A water heater marked 4 kW takes 4 minutes to heat 1 kg of water from 20 °C to 50 °C. The cost of electrical energy per kWh is $0.120. What will be the total cost of energy consumption?

The total cost of the energy consumption for the given time period is $0.0364

The given parameters include;

power rating of the heater, P = 4 kW = 4000 Wtime taken to completely boil the water,mass of the water, m = 1 kginitial temperature of the water, t₁ = 20 ⁰Cfinal temperature of the water, t₂ = 50 ⁰Cspecific heat capacity of water, c = 4200 J/kg⁰Ccost of electrical energy = $0.12

The total energy consumed in the process of heating the water;

Total electrical Energy  = Energy of the heater (kWh) + Energy of the heated water (kWh)

Energy of the heater (kWh) = power x time

                                = 4 kW x 0.067 h

                                 = 0.268 kWh

Energy of the heated water (J) = mcΔt

where;

Δt is the change in temperature = t₂ - t₁

                                                      = 50 ⁰C  -  20 ⁰C = 30⁰C

Energy of the heated water (J) = 1 x 4200 x 30

                                               = 126,000 J

Electrical power of the heated water (Watts) =

Energy of the heated water (kWh) =

Total electrical Energy  = 0.268 kWh  +  0.035 kWh

                                       = 0.303 kWh

The total cost of the energy consumed is calculated as;

Therefore, the total cost of the energy consumption is $0.0364

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This is the answer: body 1 + engine 2