Energy is the capacity for doing work. It may exist in a variety of forms such as thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear. It may be transferred from one type of energy to another. For example,

• Heating water by gas:
  Chemical energy ---> thermal energy
• Heating water by electricity:
  electric energy ---> thermal energy
• Running nuclear power plant:
  Nuclear energy ---> electric energy
• Flying rocket:
  Chemical energy ---> thermal Energy ---> Kinetic Energy

Kinetic Energy (KE): The energy that a system possesses as a result of its motion.

      KE = mv²/2

where
      m = mass of the system
      v = velocity of the system

If an object of mass m changes velocity from v₁ to v₂. thus the change of its kinetic energy is:
      
      ΔKE = 1/2 (v₂ ²- v₁ ²)

Potential Energy (PE): The energy that a system possesses as a result of its elevation in a gravitational field or change of configurations.

Gravitational potential energy (elevation in a gravitational field):

      PE = mgz

where
      m = mass of the system
      z = height relative to a reference frame

Moving an object from location A to B, its gravitational potential energy change is:

     ΔPE = mg(Z_B - Z_A)

Elastic Potential Energy

Elastic potential energy (change of configurations):

      PE = 1/2 kx²

where
       k = spring constant
      x = change in spring length

If a spring elongates from L₁ to L₂, the elastic potential energy stored in the spring is :
      
      ΔPE = 1/2 k L₂ ²- 1/2 k L₁ ²

Internal energy (U): The energy associated with the random, disordered motion of molecules. It is the sum of the kinetic and potential energies of all molecules.

• Experience has shown that for most substances with no phase change involved, internal energy strongly depends on temperature. Its dependence on pressure and volume is relatively small.
• It is not possible to calculate the absolute value of the internal energy of a body. Only internal energy change of a system can be determined.
• Internal energy is a property.

Total Energy (E): The sum of all forms of energy exist in a system. The total energy of a system that consists of kinetic, potential, and internal energies is expressed as:

      E = U + KE + PE = U + mv²/2 + mgz

The change in the total energy of a system is:

     ΔE = ΔU + ΔKE + ΔPE

Enthalpy is a thermodynamics property of a substance and is defined as the sum of its internal energy and the product of its pressure and volume.

      H = U + PV

Experiment shows that the temperature rise of liquid water due to heat transfer to the water is given by

      Q = m c (T₂ - T₁)

where
      Q = heat transfer to the water
      m = mass of water
      T₂ - T₁ = temperature rise of the water
      c = specific heat, an experiment factor

In general, the value of specific heat c depends on the substance in the system, the change of state involved, and the particular state of the system at the time of transferring heat. Specific heat of solids and liquids is only a function of temperature but specific heat of gaseous substances is a function of temperature and process.

Specific heat at constant volume is the change of specific internal energy with respect to temperature when the volume is held constant (Isochoric process).

For constant volume process:

Specific heat at constant pressure is the change of specific enthalpy with respect to temperature when the pressure is held constant (Isobaric process).

For constant pressure process