How much water can be heated from 20 to 100 degrees C. Having spent 0.5 kWh of energy

How much water can be heated from 20 to 100 degrees C. Having spent 0.5 kWh of energy, if the heat output of the electric heater is 70%?

Here are the data from the given in the SI system:
t1 = 20 ° C = 20 + 273 = 293 K
t2 = 100 ° C = 100 + 273 = 373 K
η = 70% = 0.7
W = 0.5k W * h = 1.8 * 10 ^ 6 J.
1. Expression for determining electricity consumption:
W = P * τ
2. Power required to heat water:
P = Q / τ, Q – where the amount of heat, τ – heating time.
3.we substitute this into the formula from point 1:
W = P * τ = τ * Q / τ = Q
4. The amount of heat spent on heating the body is equal to the product of the specific heat capacity of the substance, body weight and the difference between the final and initial temperatures.
Q = c * m * (t2-t1), where c is the specific heat capacity of the substance, m is the mass of the substance, t2 and t1 are the final and initial temperatures, respectively.
5. Heater efficiency:
η = Wnat / W consumption
Wnat = W consumption * η
6. Let’s substitute all this into the expression from point 3:
W = Q
W cons * η = c * m * (t2-t1)
Let us express the mass from this expression:
m = W cons * η / (c * (t2-t1))
Let’s substitute the numerical values, taking into account that the specific heat capacity of water according to the reference book is c = 4200 J / kg * K.
m = W cons * η / (c * (t2-t1)) = (1.8 * 10 ^ 6) * 0.7 / (4200 * (373-293) = 3.75 kg.
Answer: 3.75 kg.