Atkins says "The work needed to change an adiabatic system from one specified state to another specified state is the same however the work is done." and then later it says if we do the same process but diathermically, then we will have to do MORE work than before and this is the definition of heat absorbed.

$q = w_{ad} -w$

But I don't understand what they mean, this seems backwards. Shouldn't it take less work?

Question

Atkins says "The work needed to change an adiabatic system from one specified state to another specified state is the same however the work is done." and then later it says if we do the same process but diathermically, then we will have to do MORE work than before and this is the definition of heat absorbed.

$q = w_{ad} -w$

But I don't understand what they mean, this seems backwards. Shouldn't it take less work?

anonymous · Answer

The reasoning I have is that we can compress a cylinder from $V_i$ to $V_f$ adiabatically and there's nowhere for the increase in temperature to flow so the pressure will be higher than if we had compressed it by the same amount diathermically since that extra heat created by compression can flow out, causing less resistance to the work being done.

Maybe I'm confusing the system with the surroundings though... I guess my mind doesn't see it clearly.

anonymous · Answer

Wait wait I think this equation makes perfect sense, 

$w_{ad} = w_{di}+q$

The diathermic work plus the heat is the same as the adiabatic work. Ok nevermind, the equation is correct but their reasoning just sort of seemed wrong to me. I think their example is describing heat being absorbed and then go on to use an example where there is a negative amount of heat absorbed... In other words heat is lost. Kind of ridiculous, but at least now I see why I was confused.