# Homework Help: Pressure Volume graph finding total mole of gas

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1. Nov 5, 2014

### cycrups

1. The problem statement, all variables and given/known data
An ideal monoatomic gas undergoes the following cycle:
from 1.) V1 = 1m3, p1=2.5kPa, T1=200k to 2) V2=1m3, p2=7.5kPa then to 3)V3=3m3, p3=2.5kPA, and 4) back to 1).

a. Sketch
b. How many mole of gas are in the process?
c. Give the missing temperatures at positions 2. and 3.
d. Find the efficiency of this cycle
e. Compare this efficiency with that of a Carnot cycle between the highest
and lowest temperatures reached in the above cycle.

The transition from 2 → 3 is a linear decrease of the pressure as a function of the
volume

2. Relevant equations

PV=nRT

3. The attempt at a solution

I drew the graph

http://imgur.com/7tSPE0k

for the first 1 I used n = PV/RT and got 1.5... moles. Now for the second one how should I do it when I have two unknowns. Knowing that from point 1) V1 = 1 and p1 = 2.5 to point 2) pressure changed and there is a linear line going down in the graph the Temperature is not the same in point one. Having two unknowns how to find number of moles in the second part?

Last edited: Nov 5, 2014
2. Nov 5, 2014

### BvU

I think the idea is that the number of moles stays the same....so there is only one unknown

I do miss a question in you problem statement, though... What are you supposed to find from this cycle ?

3. Nov 5, 2014

### cycrups

Ah Sorry I didn't write the whole question.
b. How many mole of gas are in the process?
c. Give the missing temperatures at positions 2. and 3.
d. Find the efficiency of this cycle
e. Compare this efficiency with that of a Carnot cycle between the highest
and lowest temperatures reached in the above cycle.

4. Nov 5, 2014

### BvU

So, finding the temperature at point 2 is no longer a problem ?

5. Nov 10, 2014

### cycrups

Yes it a no problem. I got them thanks! just the last quesiton I don't know how to solve it

6. Nov 10, 2014

### BvU

Well, I've seen the sketch, seen the 1.5 moles, so a) and b) are in the pocket.
I can kind of guess T2 but have no idea about T3 :)
So I wonder what came out of c) and d) ;)

For the Carnot cycle there is a clear efficiency expression, see e.g. here

7. Nov 11, 2014

### cycrups

I got both for T2 and T3 same temperatures.

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