# Entropy of water and reservoir

#### Slepton

1. 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?

2. Homework Equations

$$\Delta$$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)

3. 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.

Related Introductory Physics Homework Help News on Phys.org

#### Andrew Mason

Science Advisor
Homework Helper
1. 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?

2. Homework Equations

$$\Delta$$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)

3. 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:

$$\Delta S = \Delta Q/T$$

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

#### FourierX

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

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