Change in Entropy
Entropy changes whenever there is a transfer of heat. The change in
entropy is the heat added divided by the temperature at which the transfer
took place. Expressed as an integral:
| ΔS = Sf - Si |
= |
∫ |
| dQ
|  |
| T
|
|
If the heat transfer takes place at a single temperature, the change in
entropy is simply:
| isothermal process: ΔS |
= |
| Q
| |
| T
|
|
If the heat transfer takes place over a range of temperatures then, as
long as ΔT is small compared to the absolute temperature T, the change
in entropy is approximately:
| ΔS
| = |
| Q
| |
| Tavg
|
|
For an ideal gas, it can be shown that the change in entropy is given by:
| ΔS
| = nR ln |
( |
| Vf
| |
| Vi
|
|
) |
+ n CV ln |
( |
| Tf
| |
| Ti
|
|
) |