# Entropy formula

1. Oct 9, 2015

### bharghav123

hey guys,Entropy is supposed to be a measure of disorder in a a system then why is the formula ∫dQ/T used.I can understand why entropy increases with the energy in the system but why is the absolute temperature of the system relevent, is it a proportionality constant ? please enligthen me on this Q. it would do me a huge favour

2. Oct 9, 2015

### stockzahn

Hi,

entropy does not increase with energy, but with transferred heat. If you take the disorder of a system as a model:

You can increase the energy (isentropically) of a gas by compressing it. The temperature increases, which makes the molekules move faster, but the pressure constraints the movement again - the disorder stays the same.

If you heat the gas (isothermically as you indicated in your post), the velocity of the molecules increases and the pressure decreases - both are effects which increase the the freedom of the particles (and increases the "disorder").

The absolute temperature is relevant, because temperature is a measure for the mean kinetic energy of the single particles. A larger temperture is the same as higher velocities of the molecules. With the same amount of heat transferred at different temperatures, the velocity increase is smaller at higher temperatures because the kinetic energy is proportional to the velocity to the power of two - less change in movement, less increase of disorder.

3. Oct 9, 2015

### Staff: Mentor

From the standpoint of disorder, entropy is derived in Statistical Thermodynamics by looking at the distribution of energy states of a system. That development clearly illustrates how absolute temperature comes into play.

Chet