The first law of thermodynamics, also known as the conservation of energy principle, states:

The first law is based on experimental observations. It can not be proved mathematically, but no known process in nature violates the first law.

During a process, the first law can be expressed as:
the net change in the total energy during a process is equal to the difference between the total energy entering and leaving the system during that process. In an equation format, the energy balance for a system is:

(Total energy entering the system)
-
(Total energy leaving the system)
=
(Net change in the total energy of the system)

or,

      E_in- E_out = ΔE_system

The rate form of the energy balance of a system is:

( Rate at which energy entering the system)
-
(Rate at which energy leaving the system)
=
(time rate of change in the total energy of the system)

or,

Energy is transferred to or from a system by three forms: heat, work and mass flow. For a closed system, the only two forms are heat and work since no mass crosses its boundaries.

1. Heat transfer (Q)
Heat transfer is the energy interaction caused by a temperature difference between a system and its surroundings. Heat transfer to a system (heat gain) will cause the internal energy of the system to increase, and heat transfer from a system (heat loss) will cause the internal energy of the system to decrease.

2. Work (W)
The energy interaction that is not caused by a temperature difference between a system and its surroundings is work. Work transferred to a system will increase the energy of the system, and work transferred from a system will decrease the energy of the system.

3. Mass flow
When mass enters a system, the energy of the system increases because of the energy accompanied by mass. Also the energy of the system decreases when mass leaves the system.

Heat and work have been introduced in the previous sections. Systems that involve energy balance with mass flow are considered in the following section.

Note that net transfer of a quantity is equal to the difference between the amounts transferred in and out, the energy balance can be written as:

(Q_in - Q_out ) + (W_in - W_out) + (E_mass,in - E_mass,out) = ΔE_system

All the quantities of the six terms in the left are positive amounts since the direction of the energy transfer is described by the subscripts "in" and "out".

The energy change of a system during a process is:

Energy change
=
Energy at final state
-
Energy at initial state

or,

      ΔE_system = E_system@final - E_{system@initial}

From the discussion in the previous section, it is known that the change in the total energy of a system during a process is the sum of the changes in its internal, kinetic, and potential energies.

      ΔE = ΔU + ΔKE + ΔPE