# PV Diagram Problem (ideal efficiency vs actual efficiency)

#### stonecoldgen

1. 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

2. Homework Equations
1atm=101,300Pa
PV=nRT
1-TL/TH=$\epsilon$
$\epsilon$actual=Wout/Qin

3. 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=$\epsilon$ 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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#### stonecoldgen

is there anyone there?

#### Andrew Mason

Homework Helper
Find the ideal and the actual efficiency of the cycle

2. Homework Equations
1atm=101,300Pa
PV=nRT
1-TL/TH=$\epsilon$
$\epsilon$actual=Wout/Qin

3. 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=$\epsilon$ 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

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