# Find the total entropy of the system?

1. Dec 6, 2011

### gibson101

1. The problem statement, all variables and given/known data
If 2.00 m3 of water at 0°C is frozen and cooled to -25°C by being in contact with a great deal of ice at -25°C, what would be the total change in entropy of the process?

2. Relevant equations
ΔS=Q/T Q=mL Q=mcΔT

3. The attempt at a solution
2000 * 4190 * ln (273/(273-25) + 2000* 336000/273 = 265854.8 J/K
Why is natural log being used?

2. Dec 6, 2011

### I like Serena

Hi gibson101!

The natural log is used because ΔS depends on the temperature, which is changing during cooling.
This means that ΔS needs to be integrated ($\Delta S=\int {dQ \over T}$) yielding the natural log.