Find the volume and temperature after the isobaric expansion

[Benny]

Hello Physics Forums users, I am stuck on a question. Can someone please help me out?

Q. In a non-Carnot engine, a volume of 100 cm^3 of air, initially at 0 degrees celsius and 1 atm pressure, is compressed isothermally until its volume is 10 cm^3.

The gas is then expanded at constant pressure until its volume and temperature are such that an adiabatic expansion will return the gas to its final state.

The ratio of the molar specific heats of air is $$\gamma = 1.40$$.


Find the volume and temperature after the isobaric expansion.

I really don't know what to do. I'm pretty sure that the question is related to P-V(pressure-volume) diagrams. So I considered the changes in parts.

1. Using PV= nRT for the gas at the start(point 1) and then just after the compression(point 2) and dividing the resulting equations (whilst noting that temperature is constant), I get $$P_1 V_1 = P_2 V_2$$.

Solving for $$P_2$$ I get the pressure of the gas just after the compression to 10 cm^3 as 10 atm.

I can't get much further than this. I find these questions to be slightly easier if I have a P-V diagram to work with but for this question I don't have one. The main problem I have is probably to do with the second paragraph of the question "The gas is then expanded at constant pressure..." I don't really understand how I can use the information in that paragraph.

Answer: 19.3 cm^3 for volume.

Any help would be good, thanks.

 

[Yegor]

The main problem I have is probably to do with the second paragraph of the question "The gas is then expanded at constant pressure..." I don't really understand how I can use the information in that paragraph.

You were good when

1. Using PV= nRT for the gas at the start(point 1) and then just after the compression(point 2) and dividing the resulting equations (whilst noting that temperature is constant), I get .

Try making the same procedure for isobaric process. You'll obtain also any equation. Then add equation of adiabatic process.
And it's very useful to learn drawing P-V diagramms. It's not too difficult.

 

[Benny]

Ok, thanks for the help Yegor.