Calculate Turbine gross and net output

[Nemo's]

Homework Statement

A steam power plant consists of a boiler, a turbine, a condenser and a pump. The temperature of the inner walls of the boiler is 350oC and the temperature of the condenser cooling water is 20oC. During a certain interval of time, the heat added to the boiler is 2.9x106 kJ and the heat rejected in the condenser is 2.1x106 kJ. If the pump work is 250000 kJ, estimate : a. The turbine gross and net output. b. The thermal efficiency of the power plant. c. The maximum possible efficiency of the power plant.
[/B]

Homework Equations

Second law of thermodynamics.

The Attempt at a Solution

Applying law of conservation of energy to get Wout (Turbine work)
Win-Wout+Qh-Ql=0
250M-Wout+2.9G-2.1G=0
Wout=250.8 MJ

 

[SteamKing]

Homework Statement

A steam power plant consists of a boiler, a turbine, a condenser and a pump. The temperature of the inner walls of the boiler is 350oC and the temperature of the condenser cooling water is 20oC. During a certain interval of time, the heat added to the boiler is 2.9x106 kJ and the heat rejected in the condenser is 2.1x106 kJ. If the pump work is 250000 kJ, estimate : a. The turbine gross and net output. b. The thermal efficiency of the power plant. c. The maximum possible efficiency of the power plant.
[/B]

Homework Equations

Second law of thermodynamics.

The Attempt at a Solution

Applying law of conservation of energy to get Wout (Turbine work)
Win-Wout+Qh-Ql=0
250M-Wout+2.9G-2.1G=0
Wout=250.8 MJ

What's the gross output of the turbine? The net output? What about parts b) and c)?

 

[Nemo's]

What's the gross output of the turbine? The net output? What about parts b) and c)?

I actually don't understand the difference between the net and gross outputs.
a)I need to make sure that it's correct to get the turbine work output using the law of conservation of energy so I can proceed to b.
b) If I get the turbine output power from a then the efficiency=total power input/total power output =Wout/250M
c)Maximum efficiency =1-TL/TH =1- ((20+273)/(350+273))=0.53=53%
Please correct me if I am wrong.

 

[SteamKing]

I actually don't understand the difference between the net and gross outputs.
a)I need to make sure that it's correct to get the turbine work output using the law of conservation of energy so I can proceed to b.
b) If I get the turbine output power from a then the efficiency=total power input/total power output =Wout/250M
c)Maximum efficiency =1-TL/TH =1- ((20+273)/(350+273))=0.53=53%
Please correct me if I am wrong.

The turbine is the only thing between the boiler and the condenser. What does that tell you about the gross work output?

The pump is between the condenser and the boiler. Part of the gross output of the turbine must be used to drive the pump. Net work output is ...?

 

[Nemo's]

The turbine is the only thing between the boiler and the condenser. What does that tell you about the gross work output?

The pump is between the condenser and the boiler. Part of the gross output of the turbine must be used to drive the pump. Net work output is ...?

I think that makes the gross work output = turbine work output = 250.8M and the net output =turbine work output - pump work = 0.8M (according to my previous calculations).

 

[SteamKing]

I think that makes the gross work output = turbine work output = 250.8M and the net output =turbine work output - pump work = 0.8M (according to my previous calculations).

Your original calculation 1) doesn't make sense and 2) is arithmetically incorrect

Applying law of conservation of energy to get Wout (Turbine work)
Win-Wout+Qh-Ql=0
250M-Wout+2.9G-2.1G=0
Wout=250.8 MJ

2.9 G - 2.1 G = 800 M joules

250 M + 800 M = 1050 M joules - Wout = 0

So, how did you come up with Wout = 250.8 M joules? None of your original numbers even have that degree of precision.

 

[Nemo's]

Your original calculation 1) doesn't make sense and 2) is arithmetically incorrect2.9 G - 2.1 G = 800 M joules

250 M + 800 M = 1050 M joules - Wout = 0

So, how did you come up with Wout = 250.8 M joules? None of your original numbers even have that degree of precision.

Yes I made an arithmetic mistake. Wout should be 1050M according to my original calculation. so net output 1050-250=800M

I think I know why my original calculation doesn't make sense. I should appply the first law of thermodynamics. However, I don't know the mass or the enthalpy.

 

[SteamKing]

Yes I made an arithmetic mistake. Wout should be 1050M according to my original calculation. so net output 1050-250=800M

No, this is still wrong, but it is arithmetically correct. Where does the 1050 come from?

I think I know why my original calculation doesn't make sense. I should appply the first law of thermodynamics. However, I don't know the mass or the enthalpy.

You don't need to know either. You're given the total heat quantities, which is what you would have obtained from knowing the mass flow rates and the enthalpies anyway.

 

[Nemo's]

No, this is still wrong, but it is arithmetically correct. Where does the 1050 come from?

You don't need to know either. You're given the total heat quantities, which is what you would have obtained from knowing the mass flow rates and the enthalpies anyway.

O.k what if I say turbine work output = Qh-Ql=2.9G-2.1G=800M would that be correct? I am not sure because similarly I was expecting pump work = 2.9G-2.1G to apply but it doesn't.

 

[SteamKing]

O.k what if I say turbine work output = Qh-Ql=2.9G-2.1G=800M would that be correct?

Gross or net output?

I am not sure because similarly I was expecting pump work = 2.9G-2.1G to apply but it doesn't.

Why would you think that? The pump work is explicitly given as 250,000 kJ, or 250 MJ, in the problem statement.

2.9 GJ - 2.1 GJ ≠ 250 MJ

 

[Nemo's]

Gross or net output?

Gross=800M

Why would you think that? The pump work is explicitly given as 250,000 kJ, or 250 MJ, in the problem statement.

2.9 GJ - 2.1 GJ ≠ 250 MJ

Net=800m-250M=550M

This makes sense to me. I hope I got it right this time.

 

[SteamKing]

Gross=800M
Net=800m-250M=550M

This makes sense to me. I hope I got it right this time.

Yes, that's much better.

 

[Nemo's]

Yes, that's much better.

b)thermal efficiency = Net Work /Qh = 550M/2.9G =19%
c) carnot efficiency = 53% (previusly calculated)

So is this the correct solution ?

 

[SteamKing]

b)thermal efficiency = Net Work /Qh = 550M/2.9G =19%
c) carnot efficiency = 53% (previusly calculated)

So is this the correct solution ?

Looks good to me.

 

[Nemo's]

Thank you so much for your help.