Irreversible isothermal Process Work External pressure not provided

[Aurelius120]

Homework Statement

An ideal gas is irreversibly isothermally expanded from $(8bar ,4L)$to$(2bar,16L)$to$(1bar,32L)$Find heat.

Relevant Equations

NA

It is clear that the process is isothermal else it is not possible to find heat absorbed.
$$W=-P_{ext}(\Delta V)$$

However $P_{ext}$ is not given. How do I proceed?
I tried taking $W=-(P_2V_2-P_1V_1+P_3V_3-P_2V_2)=\Delta(PV)$ but it is wrong for obvious reasons.

 

[Aurelius120]

The one solution I found uses
$W_1=-(2)(16-4)$ and $W_2=-(1)(32-16)$
$W=(W_1+W_2) bar.Litre=-4000J$
And $Q=4000J$

How external pressure becomes $2\ bar$ and $1\ bar$ is beyond me. It also seems wrong that $P_{ext}$ should change in an irreversible process? That is like the only thing that is good about irreversible calculations.

 

[Herman Trivilino]

Sketch a PV diagram of the process. Do you know what an isotherm looks like for an ideal gas?

 

[Aurelius120]

Sketch a PV diagram of the process. Do you know what an isotherm looks like for an ideal gas?

Something like this correct?

 

[Herman Trivilino]

Looks like you've found the way!

How external pressure becomes $2\ bar$ and $1\ bar$ is beyond me.

A slow compression expansion.

It also seems wrong that $P_{ext}$ should change in an irreversible process?

A dramatic example would be an explosion.