Question

Thermodynamics and Statistical Mechanics Problem:

1. You have just microwaved a cup of tea for too long and it is boiling, too hot to drink. You look around and see a punchbowl containing ice floating in water. You thoroughly mix one cup of water (no ice) from the punchbowl with your cup of tea in a thermos bottle. What is the change in entropy of the pint of liquid? Does the sign of the change make sense? Explain.

Answer 1

Since the tea is boiling, its temperature is 100^o C = 373 K

The water is containing ice means that the temperature of water is 0⁰ C = 273 K

Now, as we are mixing equal quantities of water and tea, we can say that the temperature of the system will come into their average of 323 K (Assuming that the specific heat does not change with temperature and tea has the same specific heat as water.

The specific heat capacity of water= 1 calorie (4.184 J)

So, the change in entropy is given by

dQ = msdT

Mow, there are two processes. heating of water and cooling of tea.

for a pint of liquid, =473.176 ml = 0.473176 g

It takes less energy to cool down from higher temperature than from lower temperature. So, heating of ice to 323 K increases the entropy more than it is reduced for cooling of water from 373 K to 323 K