Thermodynamics closed cycle entropy cycle

In summary, the conversation discusses a closed cycle heat engine operating between two heater reservoirs. The figure shows a plot of temperature versus entropy for the engine's 3 reversible processes. The conversation goes on to discuss the calculation of heat absorbed and rejected by the engine, as well as the calculation of work performed in one cycle. The efficiency of the engine is also discussed and shown to be (T1-T2)/2T1. There is a question about a possible different equation for a system in contact with both reservoirs.
  • #1
Liquidxlax
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Homework Statement



The figure below shows a plot of temperature T versus entropy S for the closed cycle of a particular heat engine (not necessarily an ideal gas) which consists of 3 processes and which operates between two heater reservoirs, a hot reservoir with temperature T1 and a cold reservoir with temperature T2. Assume that each of the 3 processes is reversible.

A B

C

it's a triangle like that with T in the y direction and entropy in the x direction.

a) show that the heat Q1 absorbed by the engine in the process a to b and the heat Q2 rejected by the engine in process b to c are given by

Q1 = T1(S2 - S1) and Q2 = (S2 - S1)((T1+T2)/2)

b) calculate the work Wby performed by the engine in one complete cycle in terms of T1, T2, S1, and S2.

c) use the def of the efficiency eta = Wby/Q1 to show that

eta= (T1-T2)/2T1

Homework Equations





The Attempt at a Solution



ΔS = ∫dQ/T1 because from a to b it's constant temp

so pretty simple to get Q1

I'm not sure how Q2 arises especially that it is (T1+T2)/2

ΔS = ∫dQ/T = ∫cvndT/T but that wouldn't give me the right answer unless there is some algebra involved

any help will be appreciated thanks
 
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  • #2
Is ther a different equation for a system in contact with both reservoirs?
 
  • #3
can anyone give me an idea, I'm still having problems with the Q2 = (S2-S1)((T1+T2)/2)
 

What is a closed cycle in thermodynamics?

A closed cycle in thermodynamics refers to a system in which no mass is exchanged with the surroundings, but energy can be exchanged in the form of heat or work. This means that the initial and final states of the system are the same and there is no net change in the system's internal energy.

What is entropy in a closed cycle?

Entropy in a closed cycle is a measure of the disorder or randomness of a system. In a closed cycle, the total entropy remains constant, as the system returns to its initial state. This is because the change in entropy due to heat transfer into the system is equal to the change in entropy due to work done by the system, resulting in no net change in entropy.

How is entropy related to the efficiency of a closed cycle?

In a closed cycle, the efficiency is directly related to the change in entropy. The efficiency of a closed cycle is the ratio of the work done by the system to the heat input. As the entropy of the system increases, the efficiency decreases, as more energy is lost due to the increase in disorder.

What are some examples of closed cycle systems?

Some examples of closed cycle systems include the Carnot cycle, Stirling cycle, and the Rankine cycle. These systems are commonly used in heat engines, refrigeration systems, and power plants.

What are the applications of closed cycle thermodynamics?

Closed cycle thermodynamics has various applications in engineering, including power generation, refrigeration, and air conditioning. It also plays a crucial role in understanding the efficiency of heat engines and the second law of thermodynamics.

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