Entropy of a Refrigerator: Is It Constant?

In summary, the conversation discusses a question about a recent AP free response problem involving a simple refrigerator. The question is about whether the removal of heat from the gas will decrease its entropy, and the answer key states that because the gas returns to the same state, the entropy is the same. The conversation goes on to explain that in thermodynamics, heat is treated as a fluid flowing through a substance, and in one cycle, the internal energy of the gas remains the same. Therefore, even though heat is removed from the gas, its energy is not decreased and the entropy of the gas remains constant. This is because entropy is a state variable and the overall entropy of the system continually increases.
  • #1
turdferguson
312
0

Homework Statement


Ive got a question regarding a recent AP free response, http://www.collegeboard.com/prod_downloads/ap/students/physics/b_physics_b_frq_03.pdf
Problem 5 is about a simple refrigerator, work is applied and heat is removed keeping temperature constant.

My question is on part (e). I think heat being removed from the gas would cause entropy to decrease. However, the answer key states that because the gas returns to the same state, entropy is the same. Who is right and if it is constant, why?

Homework Equations


change in entropy = Q/T


The Attempt at a Solution


Less heat, less entropy
 
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  • #2
turdferguson said:

Homework Statement


Ive got a question regarding a recent AP free response, http://www.collegeboard.com/prod_downloads/ap/students/physics/b_physics_b_frq_03.pdf
Problem 5 is about a simple refrigerator, work is applied and heat is removed keeping temperature constant.

My question is on part (e). I think heat being removed from the gas would cause entropy to decrease. However, the answer key states that because the gas returns to the same state, entropy is the same. Who is right and if it is constant, why?

Homework Equations


change in entropy = Q/T

The Attempt at a Solution


Less heat, less entropy
This is one of the conceptual problems that occurs because we talk about heat and not heat flow. We now think of heat as energy but in thermodynamics we use terminology from the mid 1800s as if it were a fluid flowing through a substance. In thermodynamics, Q is heat flow.

In one cycle, heat is added to the gas (AB) then work is done on the gas (BC) and then heat is removed from the gas (CA). The internal energy of the gas is the same when it returns to A. The energy that is removed as heat from C to A consists of the heat added from A to B + the work done in compressing from B to C. Qh = Qc + W, where Qh is the heat delivered to the hot reservoir. Since Qh > Qc, there is heat removed (better to say: a greater flow of heat out of the gas than the heat flow into the gas). However this does not mean that there is energy removed. The energy at A is the same.

Since entropy is a state variable, the entropy of the gas is the same from A back to A. The entropy of the system (consisting of the gas + the hot and cold reservoirs) continually increases, however.

AM
 
  • #3
.

I can provide a response to this question by explaining the concept of entropy and its relationship to refrigerators.

Entropy is a measure of the disorder or randomness in a system. In a refrigerator, the system is the gas inside the refrigerator. When work is applied to the gas, it compresses and its temperature increases. This increases the energy of the gas molecules and therefore increases the randomness of their motion, resulting in an increase in entropy.

However, when heat is removed from the gas, it decreases the energy of the gas molecules and decreases their randomness, resulting in a decrease in entropy. So, in this case, your intuition is correct in that removing heat from the gas would cause the entropy to decrease.

But, it is important to note that the refrigerator is a closed system, meaning that no matter or energy can enter or leave the system. When the gas returns to its original state, it means that the amount of heat removed is equal to the amount of work done on the gas. This is because energy cannot be created or destroyed, only transferred from one form to another.

Therefore, the change in entropy for the gas would be zero, as the heat and work cancel each other out. In other words, the overall disorder or randomness in the system remains constant.

So, both you and the answer key are correct in a way. The entropy of the gas does decrease when heat is removed, but it returns to its original value when the gas returns to its initial state. This is because the system is closed and there is no net change in energy or disorder.

In summary, the entropy of a refrigerator is not constant, but it can return to its initial value if the system is closed and the heat removed is equal to the work done on the gas.
 

1. What is entropy and how does it relate to a refrigerator?

Entropy is a measure of the disorder or randomness in a system. In the context of a refrigerator, it refers to the level of disorder or randomness of the particles and energy inside the refrigerator. As the particles inside the refrigerator interact and exchange energy, their level of disorder increases, leading to an increase in entropy.

2. Is the entropy of a refrigerator constant?

No, the entropy of a refrigerator is not constant. It changes as the particles and energy inside the refrigerator interact and exchange energy. As the refrigerator operates, its internal system becomes more disordered, causing an increase in entropy.

3. How does the second law of thermodynamics relate to the entropy of a refrigerator?

The second law of thermodynamics states that the total entropy of a closed system always increases over time. This law applies to a refrigerator as well, as the internal system of the refrigerator becomes more disordered over time, leading to an increase in entropy.

4. Can the entropy of a refrigerator be reduced?

Technically, yes, the entropy of a refrigerator can be reduced. However, it would require an external source of energy to be applied, such as cleaning or maintenance, to decrease the disorder of the particles and energy inside the refrigerator. Without an external input of energy, the entropy of a refrigerator will continue to increase.

5. How does the efficiency of a refrigerator relate to its entropy?

The efficiency of a refrigerator is inversely proportional to its entropy. This means that as the entropy of a refrigerator increases, its efficiency decreases. This is because a higher level of disorder inside the refrigerator requires more energy to maintain a lower temperature, resulting in a less efficient operation.

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