PV Diagram Problem (ideal efficiency vs actual efficiency)

In summary: J is asking for the ideal and actual efficiency of a cycle for 4.87moels of an ideal gas. The cycle is shown on a PV diagram and the path ab is along an isothermal line. Pressure is in atm and volume in m3. To find the ideal efficiency, the temperature at points a and b (1,200K) and point c (400K) are used with the equation 1-TL/TH=\epsilon to get 67%. However, to find the actual efficiency, the heat flow in and out of the gas must be calculated. This can be found by determining which parts of the cycle involve heat flow in and out, and using the first law of thermodynamics. The relationship between heat flow
  • #1
stonecoldgen
109
0

Homework Statement


The PV diagram below (I will describe it) shows a cycle for 4.87moels of an ideal gas. The path ab is along an isothermal line.

Pressure is in atm and volume in m3


Point a: (.08, 6)
Point b: (.24,2)
Point c: (.08, 2)


Find the ideal and the actual efficiency of the cycle

Homework Equations


1atm=101,300Pa
PV=nRT
1-TL/TH=[itex]\epsilon[/itex]
[itex]\epsilon[/itex]actual=Wout/Qin




The Attempt at a Solution


First of all, convert the pressures in atm to Pascals, to make life easier.


The temperature at a and b is 1,200K, the temperature at c is 400K. (found with PV=nRT)

so i thought that plugging that into 1/TL/TH=[itex]\epsilon[/itex] would give me the ideal efficiency. I got 67%


However, I don't know how to get the actual efficiency. I don't know what Qin and Wout are exactly
 
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  • #2
is there anyone there?
 
  • #3
stonecoldgen said:
Find the ideal and the actual efficiency of the cycle

Homework Equations


1atm=101,300Pa
PV=nRT
1-TL/TH=[itex]\epsilon[/itex]
[itex]\epsilon[/itex]actual=Wout/Qin

The Attempt at a Solution


First of all, convert the pressures in atm to Pascals, to make life easier.

The temperature at a and b is 1,200K, the temperature at c is 400K. (found with PV=nRT)

so i thought that plugging that into 1/TL/TH=[itex]\epsilon[/itex] would give me the ideal efficiency. I got 67%
I will assume that this is an engine cycle so it goes from c to b to a back to c.

Efficiency is η = W/Qh = Qh-Qc/Qh

You cannot use η = 1 - Tc/Th because this is not a Carnot cycle.

So you have to determine Qh and either Qc or W.

Let's try to calculate heat flow in and out. We start by finding which parts of the cycle involve heat flow in and out.

Does heat flow into the gas during ba? How about ac? cb? Hint: Apply the first law.

When does heat flow OUT of the gas? (hint: again apply the first law).

Next, we have to calculate the heat flow IN and the heat flow OUT. To do this we have to know the relationship between heat flow and work or change in internal energy. Cv and Cp and ΔT are used to determine the heat flow in constant volume and constant pressure processes. For the isothermal part, does the internal energy change? So what is the relationship between heat flow and work in this part?

Finally, when you determine the Qh and Qc apply the efficiency formula to determine efficiency, η.AM
 

1. What is a PV diagram and how is it used in analyzing efficiency?

A PV (pressure-volume) diagram is a graphical representation of the thermodynamic processes that occur in a system. It plots the pressure on the y-axis and volume on the x-axis. In analyzing efficiency, PV diagrams are used to compare the ideal efficiency of a system (based on theoretical calculations) to the actual efficiency (based on real-world measurements).

2. What is the difference between ideal efficiency and actual efficiency?

Ideal efficiency refers to the maximum efficiency that a system can achieve based on theoretical calculations. It assumes that there are no energy losses or inefficiencies in the system. Actual efficiency, on the other hand, takes into account real-world conditions and factors in energy losses and inefficiencies that may occur in a system.

3. How is the ideal efficiency calculated for a PV diagram problem?

The ideal efficiency for a PV diagram problem can be calculated using the formula: efficiency = (work output/work input) x 100%. Work output is the area under the curve on the PV diagram, while work input is the area under the isothermal (constant temperature) line on the diagram.

4. What factors can affect the actual efficiency of a system in a PV diagram problem?

Several factors can affect the actual efficiency of a system in a PV diagram problem, including friction, heat losses, and mechanical losses. These factors can cause energy to be lost and reduce the overall efficiency of the system.

5. How can the actual efficiency of a system be improved in a PV diagram problem?

To improve the actual efficiency of a system in a PV diagram problem, measures can be taken to minimize energy losses and inefficiencies. This can include using lubricants to reduce friction, insulating the system to prevent heat losses, and using more efficient components or designs to reduce mechanical losses.

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