What is the minimum pressure in an evacuated tank half-filled with 40°C water?

[giacomh]

Homework Statement

A tank half-filled with 40°C water is to be evacuated. What is the minimum pressure that can be expected in the space above the water?

Homework Equations

Vp water @ 40 degrees = 3.38

The Attempt at a Solution

I would have just subtracted the vapor pressure from the atmospheric pressure, but no temperature is given in this problem. I don't know how to take into account the fact that it's a half-empty tank.

Thanks!

 

[CWatters]

Been a long time since I did this so perhaps wait for a better answer. Meanwhile ..

http://www.engineeringtoolbox.com/humid-air-ideal-gas-d_677.html

the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases

So perhaps apply the Ideal Gas law PV=nKT assuming constant temperature to the dry air. (eg volume doubles so pressure halves).

Not sure what to do about the water vapour? Do you need to subtract the vapour pressure before halving as above?

But what if some water vapour remains? Perhaps you need add it back again or calculate the reduced vapour pressure to add back?

What do they mean by "evacuated"? Just the liquid water drained or the air and water vapour removed as well? Not sure there is enough info to answer the problem?

 

[Chestermiller]

If you evacuate all the gas from above the water, enough water will evaporate into the head space such that the pressure will equilibrate to the equilibrium vapor pressure of water at 40 degrees. It only takes a very small amount of evaporation to do this. The gas in the head space will be pure water vapor.