How does the efficiency of a reactor affect the amount of power it produces?

[stalebrownies]

Homework Statement

A boiling water reactor has a mass flow rate of 1266.4 kg/s. The water enters the reactor at 250 °C. It boils at 291.5 °C. It exits the core at 500 °C. The specific heat of water at 7.5 MPa is 4.380 kJ/kg/°C, the latent heat of vaporization is 2357 J/kg and the specific heat of steam is 1801 J/kg/°C. The water heating process is 90% efficient. To estimate the actual power of the reactor we suppose that energy in the water is only stored as heat.

1. Compute power used by the reactor core to bring the water to a boil. (in MW)

2. Compute power used by the reactor core to turn the water from liquid to steam. (in MW)

3. Compute power used by the reactor core to heat the steam. (in MW)

4. Compute the power of the reactor core. (Sum of 1, 2, and 3) (in MW)

5. How much mass of enriched uranium fuel is "burnt" every second? (in grams)

The Attempt at a Solution

For question 1, I found the power to be equal to

specific heat of water given * flow rate * (temp water boils - temp water enters)
4.38 KJ/kg/C * (291.5 - 250)°C * 1266.4 kg/s = 230.19 MW
Because it's 90% efficient, 230.19 MW / 0.9 = 255.77 MW (This answer is incorrect)

I'd appreciate it if someone could help me with the first question. Then I should be able to do the others.

 

[SteamKing]

Why do you need to know the latent heat of vaporization of a substance?