# Homework Help: Plotting Carnot Engine Cycle on PV Diagram

1. Mar 26, 2017

### Sorelle

1. The problem statement, all variables and given/known data
I am tasked to create a PV Diagram of a Carnot Engine Cycle. I must find pressure, volume, Q, W, ΔU, and ΔS on all four points. This is what has been given to me by my teacher:

a to b : Isothermal
c to d: Isothermal

TC = 300 K
TH = 1700 K
pc = 1.01*105 Pa
vc = 0.01 m3
Qa to b = 300 K
γ (gamma) = 1.40

2. Relevant equations
(1) p1v1=p2v2
(2) W=nRT ln(V2/V1)
(3) p1v1γ=p2v2γ
(4) W= p1v1=p2v2 / (γ-1)
(5) T1V1(γ-1) = T2V2(γ-1)
(6) W = nRT ln(V2/V1)
(7) pv = nRT

3. The attempt at a solution
Using the above equations I managed to get point b's pressure and volume. What I got for point b:
vb = 0.028 m3
pb = 2.389*104 Pa
First, I used the gas law equation (7) to get moles. This came out to n = 0.405 moles. Then, I used equation (5) to get volume, solving for Vb(y-1). I then used equation (3) to get pressure, solving for pb. I then got W = -852.7 J for the path b to c using equation (4). This seems kind of odd to me and I'm not sure if its correct because it's doing more work than the amount of heat it is providing. I assume Qa to b = is QH ? It seems so low though.

I'm trying to figure out how am I going to get points d and a without knowing pressure or volume on those points. A class mate had suggested I used equation (5) for a to b and c to d, but those paths are isothermal. Isn't equation (5) adiabatic only? I don't know if I can even use the gas law because I'd need pressure or volume and I don't have that.

There is also the idea that I have to use equation (6) and solve for volume that way. The problem is I don't know where to start. I'm a little rusty on my calculus (it's been about 4 years). I tried to break it down to W = nRT(ln (V2) - ln (V1))= nRT( 1/V2 - 1/V1), but this doesn't seem to help and I may have done it wrong.

I'd be grateful for any kind of help.

2. Mar 31, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.