# Energy Analysis of Control Volumes at Steady State

## Homework Statement

Steam enters a well insulated nozzle at...

Pressure1 =300lbf/in^2
Temp1 =600 degrees F
Velocity1 =100 ft/s

The steam exits the nozzle at...

Pressure2 =40lbf/in^2
Temp2 =?????
Velocity2 =1800ft/s

For steady-state operation, and neglecting potential energy effects, determine the exit temperature in F

## Homework Equations

Energy rate balance
Mass rate

## The Attempt at a Solution

I began by stating that heat transfer is zero since the nozzle is well insulated. Then I stated that work is also zero since the steam is traveling through a nozzle and not some kind of paddle wheel or device as such. Next I stated that PE was zero since this was a given.

Then, I set up my conservation of energy for a control volume equation.

0 = (mass rate)[(h1-h2)+(1/2)(vel(1)^2-vel(2)^2)]

The next thing I did was to consult my tables. Due to having two quantities I could use at the entrance of the nozzle I found that h1 was 1314.5 Btu/lb as was stated in the properties of superheated water vapor table.

So now I have,

0 = (mass rate)[(1314.5-h2)+(1/2)((100)^2-(1800)^2)]

My two unknowns are the mass rate and h2. Now if I could somehow solve for the mass rate I could determine h2 and then use my tables and linear interpolation to solve for the temp at exit, but I can't figure out how to solve for the mass rate without having an area of the nozzle or knowing the density of steam in these given conditions. This leads me to think that I may be I'm using the wrong equation and don't need to find the mass rate after all?

So my question is, how would I solve for mass rate or am I using the right equation?

Thanks.

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