# Same temperature and entropy

1. Feb 10, 2008

### Antonio2090

Does entropy change when temperature remains constant? What if heat is added into a system, while the volume expands and the pressure drops at a constant temperature? Is there any change in entropy?

2. Feb 10, 2008

### Mapes

Does entropy change when temperature remains constant?

Yes, entropy can change even at constant temperature. For example, adding material into a system increases entropy, as does any irreversible isothermal process such as free expansion of a gas into a vacuum.

What if heat is added into a system, while the volume expands and the pressure drops at a constant temperature? Is there any change in entropy?

Yes, heating a system always increases its entropy. Another way to view this process is that the temperature is the same, but the space for atomic motion has increased because the volume increased. There are therefore more available microstates for the system, which is equivalent to saying the entropy has increased.

3. Feb 11, 2008

### Andy Resnick

It can. For example, let's look at the Gibbs Free energy- this is the change of free energy for processes occuring at constant T and P:

$$\Delta G = \Delta H - T\Delta S$$

G is the Gibbs free energy, H the enthalpy, T temeprature, S entropy. There are lots of processes that use this relationship: phase transitions, chemical reactions, etc. The sign of $$\Delta G$$ tells you if the processes is spontaneous or not- in biochemical reactions, non-spontaneous reactions are generally powered by using the chemical energy in adenosine triphosphate (ATP) or guanine triphosphate (GTP)- but not in the way elementary texts describe.

The Gibbs free energy is related to the chemical potential: specifically, if a chemical is out of equilibrium concentrations. The relative concentration of ATP to ADP is kept about 10^10 times out of equilibrium by organisms (IIRC), and this is the source of energy used to power reactions, and by which we have the ability to locally decrease our entropy.