Heat Cycles, Work, and Efficiency

In summary, The correct equation to find work is the integral of PdV, done consistently with the diagram. The attempted solution using the first equation for work is incorrect and the correct answer should be in terms of P1 and V1. Using the area of the rectangle to find work results in an efficiency of 17%.
  • #1
Marcin H
306
6

Homework Statement


New Doc 13_1.jpg


Homework Equations


W=-∫PdV
ε=W/Q
PV=nRT
COP=Q/W


The Attempt at a Solution


Using the first equation for work, I got W=-nrT*ln(3V1/V1) but I don't think that is right. Is this the wrong formula to use for this problem? My answer should be in terms of P1 and V1.
 
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  • #2
That is not the correct integration of PdV for the process shown in the figure.
 
  • #3
Chestermiller said:
That is not the correct integration of PdV for the process shown in the figure.
What equation can I use to find the work then?
 
  • #4
Marcin H said:
What equation can I use to find the work then?
You can use the integral of PdV. Just do it in a way that is consistent with what you see in the diagram.
 
  • #5
Chestermiller said:
You can use the integral of PdV. Just do it in a way that is consistent with what you see in the diagram.
I just took the area of the rectangle. So W=2P1V1. I got an efficiency of 17% with that.
 

1. What is a heat cycle?

A heat cycle is a thermodynamic process in which heat is added to a system, causing it to undergo a series of changes in temperature, pressure, and volume, before returning to its initial state. It is often used in engines and power plants to convert heat energy into mechanical work.

2. How does a heat cycle work?

In a heat cycle, heat is added to a system at a high temperature, causing it to expand and do work. The system then releases heat at a lower temperature, causing it to contract and return to its original state. This cycle can be repeated to continuously convert heat energy into work.

3. What is thermal efficiency?

Thermal efficiency is a measure of how well a heat cycle converts heat energy into work. It is calculated by dividing the work output by the heat input. The higher the thermal efficiency, the more efficient the heat cycle is at converting heat into work.

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

The efficiency of a heat cycle can be improved by reducing energy losses, such as through minimizing heat loss to the surroundings or reducing friction in the system. Additionally, using more efficient materials and designs can also improve the efficiency of a heat cycle.

5. What are some examples of heat cycles?

Some common examples of heat cycles include the Carnot cycle, which is used in idealized heat engines, and the Rankine cycle, which is used in steam power plants. Other examples include the Otto cycle in gasoline engines, the Brayton cycle in gas turbines, and the Stirling cycle in Stirling engines.

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