Engg Thermodynamics L2 - Application of Zeroth Law

  • Temperature Measurement

  • Different types of thermometers

Temperature Measurement

For measurement of temperature

  • a reference body is used which is called 'thermometer'.

  • a physical characteristics (such as volume, pressure, emf etc.) which changes with change in temperature. This property is called 'thermometric property'.

Suppose temperature t varies with thermometric property x as:

t(x) = ax; where a is a constant.

when value of property x = x1

t(x1) = ax1

when value of property x = x2

t(x2) = ax2

Hence; t(x2)/t(x1) = x2/x1

Thus unknown temperature may be calculated if we know value of thermometric property at a reference point and its variation with the temperature.

Triple point of water (temperature at which ice, liquid water and water vapor exist together) is chosen as a reference point and arbitrarily given a temperature of 273.16 K.

Different types of thermometers

1. Constant Volume Gas Thermometer

t(p) = 273.16*(p/pt)

Pressure is thermometric property and pt represents pressure at triple point.

A gas thermometer is shown in the figure 1. Pressure in the bulb is given as

p = po + ρmgh

When the bulb is brought in contact with a body at temperature t, gas in the bulb expands and pushes the liquid in manometer downwards. To maintain constant volume, manometric tube is adjusted such that mercury in the manometer again touches the point A. Pressure at this state is recorded by measuring h. Since the volume is constant, change in temperature is given as:

∆t = V ∆p/R

Gas Thermometer

2. Constant Pressure Gas Thermometer

t(V) = 273.16*(V/Vt)

Volume is thermometric property and Vt represents volume at triple point.

For a constant pressure gas thermometer (Fig. 1), mercury level is adjusted such that h remains constant. Change in temperature is given as:

∆t = p ∆V/R

3. Electrical Resistance Thermometer

t(R) = 273.16*(R/Rt)

Electrical resistance is thermometric property and by measuring change in its value temperature change may be measure.

4. Thermocouple

t(ε) = 273.16*(ε/εt)

Thermocouple works on the principle of seebeck effect. When two wires of dissimilar metals are joined together, an emf is generated depending on the temperature difference between hot and cold junction (fig. 2). Measurement of emf gives a measure of temperature of the body.

Untitled_edited.png

5. Liquid in Glass Thermometer

t(L) = 273.16*(L/Lt)

Example

Reference Books

1. Engineering Thermodynamics by P. K. Nag

2. Fundamentals of Thermodynamics by Borgnakke, Sonntag