Units for Mass, Length, Time and Force

meter (m)
foot (ft)
second (s)
second (s)
kilogram (kg)
slug (slug)
newton (N)
pound (lb)
blue = derived units


There are two widely used systems of units: the International System (or Systeme International d'Unites in French), S.I.; and the English System.

The base units in the S.I. system are meters (m) for length, second (s) for time, and kilogram (kg) for mass. The force unit is derived using Newton's 2nd Law:

     F = ma = 1 kg (1 m/s2) = 1 kg m/s2 = 1 N

The base units in the English system are foot (ft) for length, second (s) for time, and pound-force (lbf) for force. The mass unit is derived using Newton's 2nd Law:

     m = F/a = 1 lb/(ft/s2) = 1 lb s2/ft
         = 1 slug = 32.174 lbm

The table to the left compares the two systems. All the units in thermodynamics can be derived from these base units. Details of the thermodynamic units will be introduced in the following sections.


Definition of Pressure

The absolute pressure (P) is the force acting on unit area.

In the SI system, the unit for pressure is Pa, Pascal. In the English system, it is psi.

      Pa = N/m
      psi = lbf/in2

Since Pa is a small unit in the SI system, other units are also used in thermodynamics, such as:

      1 bar = 105 Pa
      1 kPa = 103 Pa
      1 MPa = 106 Pa
      1 atm = 101325 Pa


The air surrounding the earth can be treated as a homogeneous gas, called atmosphere. Atmospheric pressure (Pa) is the pressure due to the force by the atmosphere mass. Standard atmospheric pressure is 101325 Pa.



Barometer is a device used to measure the atmospheric pressure.

     Pa = ρ g h

     ρ = The density of the working liquid, kg/m3
     g = The acceleration of gravity, 9.8 m/s2
     h = The height of the working liquid in the tube, m



Gage Pressure and Vacuum Pressure

Gage pressure (Pg) is the difference between the absolute pressure and the atmospheric pressure if the difference is positive. If the difference is negative, it is called vacuum pressure (Pv).

     Pg = P - Pa (P > Pa)
     Pv = Pa- P (P < Pa)

Absolute pressure is used in thermodynamic relations and tables.


U-Tube Manometer
Click to View Movie (96 kB)

U-Tube Manometer is used to measure pressure difference. One end of it is open to the atmosphere and the other end is connected to the equipment whose pressure is needed to be measured.

At the right side,

      P1 = Pgas + ρgas g h1

Usually, the second term on the right hand of the previous equation is negligible since the density of the work fluid is much larger than the density of the gas.

      P1 = Pgas

At the left side,

      P1 = Pa + ρworking fluid g h1

Combine the two equations above, the pressure in the gas tank can be determined as

         Pgas = Pa + ρworking fluid g h1



    Temperature and the Zeroth Law

The Zeroth Law


The measurement of the degree of hotness or coolness is temperature.

If two bodies at different temperatures are brought together, the hot body will warm up the cold one. At the same time, the cold body will cool down the hot one. This process will end when the two bodies have the same temperatures. At that point, the two bodies are said to have reached thermal equilibrium.

The Zeroth Law of thermodynamics states:

Two bodies each in thermal equilibrium with a third body will be in thermal equilibrium with each other.

The Zeroth Law of thermodynamics is a basis for the validity of temperature measurement.

    Temperature Scales



To establish a temperature scale, two fixed, easy duplicated points are used. The intermediate points are obtained by dividing the distance between into equal subdivisions of the scale length.

Temperature Scale
Fixed Point 1
Fixed Point 2
Fahrenheit Scale (oF)
Freezing Point of Water = 32.0
Boiling Point of Water = 212.0
Celsius Scale (oC)
Freezing Point of Water = 0.0
Boiling Point of Water = 100.0
Thermodynamic Temperature Scale (K)
The pressure of an ideal gas is zero =  0.0
The Triple Point of Water = 273.16

Relations between Different
Temperature Scales

The relations between the above temperature scales are:

      T (K) = T(oC) + 273.15
      T (oF) = 1.8T(oC) + 32.0
      T (oF) = 1.8 (T(K)-273.15) + 32.0

The thermodynamic temperature scale in the English system is the Rankine scale. The temperature unit on this scale is the rankine, which is designated by R. The thermodynamic temperature scale in S.I. system (K) and English system (R) are related by

      T(R) = 1.8 T(K)




Click to View Movie (37 kB)

Thermometers measure temperature, by using materials that change in some way when they are heated or cooled. In a mercury or alcohol thermometer the liquid expands as it is heated and contracts when it is cooled, so the length of the liquid column becomes longer or shorter depending on the temperature. Modern thermometers are calibrated in standard temperature units such as Fahrenheit or Celsius. Three practical points for using thermometer are:

  • The thermometer should be isolated to everything except the body which temperature is measured. The general method is to immerse the thermometer in a hole in a solid body, or directly in a fluid body.
  • When thermal equilibrium is reached, the thermometer can indicate its own temperature as well as the body measured. The thermometer should be small relative to the body so that it only has a small effect upon the body.
  • The thermometer must not be subject to effects such as pressure changes, which might change the volume independently of temperature.

Digital thermometers almost replace the mercury ones in nowadays because they are more accuracy and more easy to use.

Digital Thermometer