Show that the change in entroy is

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In summary: W = Q_{in} - Q_{out} and \Delta S = S_{f} - S_{i}. However, the most relevant equations for this scenario are dS_h = -dQ_h/T_h and dS_c = +dQ_c/T_c, which show the change in entropy for the hot register and cold register, respectively. The total change in entropy for the system is calculated as dS_{total} = dS_h + dS_c = dQ_c/T_c-dQ_h/T_h. This demonstrates that the change in entropy for a cycle of a heat engine is determined by the heat transfer and
  • #1
endeavor
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Show that the change in entropy for a cycle of a heat engine is
[tex]\Delta S = \frac{Q_{cold}}{T_{cold}} - \frac{Q_{hot}}{T_{hot}}[/tex]
 
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Please show some working or thoughts...
 
  • #3
Well, I was thinking about
[tex]W = Q_{in} - Q_{out} = Q_{hot} - Q_{cold}[/tex]
or that
[tex]\Delta S = S_{f} - S_{i}[/tex]
But I'm not sure where to go from here...
 
  • #4
endeavor said:
Well, I was thinking about
[tex]W = Q_{in} - Q_{out} = Q_{hot} - Q_{cold}[/tex]
or that
[tex]\Delta S = S_{f} - S_{i}[/tex]
But I'm not sure where to go from here...
You are to assume an isothermal heat transfer from the hot register to the gas and an isothermal flow from the gas to the cold register.

The change in entropy for the hot register in the transfer from the hot register to the gas is:

[tex]dS_h = -dQ_h/T_h[/tex]

Similarly, the change in entropy of the cold register in extracting the heat from the gas to the cold register results in a change of entropy to the cold register of:

[tex]dS_c = +dQ_c/T_c[/tex]

The total change in entropy of the system (hot register + cold register) is:

dS_{total} = dS_h + dS_c = dQ_c/T_c-dQ_h/T_h[/tex]

AM
 

1. What is entropy and why is it important in science?

Entropy is a measure of the disorder or randomness in a system. It is important in science because it helps us understand how energy and matter are distributed and transformed in a system, and how natural processes tend towards increasing disorder over time.

2. How is the change in entropy calculated?

The change in entropy, denoted as ΔS, is calculated using the equation ΔS = Q/T, where Q is the energy transferred and T is the temperature in Kelvin. This equation is based on the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time.

3. Can entropy be negative?

Yes, entropy can be negative. This means that the system is becoming more ordered or structured. However, in a closed system, the overall change in entropy will always be positive.

4. How does entropy relate to the concept of equilibrium?

Entropy is closely related to the concept of equilibrium, which is the state where there is no net transfer of energy or matter between different parts of a system. At equilibrium, the entropy is at its maximum, and any changes in the system will result in a decrease in entropy.

5. What are some real-world examples of the change in entropy?

Examples of the change in entropy can be seen in processes such as melting ice, where the solid state with low entropy is transformed into liquid with higher entropy. Other examples include chemical reactions, weather patterns, and the formation of stars and galaxies in the universe.

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