Title: 1.3 Thermal energy

Determine the monthly energy demand for hot water (in kWh) of a four-person household in January. Assume that each of the four persons needs on average 40 liters of hot water per day and the water is heated from 10°C to 50°C. (Hint: January has 31 days and Cp,water = 4,18 kJ/(kgK))

Q: [...] kWh
A: 230.36/230,36/230.4/230,4/230

Q = m ∙ cp,water ∙ ΔT = 4960 kg ∙ 4,18 kJ/kg°C ∙ 40 °C = 849,312 kJ = 230.36 kWh

m = 4 ∙ 40 l/d ∙ 1 kg/l ∙ 31 d = 4960 kg

In a flat, an electric heater is used to heat up water from 40°C to 70°C. The water has a constant mass flow of 0.05 kg/s.

Q: Determine the rate of heat addition to the water.

          [...] kW
A: 6,27/6.27
Q: The electric heater requires an electric power input of 6.5 kW. What is the efficiency 𝜂 of the electric heater?

          [...] %
A: 96/96.46

Q̇ =  ṁ ∙ cp,Wasser ∙ ΔT = 0.05 kg/s  ∙ 4,18 kJ/kg°C ∙ 30 °C = 6,27 kW

𝜂 = Q̇/Pel = 96%