Power output of a coal burning power plant

[SeanWade]

Homework Statement

A coal power plant with 30% efficiency burns 10 kilograms of coal per day. (Take the heat of combustion of coal to be 30 MJ/kg)
a) what is the power output of the plant?
b) At what rate is thermal energy being discarded by this plant?
c) If the thermal energy is carried away by water whose temperature is not allowed to increase by more than 5°C, calculate the rate at which water must flow away from the plant.

*note: I already have the solution, I just don't understand it.*
Specifically my questions would be
1) If the efficiency is 30%, then doesn't that mean that the plant only turns 30% of the coals energy into useful energy? The answer says that 70% is converted to useful energy.
2) Is discarded energy just the amount of energy that isn't converted into useful energy?
3) Lastly (and I realize that this is a very vague request), can someone explain from start to end the solution to part c? I can make guesses as to the other parts of the problem, but this one completely baffles me.

Homework Equations

I have no idea where the equations in the answer came from. We weren't provided any in the chapter that would be specifically relevant to this problem.

The Attempt at a Solution

I attached a picture of the solution (the text wouldn't copy properly)

 

[rock.freak667]

The calculation for part 'a' says 70% but the calculation uses 30%. So really you are correct and the actual calculation is correct, the wording is incorrect.

b) Yes, that is why they put 70% in the calculation i.e. 70% of the energy is not used.

c) From part b, you will get the rate of discarded energy in W (P_discarded).

The amount of energy required to raise the temperature of a substance is given by E=mcΔθ (see here for more information)

So the rate at which the energy will be transferred to the water is P=(m/t)cΔθ. Since you are transferring P_discarded, then P=P_discarded

 

[SeanWade]

Thanks, that helped a lot!