An electric shower heater is rated at 8.4 kW and raises the temperature of flowing water from 16 °C to 36 °C. What is the mass of water passing through the shower in a time of 1.0 second? (specific heat capacity of water = 4200 J kg –1 °C–1 ; assume that all the electrical energy is used to raise the temperature of the water; assume no heat is transferred to the surroundings)

Answer:

19) E

Q = mcAT
Q is basically the amount of heat lost or gained (in joules).
We have been given the power as 8.4 kW = 8400 W
Power is work done per unit time. P = W/t. Since we want the mass of water passing through
the shower in 1 second, we can deduce the following: P = W/1 = P = W
Work done in this case is equal to the energy lost or gained by the system (Q). W=Q=P
P = mcɅT
8400 = m x 4200 x (36-16) =
m = 0.1 kg = 100 g
= m x 4200 x 20