Entropy chance with a carnot cycle?

In summary, in a Carnot cycle, the gas expands adiabatically from 200 degrees to 500 degrees with an efficiency of 38.8%. The entropy change of the gas during the expansion is 0, as the process is adiabatic and there is no heat transfer.
  • #1
coffeem
91
0
in a carnot cycle the gas expands adiabatically from 200 degrees to 500 degrees. what is the efficecy? and what is the entropy change of the gas during the expansion?

sorry - i got the efficiency to be: 38.8%

however I am unsure how to work out the entropy chance? any hints?
 
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  • #2
however my thinking is that if the the system is adiabatic... then the entropy will stay constant... then it will be 0? am i on the right lines? thanks
 
  • #3
Hi I am still struggling with this. any advice? thanks
 
  • #4
coffeem said:
however my thinking is that if the the system is adiabatic... then the entropy will stay constant... then it will be 0? am i on the right lines? thanks

If ΔS=dQ/T and dQ=0 for an adiabatic process then ΔS=0. So you are right.
 
  • #5


Entropy change in a Carnot cycle can be calculated using the formula: ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transfer, and T is the temperature at which the heat transfer occurs.

In this case, the gas expands adiabatically, meaning that there is no heat transfer (Q=0). Therefore, the entropy change can be calculated by considering the change in temperature (ΔT) during the expansion.

ΔS = Q/T = 0/ΔT = 0

Since the entropy change is 0, the second law of thermodynamics tells us that the entropy of the gas will remain constant during the adiabatic expansion. This means that the gas will have the same amount of disorder (entropy) before and after the expansion.

To calculate the efficiency of the Carnot cycle, we can use the formula: η = 1 - Tc/Th, where η is the efficiency, Tc is the temperature at the cold reservoir, and Th is the temperature at the hot reservoir.

In this case, Tc = 200 degrees and Th = 500 degrees.

η = 1 - Tc/Th = 1 - (200/500) = 1 - 0.4 = 0.6

Therefore, the efficiency of the Carnot cycle is 60%.

Overall, in a Carnot cycle, the entropy of the gas remains constant during the adiabatic expansion, and the efficiency can be calculated using the temperature at the cold and hot reservoirs.
 

What is entropy?

Entropy is a measure of the disorder or randomness of a system. In other words, it is a measure of the number of possible arrangements that a system can have.

How does entropy change in a Carnot cycle?

In a Carnot cycle, entropy remains constant in the isothermal processes (where heat is exchanged at a constant temperature) and increases in the adiabatic processes (where no heat is exchanged). This means that the total change in entropy over a full Carnot cycle is zero.

Why is entropy important in a Carnot cycle?

Entropy is important in a Carnot cycle because it is closely related to the efficiency of the cycle. The maximum efficiency of a heat engine (such as a carnot engine) is determined by the temperatures of the heat source and sink, and the change in entropy. A higher change in entropy results in a lower efficiency.

Can entropy decrease in a Carnot cycle?

No, entropy cannot decrease in a Carnot cycle. This is because the Carnot cycle is a reversible process, meaning that it can be run in reverse without any energy losses. In a reversible process, the change in entropy is always zero.

How is entropy related to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system (a system that does not exchange matter or energy with its surroundings) will always increase over time. In a Carnot cycle, the increase in entropy during the adiabatic processes follows this law.

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