Entropy of a system water-reservoir

• Dassinia
In summary, the conversation discusses the change in entropy of 1 Kg of water and a large heat reservoir when the water is heated from 0 degrees C to 100 degrees C. The solution for the first question is provided, but the concept of heating water without changing the entropy of the whole system is introduced. It is suggested to use a sequence of hot reservoirs at different temperatures to achieve a near-zero total entropy change.
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.

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 ..?

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

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

Dassinia said:
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.

Thank you !

1. What is the definition of entropy?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic quantity that describes the amount of energy that is unavailable to do work in a system.

2. How does entropy relate to the water-reservoir system?

In the water-reservoir system, entropy is a measure of the randomness or disorder of the water molecules. As the water molecules move and mix within the reservoir, their positions and orientations become more disordered, increasing the system's overall entropy.

3. Can entropy be decreased in a water-reservoir system?

According to the second law of thermodynamics, entropy will always increase or remain constant in any natural process. Therefore, it is not possible to decrease the entropy of a water-reservoir system without external work being done on the system.

4. How does temperature affect the entropy of a water-reservoir system?

The temperature of a water-reservoir system is directly related to the average kinetic energy of the water molecules. As the temperature increases, the water molecules will have more thermal energy and move more rapidly, resulting in a higher disorder and therefore, a higher entropy.

5. How is the entropy of a water-reservoir system calculated?

The entropy of a water-reservoir system can be calculated using the equation S=klnW, where S is the entropy, k is the Boltzmann constant, and W is the number of microstates available to the system. The number of microstates is related to the number of possible arrangements or configurations of the water molecules within the system.

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