Thermodynamics, Calculating the required mass flow

[bardia sepehrnia]

Homework Statement

1-A power plant generates 150 MW of electrical power. It uses a supply of 1000 MW from a geothermal source and rejects energy to the atmosphere through a cooling tower.
Determine:
a) The rejected power to the atmosphere in MW
b) How much air should be flowed to the cooling tower (kg/s) if its temperature cannot be increased more than 10C.

Relevant Equations

Qin-Qout=W
Q=m*cp*(T2-T1)

I have solved this question and it seemed pretty easy, but I got an extremely large number for the mass flow, I had to post the question here to make sure I did it correctly. Any help will be appreciated.

 

[BvU]

Two Three Four things.

I see a calculation that is hard to decipher:

The 1 in c_p= 1.00$\zeta$ looks like a 7.​

​

Your k and K look exactly the same​

​

And how can 8.5 10⁵ kJ/s divided by 10 kJ/kg yield 17 10⁶ kg/s ? Did you check your math ?​

The last one is more about the exercise: cooling towers evaporate water, they are not air cooled heat exchangers.

$\$

 

[bardia sepehrnia]

Two Three Four things.

I see a calculation that is hard to decipher:

The 1 in c_p= 1.00$\zeta$ looks like a 7.​

​

Your k and K look exactly the same​

​

And how can 8.5 10⁵ kJ/s divided by 10 kJ/kg yield 17 10⁶ kg/s ? Did you check your math ?​

The last one is more about the exercise: cooling towers evaporate water, they are not air cooled heat exchangers.

$\$

The question is kind of vague so I had to assume lots of things but it clearly says in question: "how much air has to flow... "and when it says :'its temperature", the question is referring to air's temperature. So I'm pretty sure it's being cooled by air.

The cp (specific heat capacity at constant pressure) of air is 1.005kJ/kg*K
The 850MW is 850*10^3 kW.

I can see I messed up the math. So (850*10^3 [kJ/s])/(1.005[kJ/kg*K]*10[K])=84577kg/s
But the mass flow is still unrealistically large.

 

[BvU]

I agree it's unrealistic, but the math is as it is. Also, your answer suggests an unrealistic precision.

But it is unrealistic to cool a power plant with air only, and that is the responsibility of the problem composer, not yours.

$\$

 

[bardia sepehrnia]

I agree it's unrealistic, but the math is as it is. Also, your answer suggests an unrealistic precision.

But it is unrealistic to cool a power plant with air only, and that is the responsibility of the problem composer, not yours.

$\$

Ok. Thank you for the help