00:03
A rigid tank contains water, half of which is in a liquid form, and the other half is in vapor form, and this is by volume.
00:13
A valve at the top of the tank is now open.
00:17
Saturated vapor is slowly withdrawn, while the heat transfer keeps the temperature inside constant.
00:22
We want to find this heat transfer required to reach a state where half the original mass is withdrawn.
00:29
So we'll take our control volume as the entire vessel.
00:33
And we'll write firstly our continuity equation as follows.
00:46
So our continuity equation is m2, the final mass of the system minus m1, the initial mass, is equal to the mass that is evacuated minus me.
00:57
So that's the continuity equation, and we can also write down the energy equation for the process.
01:04
So the final internal energy of the system, m2, u2, minus the initial energy of this, of, of, of, of the energy of, of, of, of the system m1u1 must equal to this heat transfer, which is keeping the temperature constant, minus the internal energy or the energy of the evacuated vapor, m -e -h -e.
01:30
So let's look at our two states.
01:35
So state one has a mass of liquid one, which is the total volume of liquid, half the entire volume vessel 0 .375 over its specific volume, 0 .001251 from our tables.
01:57
And so we get the initial mass of liquid to be 299 .76 kg.
02:07
The initial mass of vapor, which makes up the other half of the volume, is 0 .375 over its specific volume, 0 .0 .0 .75 over its specific volume, 0 .0.
02:24
05013 and so this mass is 7 .48 kg.
02:33
Now the internal energy of state 1, m1u1 is equal to the internal energy contributions from the liquid and from the vapor...