The rate of thermal energy transfer

[Marshiewoo]

Task:

A steady flow boiler takes in feed water at 1.5kg/s, at a temperature of 30 °C. The water is heated and turned into wet steam. This leaves at 1.5kg/s, with a pressure of 10 bar and a dryness fraction of 0.97 to the superheater, where it receives heat at a constant pressure and emerges at a temperature of 400 °C.

Determine, using steam tables:
A. the rate of thermal energy transfer in the boilet
B. the rate of thermal energy transfer in the superheater

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I have managed to find out the efficiency of the turbine, which is after the superheater.

I am not really looking for an answer, although that would be fantastic. I would mainly like somebody to explain the difference between what I have worked out (below) and what the question above is asking.


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My attempt at a different task which is slightly related:

Steam enters the turbine below from the superheater at a pressure of 20 bar and temperature 300 °C and exhaustss at a pressure of 1 bar and dryness fraction 0.95. The steam consumption rate is 1.8 tonnes per hour and the shaft output power is 0.2 MW.

Determine the turbine efficiency.



$\hat{m}$ = 0.5 kg/s
$T\omega$ = 0.2$x10^6$
Temperature in = 300 °C
Pressure in = 20 bar
Pressure out = 1 bar
Dryness fraction out = 0.95


h1)
h1 = $hg$ @ 20 bar & 300 °C
= 3025000

h2)
h2 = $hf + xhfg$ @ 1 bar
= 417 + (0.95)(2258)
= 2563000

h1 - h2 = 463000

Turbine Efficiency)
Turbine Efficiency = $\frac{T\omega}{(h1-h2)\hat{m}}$
= $\frac{0.2x10^6}{(463000)(0.5}$
= 0.86393
= 86.4%

Thank you and my apologies for the terrible use of the fantastic itex system.

 

[SteamKing]

The water didn't turn itself into steam before it reached the turbine.
A boiler was used to first heat the feed water and turn it into slightly wet saturated steam. What was the rate of thermal energy transfer required to do this?
Second, the saturated steam was then superheated. What was the rate of thermal energy transfer required for this step? Use steam tables to answer both questions.

I don't know how the question could be any more clear than as stated.

 

[Marshiewoo]

So I just use the steam tables? :s

Thanks for the reply.

 

[Marshiewoo]

The whole thermodynamics confuses me, sorry.

 

[Daniel Wilson]

I've been digging into thermodynmics in preparation for teaching a new course. I came across this thread in my quest. I'd like to try and round things off with what I hope is a correct procedure (I know this is far too late for the OP but hopefully it'll help out anyone with the same question).

(1) ∆Ḣ = ṁ (h_o - h_i)
I am using ∆Ḣto represent the rate of thermal energy transfer.
For saturated water: h = h_f
(2) For wet steam: h = h_f + x h_fg
Where x is the dryness fraction and h is the specific enthalpy

Determine specific enthalpy values at inlet and outlet from steam tables. For part A, inlet value, look at the steam table sorted by temperature, look up h_f for 30ºC. For part A, outlet values, look at steam table sorted by pressure. Look up h_f and h_fg for 10 bar. Calculate the value of h using equation (2) above.
Calculate value of ∆Ḣusing equation (1) above.
I hope that procedure makes sense.

For part B. The boiler outlet value is equal to the superheater inlet value. So just need to look up the outlet value using the super heated steam tables (for pressure of 10 bar and temperature of 400ºC). Solve using equation (1).

 

[Chestermiller]

Sure, looks good.