Entropy of a system water-reservoir

[Dassinia]

Hello,
I'm studying for my exam for tomorrow and we solved an exercise in class , but a question was not answered and I don't know how to solve it.

Homework Statement

1 Kg of water is heated at 0 degree C is brought into contact with a large heat reservoir at 100 degrees C. When the water has reached 100 degrees C, what has been the change in entropy of the water? And of the heat reservoir ? what has been the change in the entire system consisting of both water and the heat reservoir?

Show that we can heat water ( from 0°c to 100°C) without changing the entropy of the whole system.

Homework Equations

The Attempt at a Solution

For the first questions we have
ΔS(water)=4180*ln(373/273) J
ΔS(reservoir)=-418000/373 J

I don't get it how we can heat the water without changing the entropy ..?

 

[Chestermiller]

Suppose, rather than having just one hot reservoir, you had a sequence of hot reservoirs at temperatures running from 0 to 100 C. Could you figure out a way of transferring the heat so that the overall change in entropy of the 1 Kg of water plus all the reservoirs totaled zero?

Chet

 

[Dassinia]

Is it that we have to make a chain of heat baths ?

 

[Chestermiller]

Is it that we have to make a chain of heat baths ?

Pretty much. You use at heat bath at 1C to raise the temperature from 0C to 1 C, you use a heat bath at 2 C to raise the temperature from 1C to 2C, etc. This will give a total entropy change for the water plus the reservoirs very close to zero. In the limit as the temperature increments get smaller, the total entropy change approaches zero.

 

[Dassinia]

Thank you !