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# Internal Energy

The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy. This is contrast to external energy which is a function of the sample with respect to the outside environment (e.g. kinetic energy if the sample is moving or potential energy if the sample is at a height from the ground etc). The symbol for Internal Energy Change is$$ΔU$$.

### Energy on a smaller scale

• Internal energy includes energy on a microscopic scale
• It is the sum of all the microscopic energies such as:
1. translational kinetic energy
2. vibrational and rotational kinetic energy
3. potential energy from intermolecular forces

Example

One gram of water at zero °Celsius compared with one gram of copper at zero °Celsius do NOT have the same internal energy because even though their kinetic energies are equal, water has a much higher potential energy causing its internal energy to be much greater than the copper's internal energy.

### Internal Energy Change Equations

ΔU = q+w

where q is heat and w is work

An isolated system cannot exchange heat or work with its surroundings making the change in internal energy equal to zero.

ΔUisolated system = 0

Energy is Conserved

ΔUsystem = -ΔUsurroundings

The signs of internal energy

• Energy entering the system is POSITIVE (+), meaning heat is absorbed, q>0. Work is thus done on the system, w>0
• Energy leaving the system is NEGATIVE (-), meaning heat is given off by the system, q<0 and work is done by the system, w<0
• Since ΔUisolated system = 0, ΔUsystem = -ΔUsurroundings and energy is conserved.

### Quick Notes

• A system contains ONLY internal Energy
• a system does NOT contain energy in the form of heat or work
• Heat and work only exist during a change in the system
• Internal energy is a state function

### Contributors

• Lorraine Alborzfar (UCD)

08:19, 5 Dec 2013

## Classifications

Vet2
Fundamental

### Textbook Maps

This material is based upon work supported by the National Science Foundation under Grant Number 1246120