5 – 16 (a) One kilogram of water at 0°C is brought into contact with a large heat reservoir at 100 °C. When the water has reached 100°C, what has been the change in entropy of the water, of the heat reservoir, and of the universe? (b) If the water had been heated from 0°C to 100°C by first bringing it into contact with a reservoir at 50°C and then with a reservoir at 100°C, what would be the change in entropy of the universe? (c) Explain how the water might be heated from 0°C to 100°C with no change in the entropy of the universe.

(a) One kilogram of water at 0°C is brought into contact with a large heat reservoir at

100 °C. When the water has reached 100°C, what has been the change in entropy of the water, of the heat reservoir, and of the universe?

For the reservoir, the temperature of the reservoir is constant at 373 K. The heat lost from the reservoir is the heat gained by the water,

(b) If the water had been heated from 0°C to 100°C by first bringing it into contact with a reservoir at 50°C and then with a reservoir at 100°C, what would be the change in entropy of the universe?

As we found in part (a)

Now we have to do this in two steps, one from 273 K to 323 K and then from 323 K to 373 K

(c) Explain how the water might be heated from 0°C to 100°C with no change in the entropy of the universe

Clearly the entropy of the universe was less increased using two reservoirs, so if one used a large (infinite) number of reservoirs with small changes of temperature between them, the change in entropy of the universe will decrease to zero.