Calculation of heat created during compression

[Gosia]

Homework Statement

Hello, I have a task to make a heat balance of the evaporator. To do this, I was told to carry a few smaller energy balances in different parts of the evaporator. One of the things I had to calculate was the heat generated during steam compression.

-steam is entering 12818,18 kg/h the fan at temp 60 C at pressure 200 mbar (saturated conditions)
-steam durninng compression is being heated to 100 C, we want to achive 250mbar
-after that steam is being cooled by sprayed water at 65 C

I have to calculate the work of the pump and the heat that is being generated.

Homework Equations

dU=Q-W

The Attempt at a Solution

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I was trying to approach it as it is isotropic compression going from 200mbar 60C to 250C 65
by simply divieding enthalpies from steam tables and omiting whole aspect of tempreture increse. But my supervisor said that this is actually hapaning in plants, that durning compression this much amount of heat is produced due to friction and comression and it must be calculated in the project. I coudnt find any similar exercises or exampels.Is this data sufficient? I feel like I am missing something. Please help!

 

[BvU]

Hello Gosia,

I was trying to approach it as it is isotropic compression going from 200mbar 60C to 250C 65
by simply divieding enthalpies from steam tables and omiting whole aspect of tempreture increse.

Hard to follow. PLease describe the steps you mentioned separately:

-steam is entering 12818,18 kg/h the fan at temp 60 C at pressure 200 mbar (saturated conditions)

SO you have $h_i$ and $s_i$ there? namely : ?

-steam durninng compression

Assume isentropic (not isotropic -- that's something else): again: $h_{is}$ there? namely : ? So $T_{is}$ ?

In reality $h$ ends up higher than $h_{is}$ because there is an efficiency $\eta_{is} = {h_i - h_{actual} \over h_i - h_{is} }$
again: $h_{actual}$ there? namely : ? So $T_{actual}$ ?

is being heated to 100 C, we want to achive 250mbar

heated as in 'heat is added' or is it heated because of the compresssion ?
(In the latter case your $T_{actual}$ deterimines $\eta_{is}$ )

-after that steam is being cooled by sprayed water at 65 C

Strange. Why would someone do such a destructive deed ?

[edit] sheet 20 here

 

[Gosia]

Hello Gosia,

Hard to follow. PLease describe the steps you mentioned separately:

That is not necessary because this approach was totally wrong.

SO you have $h_i$ and $s_i$ there? namely : ?

Yes, evrything from steam tables

Assume isentropic (not isotropic -- that's something else): again: $h_{is}$ there? namely : ? So $T_{is}$ ?

Isentropic is not a good assumption.

In reality $h$ ends up higher than $h_{is}$ because there is an efficiency $\eta_{is} = {h_i - h_{actual} \over h_i - h_{is} }$
again: $h_{actual}$ there? namely : ? So $T_{actual}$ ?
heated as in 'heat is added' or is it heated because of the compresssion ?
(In the latter case your $T_{actual}$ deterimines $\eta_{is}$ )

Heat is beeing generated ONLY becaouse of compression. NO additional heat is beeing given by surroundings.

Strange. Why would someone do such a destructive deed ?

This is a milk evaporator, in order to have no denaturation of proteins we have to maintain tempereture below 100 C