# Internal Energy

on . Posted in Thermodynamics

Internal energy, abbreviated as U, is the total of all energies associated with the motion of the molecules in the system.  It encompasses the sum of the kinetic energy and potential energy of the particles that make up the system, such as molecules, atoms, or subatomic particles.

The internal energy of a system can change due to various factors, such as the addition or removal of heat, work done on or by the system, or changes in the system's composition or state.  The first law of thermodynamics, often referred to as the law of conservation of energy, governs the changes in internal energy of a system.

It is important to note that the internal energy is a property of the system and does not depend on the path taken to reach a particular state.  It can be measured or estimated through various techniques, including calorimetry or thermodynamic calculations.

### Internal energy formula

$$U \;=\; (3\;/\;2) \; n \; R \; T_a$$     (Internal Energy)

$$n \;=\; 2 \; U \;/\; 3 \; R \; T_a$$

$$R \;=\; 2 \; U \;/\; 3 \; n \; T_a$$

$$T_a \;=\; 2 \; U \;/\; 3 \; n \; R$$

Symbol English Metric
$$U$$ = Internal Energy $$Btu$$ $$J$$
$$n$$ = Number of Moles $$dimensionless$$ $$dimensionless$$
$$R$$ = Ideal Gas Constant $$lbf-ft\;/\;lbmol-R$$ $$J\;/\;kmol-K$$
$$T_a$$ = Absolute Temperature $$R$$ $$K$$

### Change in Internal energy formula

$$U \;=\; Q + W$$     (Change in Internal Energy)

$$Q \;=\; U - W$$

$$W \;=\; U - Q$$

Symbol English Metric
$$U$$ = Internal Energy $$Btu$$ $$J$$
$$Q$$ = Heat Transfer $$Btu\;/\;hr$$ $$W$$
$$W$$ = Total Work Done on and by the System $$lbf-ft\;/\;lbmol-R$$ $$J\;/\;kmol-K$$

Tags: Energy Kinetic Energy