Entropy of water and reservoir

In summary, the question asks about the change in entropy of water and a heat reservoir when 1 kg of water at 0 degrees C is heated and brought into contact with the reservoir at 100 degrees C. The formula for entropy change in water is given, but cannot be used for the reservoir due to its infinite heat capacity. Instead, the definition of entropy is used to determine the change in entropy of the reservoir, taking into account the signs of heat flow.
  • #1
Slepton
21
0

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?


Homework Equations



[tex]\Delta[/tex]Sw = mcln(Tf/Ti)

where
m = mass of water
c = specific heat capacity of water ( 4186 J/K)
Tf = final common temperature of water and the reservoir
Ti = initial temperature of water (and also reservoir for part b of the question)



The Attempt at a Solution


The application of formula above gave me answer for entropy change in water but not for reservoir and the whole system. Some help anticipated.
 
Physics news on Phys.org
  • #2
Slepton said:

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?


Homework Equations



[tex]\Delta[/tex]Sw = mcln(Tf/Ti)

where
m = mass of water
c = specific heat capacity of water ( 4186 J/K)
Tf = final common temperature of water and the reservoir
Ti = initial temperature of water (and also reservoir for part b of the question)



The Attempt at a Solution


The application of formula above gave me answer for entropy change in water but not for reservoir and the whole system. Some help anticipated.

You are assuming that the reservoir has an infiinite heat capacity such that any amount of loss or addition of heat will have no (an infinitessimal) change in temperature. So you cannot use this formula.

To determine the change in entropy of the reservoir just use the definition of entropy:

[tex]\Delta S = \Delta Q/T[/tex]

Since T does not change, this is simply a matter of looking at the heat flow to/from the reservoir. Be careful about the signs: - is heat flow out; + is heat flow into the reservoir.

AM
 
  • #3
consider the heat flow of the system. Negative of heat gained by 1 kg of water is the heat lost by the reservoir. From that calculate the change in entropy. Keep track of the signs.

Good luck
 

1. What is the relationship between entropy and water?

Entropy is a measure of disorder or randomness in a system. Water molecules have high entropy because they are constantly moving and interacting with each other, resulting in a more disordered state.

2. How does the entropy of water affect its physical properties?

The high entropy of water contributes to its unique physical properties, such as its high boiling point, surface tension, and ability to dissolve many substances. These properties are a result of the constant movement and interactions between water molecules.

3. What is the role of entropy in water's phase changes?

The transition between different phases of water, such as solid ice, liquid water, and gaseous water vapor, involves changes in the entropy of the system. For example, when water freezes, the molecules become more ordered, resulting in a decrease in entropy. On the other hand, when water evaporates, the molecules become more disordered, leading to an increase in entropy.

4. How does a reservoir's entropy change over time?

A reservoir is a system that is constantly exchanging energy and matter with its surroundings. As a result, the entropy of a reservoir will tend to increase over time, as more and more energy and matter become dispersed and distributed throughout the system.

5. Can the entropy of a reservoir ever decrease?

In a closed system, the total entropy remains constant, so the entropy of a reservoir cannot decrease. However, in an open system, where energy and matter can enter or leave the system, the entropy of a reservoir can decrease temporarily, but it will eventually increase again as the system reaches equilibrium.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
813
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
908
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
23
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top