Thermodynamics swimming pool question

[stevex23]

Homework Statement

You are asked to design a heating system for a swimming
pool that is 2 m deep, 25 m long, and 25 m wide. Your
client desires that the heating system be large enough to raise
the water temperature from 20°C to 30°C in 3 h. The rate of
heat loss from the water to the air at the outdoor design conditions
is determined to be 960 W/m2, and the heater must also
be able to maintain the pool at 30°C at those conditions. Heat
losses to the ground are expected to be small and can be disregarded.
The heater considered is a natural gas furnace whose
efficiency is 80 percent. What heater size (in Btu/h input)
would you recommend to your client?

Homework Equations

The Attempt at a Solution

 

[jack action]

E_water = m * c_p * T

P = E / t

P_needed = P_heated + P_losses

 

[stevex23]

Do i calculate the Energy at each temperature then take the difference?

 

[jack action]

Yes.