Heat needed? Energy needed?

Question

a. Calculate the amount of heat needed to warm 24.6 kg of water from a room temperature of 20.0°C to 60.0°C for use in a dishwasher.

b. If the water heater has an efficiency of 61%, how much energy is lost to the surroundings while heating the water for one cycle of this dishwasher?

Answer 1

(a)

 

Q = m c ΔT

 

c = specific heat of water = 4200 J / (kg degrees C)  (from tables)

 

Q = m c ΔT = (24.6 kg) [4200 J / (kg degrees C)] [(60 - 20)(degrees C)] = 4132800 J

 

(b)

 

61% efficiency means 39% of the heat is lost = (0.39)(4132800 J) = 1611792 J