Homework Question 8.47

[Lily Guo 1D]

For 8.47, why does the solutions manual use the equation (delta)H = U + P(delta)V instead of just U = q+ w? I'm also confused as to why work would be positive instead of negative because I thought that expansion work done ON a system is negative.

[Felicia Fong 2G]

I think expansion work done on a system is positive. Work done by the system would be negative.

[Sarah_Stay_1D]

For 8.47, why does the solutions manual use the equation (delta)H = U + P(delta)V instead of just U = q+ w? I'm also confused as to why work would be positive instead of negative because I thought that expansion work done ON a system is negative.

You are in a sense actually using ΔU= q + w. First you can rearrange the equation ΔH = ΔU + PΔV to be ΔU = ΔH - PΔV. Sense we know that at a constant pressure ΔH=q, we can substitute q for ΔH. We also know that w = -PΔV , so we can substitute w for -PΔV. So, know you have the familiar equation ΔU = q + w. Then you just substitute the values given in the problem.

[Angela 1K]

But that ultimately give you a negative work, whereas work done ON a system should be positive???

[Lily Guo 1D]

But that ultimately give you a negative work, whereas work done ON a system should be positive???

I just realized my mistake. Work done ON a system is positive, but EXPANSION work means that work is done on the surroundings/BY the system because the system is expanding. Therefore, work would be negative. That's my bad for not catching that, sorry!