Efficiency of a heat engine given a P-V diagram of its process

In summary, the efficiency of a heat engine is a measure of how well it converts heat energy into mechanical work. It can be determined by analyzing its P-V diagram and is affected by factors such as temperature difference, working fluid, and engine design. The efficiency cannot exceed 100% due to the laws of thermodynamics, but it can be improved by increasing the temperature difference, using more efficient fluids, and optimizing the design. Techniques such as regenerative heating and intercooling can also contribute to improving efficiency.
  • #1
XSummer32
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Homework Statement
Hello, I'm attempting a question and I'm not sure what I did wrong with my answer
This is the question:

A volume of ideal gas, Cv = 1.21R, undergoes a cyclic process, the triangle abc in the p-V diagram. It starts at point a (T = 300 K, P = 3 kPa, V = 1 L) and expands until the volume reaches 6.3 liter at point b. It then gives away heat to the environment at constant pressure until its volume decreases to point c (P = 1 kPa, V = 1 L). Finally, it absorbs heat at constant volume and gets back to point a. Find the efficiency (%) of this heat engine.

(hint: find the total net work (W) done, and identify the processes (ab and ca) in which the gas absorbs a total amount of heat Qh. The efficiency is then W/Qh.
Relevant Equations
Q - isothermal = nRT ln(v2/v1)
volume constant = nCv * Change in Temperature

Work done - Isothermal = -nRT ln (v2/v1)
Isobaric = -P * Change in volume

Efficiency = W/Qh
I post the working in the attached file
 

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  • #2
I can't read your handwriting; your post is unreadable. Just write out your last two equations using LaTex, and I'll see what you've come up with.
 

1. What is a heat engine?

A heat engine is a device that converts thermal energy into mechanical work. It operates by taking in heat from a high-temperature source, performing work, and releasing the remaining heat to a low-temperature sink.

2. How is efficiency of a heat engine defined?

The efficiency of a heat engine is defined as the ratio of the work output to the heat input. In other words, it is the percentage of the heat energy that is converted into useful work.

3. How is the efficiency of a heat engine calculated?

The efficiency of a heat engine can be calculated using the formula: efficiency = (work output/heat input) x 100%. The work output can be determined by the area enclosed by the process on a P-V diagram, while the heat input can be calculated by the area under the curve on the same diagram.

4. What factors affect the efficiency of a heat engine?

The efficiency of a heat engine is affected by several factors, including the temperature difference between the high-temperature source and low-temperature sink, the type of working fluid used, and the design of the engine. The Carnot efficiency, which is the maximum efficiency possible for a heat engine, is also influenced by the temperature difference.

5. How can the efficiency of a heat engine be improved?

The efficiency of a heat engine can be improved by increasing the temperature difference between the source and sink, using a more efficient working fluid, and optimizing the design of the engine. Additionally, reducing friction and heat losses can also improve the efficiency of a heat engine.

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