First Law of Thermodynamics for a Closed System

Conservation of Energy

Internal energy (U) is associated with microscopic motions and forces. Since this energy cannot be seen, it is usually separated from the macroscopic i.e., measurable mechanical energy in order to express the total energy of the system as:

E_total = U + Kinetic Energy (E_K) + Potential Energy (E_P)

Let us consider a closed system to which energy in the form of heat and work is supplied from its surroundings:

The first law of thermodynamics states that the total energy of the universe is constant, i.e.,

E_total (universe) = constant    or     Δ E_total (universe) = 0

 

The universe is composed of the system and its surroundings; thus, the above expression can be expressed as follows:

E_total (system) + E_total (surroundings) = 0

The increase in the total energy of the system is given by:

ΔE_total (system) = ΔU + ΔE_K + ΔE_P

Conversely, the decrease in the total energy of the surroundings is given by:

ΔE_total (surroundings) = -Q – W (where Q is heat into or out of the surroundings and W is work done on or by the surroundings)

Combining the above two equations we obtain the first law of thermodynamics for a closed system:

ΔU + ΔE_K + ΔE_P = Q + W

The differential form of this equation is as follows:

dU + dE_K + dE_P = dQ + dW

(Note: Since Q and W are path functions, these quantities in differential form are expressed as δQ and δW in some examples)

If the changes in kinetic and potential energies are negligible the equation can be simplified as:

ΔU = Q + W

The term W includes expansion and non-expansion type of work. Expansion (or contraction) work is related to the change in the volume of system. While non-expansion work includes shaft work (work done on the system by a rotating mechanical device), chemical work, electrical work, etc.