# Thermodynamics - Cycle efficiency

• Jalo
In summary, the efficiency of the given cycle can be calculated using the formula: η = 1 - Qc / Qh = 1 - Qc / T2(S2-S1), where Qc is the heat leaving the system and Qh is the heat entering the system. The area enclosed by the cycle on a T vs S graph can help determine the efficiency. It is important to note that the efficiency should not be calculated using the Carnot efficiency equation, but rather a more fundamental and simpler equation: efficiency = (W/Qh) = (work output from the engine / heat input to the engine).
Jalo

## Homework Statement

Compute the efficiency of the following cycle:

## The Attempt at a Solution

I know there's an isothermic process between a and b, where heat comes into the system, let's call it Qh.
I also know that between b and c heat will leave the system, let's call it Qc.
The process from c to a is adiabatic.

The efficiency, n, is equal to:

η = 1- Qc / Qh = 1 - Qc / T2(S2-S1)

The problem is that I don't know how to compute Qc...
Any help would be highly appreciated.
Also, if anyone has a good book on the subject I'd appreciate.

Thanks.

The area enclosed by a cycle on a T vs S graph has a physical interpretation that will help to determine the efficiency.

Don't use Carnot efficiency equation for the cycle; but use a more fundamental and simpler equation: efficiency = (W/Qh) = (work output from the engine / heat input to the engine). The numerator is obtained from the area of the triangle. You already know how to calculate (the denominator) the heat input to the engine (T2*delta S). The ratio of the two numbers gives the efficiency.

Caution: Cycles involving sloping straight line paths can sometimes be dangerous! For eg the efficiency calculation of similar cyclic triangular paths on PV plane (instead of TS plane) is a very complicated and controversial issue.

## 1. How is cycle efficiency defined in thermodynamics?

Cycle efficiency is the ratio of the work output of a thermodynamic cycle to the heat input. It is a measure of how well a system converts heat energy into mechanical work.

## 2. What factors affect the cycle efficiency of a system?

Cycle efficiency is affected by several factors such as the temperature difference between the hot and cold reservoirs, the type of cycle used (Carnot, Rankine, etc.), and the properties of the working fluid.

## 3. What is the maximum possible cycle efficiency for a given temperature difference?

The maximum possible cycle efficiency for a given temperature difference is determined by the Carnot efficiency, which is given by the ratio of the temperature difference to the maximum temperature in the cycle. It is a theoretical limit and is not achievable in real-world systems.

## 4. How can the cycle efficiency of a system be improved?

The cycle efficiency of a system can be improved by using better insulation to reduce heat loss, using more efficient heat exchangers, and using a more efficient working fluid. Increasing the temperature difference between the hot and cold reservoirs can also improve cycle efficiency.

## 5. Can cycle efficiency be greater than 100%?

No, cycle efficiency cannot be greater than 100%. This is because the maximum possible efficiency is limited by the Carnot efficiency, which is always less than 100%.

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