Determine the resistance of the heating element of a boiler operating from a network with a voltage of 120 V

Determine the resistance of the heating element of a boiler operating from a network with a voltage of 120 V, if in 18 minutes it heated 1.8 liters of water at 80 K. boiler 84%

The electric current I performed during the time t the work of Azat in the heating element of the boiler (spent work), operating from the network with voltage U, which can be calculated by the formula Azat = I ∙ U ∙ t = U² ∙ t / R, since according to Ohm’s law I = U / R. Part of Apol’s energy (useful work) was spent on heating water with a mass m = ρ ∙ V, where V is its volume, ρ is its density. To do this, it was required to transfer to it the amount of heat Apol = Q = m ∙ c ∙ ΔT = ρ ∙ V ∙ c ∙ ΔT, where c is the specific heat capacity of water, ΔT is the change in its temperature. Since the boiler efficiency is η = Apol / Azat, then (U² ∙ t / R) ∙ η = ρ ∙ V ∙ c ∙ ΔT. We obtain the calculation formula for determining the resistance of the heating element of the boiler: R = (U² ∙ t ∙ η) / (ρ ∙ V ∙ c ∙ ΔT). From the condition of the problem it is known (given) that the boiler operates from a network with a voltage of U = 120 V, and for t = 18 minutes = 1080 s it was heated V = 1.8 l = 0.0018 m³ of water at ΔT = 80 K, the efficiency of the boiler η = 84% = 0.84. From the reference tables we find ρ = 1000 kg / m³; s = 4200 J / (K ∙ kg). Let’s substitute the values ​​of physical quantities in the formulas and make calculations: R = (120² ∙ 1080 ∙ 0.84) / (1000 ∙ 0.0018 ∙ 4200 ∙ 80); R = 21.6 ohms.
Answer: The resistance of the heating element of the boiler is 21.6 ohms.