# Finding Minimum Work to Compress Water

## Homework Statement

Find the minimum work to compress 1 kg of water isothermally from p1=1 bar, T1=120C to a volume that is 1/3 the original volume.

## Homework Equations

Energy balance Q-W=U+KE+PE

## The Attempt at a Solution

So first I found the phase of the water (p<psat for that temp so superheated vapor)
I found the properties (v,u,h,s) for that temperature and pressure in the superheated table.
I can use the specific volume at 1 to find the specific volume at 2 because mass stays constant (closed system) and it's just 1/3 v1. I used that specific volume to determine the state at 2 (in between vf and vg so it's in the saturated liquid vapor phase). I found the quality using tables so I can calculate u, h, s.

I'm mostly confused about the energy balance: I'm pretty sure I can neglect KE and PE. Is there a Q value though? When I went over this problem with the professor he hinted at using TdS equations (Gibbs?) for finding the heat. The Tds equation that I know is Tds=du+Pdv (which is similar to the energy balance since Pdv is the work and du is the the change in internal energy). Do I do W=du+Tds?

Or maybe it is okay to just assume no heat transfer and do W=U and then do m(u2-u1). I'm mostly confused about when you can assume things when doing energy balance.

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