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.

 

[Mister T]

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?

 

[Mister T]

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.