Entropy change in an isolated system

In summary: ENDING:In summary, when a solid with constant heat capacity and initial temperature To is brought into contact with a hotter reservoir temperature T1 and allowed to reach equilibrium in an isolated system, the change in entropy of the universe will be greater than 0. This is because the total change in entropy is the sum of the change in entropy of the reservoir and the solid, and the change in entropy of the solid is always greater in magnitude due to the temperature difference. The change in entropy can be calculated using the equations dS = dQ/To for the solid and dS = -dQ/T1 for the reservoir. This shows that the total change in entropy is dependent on the initial and final temperatures of both the solid and the reservoir
  • #1
indie452
124
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hi I am having a few conception problems with entropy

problem:
a solid with constant heat capacity and initial temp To, is brought in contact with hotter reservoir temp T1 and allowed to come into equilibrium. This is all isolated.

a) is the change in the entropy of the universe negative zero or positive thanks to the systems process. explain why
b) calculate entropy change to solid
c) calculate entropy change to reservoir

a) i would have thought that the entropy change of the universe is zero because entropy change is dQ/T and the change in Q for both systems is the same (for the solid its +ve and reservoir -ve)

b) dS = dQ/To
c) dS = -dQ/T1

is this right?
 
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  • #2
indie452 said:
hi I am having a few conception problems with entropy

problem:
a solid with constant heat capacity and initial temp To, is brought in contact with hotter reservoir temp T1 and allowed to come into equilibrium. This is all isolated.

a) is the change in the entropy of the universe negative zero or positive thanks to the systems process. explain why
b) calculate entropy change to solid
c) calculate entropy change to reservoir

a) i would have thought that the entropy change of the universe is zero because entropy change is dQ/T and the change in Q for both systems is the same (for the solid its +ve and reservoir -ve)
The heat flow out of the reservoir is at the higher reservoir temperature.

The total heat flow out of the reservoir (negative) has to be equal in magnitude to the (positive) heat flow into the solid. But since the temperature of the solid is always less than that of the reservoir, the change in entropy of the reservoir (dS = dQ/T), which is negative, will have a smaller magnitude than the positive change in entropy of the solid. So the total change in entropy will be greater than 0.

b) dS = dQ/To
c) dS = -dQ/T1

is this right?
That is the initial differential change in entropy. The total change is:

[tex]\Delta S = \Delta S_{res} + \Delta S_{sol}[/tex]

where:

(1) [tex]\Delta S_{res} = \int_{T_{ir}}^{T_{fr}} m_{res}C_{res}\frac{dT}{T} = m_{res}C_{res}\ln{\frac{T_{fr}}{T_{ir}}[/tex]

and

(2) [tex]\Delta S_{sol} = \int_{T_{is}}^{T_{fs}} m_{sol}C_{sol}\frac{dT}{T} = m_{sol}C_{sol}\ln{\frac{T_{fs}}{T_{is}}[/tex]AM
 

1. What is entropy change in an isolated system?

Entropy change in an isolated system refers to the overall change in the measure of randomness or disorder of a system that is not influenced by any external factors or energy.

2. How is entropy change different from energy change?

While energy change refers to the transfer of energy from one form to another, entropy change is a measure of the overall disorder of a system regardless of the type of energy present.

3. What causes entropy change in an isolated system?

Entropy change is caused by the spontaneous movement of particles within a system, leading to a more disordered state.

4. How is entropy change related to the Second Law of Thermodynamics?

The Second Law of Thermodynamics states that the total entropy of an isolated system will always tend to increase over time. This means that in an isolated system, entropy change will always result in a more disordered state.

5. Can entropy change be reversed in an isolated system?

No, entropy change in an isolated system is irreversible. This is due to the fact that energy cannot be created or destroyed, and the spontaneous movement of particles will always result in an increase in entropy over time.

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