This is an example in which we feed high pressure water to a throttle. Exiting the throttle
is at low pressure and the question is what is the exit temperature and what phase or
phases are present? If more than one phase like liquid and vapor then how much of each? So,
the solution to this problem is to apply the first law. It is a flow system. It is at steady
state which means any derivative with respect to time in the first law are zero. We will
assume it is adiabatic so that Q is 0. The residence time and the throttle are short
so there is not much time for heat transfer. There is no work being done. So the first
law simplifies to delta H is 0. This is assuming that kinetic energy is small. Namely the velocities
are not very high, so are insignificant relative to enthalpy. The system example is a tube
where we are feeding 5 MPa at 200 degrees C. If we look in the steam tables for water
this is liquid water. The exit is a 0.2 MPa and the question is what is the exit temperature.
So we have this pressure drop across the throttle. Let's call the inlet 1 and the outlet 2. The
first law reduces to H1 = H2. We can go to the steam tables for our inlet conditions
and find that the enthalpy is 853.7 and that has units of kJ/kg. That means that is also
the value for H2. Like wise if we go to the steam tables and look at the conditions at
0.2 Mpa enthalpy for a liquid if it were at saturation conditions 504.7 kJ/kg. Let's write
this for saturation. Enthalpy of the vapor is much higher than that so that delta H liquid
to vapor is 2201.53 kJ/kg. Since we are at 0.2 MPa and we have more enthalpy in saturation
liquid but less than the vapor namely H2 is greater than H of the liquid at saturation
conditions but it is less than H of the vapor at saturation conditions. That means that
we have 2 phases and we have steam with some quality. This also means that the temperature
must be the saturation temperature. The saturation temperature from the steam tables is 120.2
degrees Centigrade. H2 which is 853.7 must equal H for the liquid plus x times delta
H liquid to vapor. In other words we have liquid and we have some fraction that is vapor.
"x" is quality. You can look up these two values from the steam table so 853.7 equals
504.7, that's the enthalpy of the liquid, and then the enthalpy change such that if we now
solve this for "x" 0.1585. So "x" is about 0.16. That means that the effluent from the
throttle is 16% vapor and 84% liquid.