – f (x2) / x_{1} –x_{2}

(2.5) => b = f (x_{1}) – ax_{1}

= f(x_{1}) – f(x_{1}) – f(x_{2}) / x_{1} – x_{2} . x_{1}

= x_{1} f (x_{1}) – x_{2} f (x_{1}) – x_{1} f( x_{1}) + x_{1} f (x_{2}) / x_{1 }–x_{2}

b = x_{1} f (x_{2}) – x_{2} f(x_{1}) / x_{1} –x_{2}

Inserting the value of a and b in (2.4), we get

F(x) = f(x_{1}) – f(x_{2}) / x_{1 }–x_{2} .x + x_{1} f(x_{2}) – x_{2 }f (x_{1}) / x_{1} –x_{2}

Note : If b = 0 then equation (2.7) reduces to

F(x) = f(x_{1}) – f(x_{2}) / x_{1} –x_{2} . x

and we have

b = 0 = x_{1} f(x_{2}) –x_{2} f (x_{1}) / x_{1} –x_{2})

Two commonly used scales are Celsius scale and Fahrenheit scale. Symbols C and Fare used to denote the readings on the two scales. Before 1954, the two fixed points used are steam point (boiling point of water at standard atmospheric pressure and the ice point (freezing point of water)

Temperature Celsius scale Fahrenheit scale

Steam point 100 212

Ice point 0 32

Interval 100 degrees 180 degrees

100 -0 /C -0 = 212 – 32 /F -32

100 / C = 180 / F -32

5 /C = 9 / F -32

C /5 = F -32 / 9

**2.2.3 Method in Use On and After 1954**

On and after 1954, Kelvin suggested that only one fixed point is necessary to establish a temperature scale. This fixed point is the triple point of water. The value of the triple point of water is 0.01^{o}C or 273.16 K. Correspondingly, the ice point of 0 ^{o }c on the Celsius scale becomes 273.15 K on Kelvin scale. Let us use t^{o }C for Celsius scale and T for Kelvin scale.

Then

Tin Kelvin= 273.15 + t^{o }C.

The triple point of water in the Fahrenheit scale is 32.02!!F and for Rankine scale is 491.69R

T in Rankine scale = 459.67 t^{o}F

**Table 2.2**

Fixed point Celsius Kelvin Falzrenlieit Rankine

Steam point 100 373.15 212 671.67

Triple point of water 0.01 273.16 32.02 491.69

Ice point 0 273.15 32 491.67

Absolute zero – 273.15 0 – 459.67 0