a) Family Smith has already installed PV in their house. Now, they also want to cover their needs for warm water with solar energy. For this, they consider having a solar thermal water heating system. Considering that the need for warm water is 100L/day, the water has to be heated from 10 to 60ºC and the specific heat capacity of liquid water is 4.18 J/gK.
What is the total energy, in Wh/day, that the system will need to supply to cover the warm water demand?
b) Considering an efficiency of 70% and an irradiance of 1000W/m2 for 3 equivalent sun hours, how much collector area, in m2, will be needed to cover the demand?
c) If only half of the hot water needed has to be stored, at least how big, in L, should the storage tank be?
a) 5805.36
b) 2.76
c) 50
a) To determine the total energy required to heat the water, we need to calculate the energy required to heat 100L of water from 10 to 60ºC.
The formula to calculate the energy required to heat a substance is:
Energy = mass × specific heat capacity × temperature difference
First, we need to convert the mass of water to grams, as the specific heat capacity is given in J/gK. Since 1L of water weighs approximately 1kg, the mass of 100L of water is 100kg (or 100,000g).
Using the formula, the energy required to heat 100L of water from 10 to 60ºC can be calculated as follows:
Energy = 100,000g × 4.18 J/gK × (60 - 10)ºC
Simplifying the calculation:
Energy = 100,000g × 4.18 J/gK × 50ºC
Energy = 20,900,000 J
Now, we need to convert the energy from joules to watt-hours (Wh). Since 1 Wh is equal to 3600 joules, we can calculate the total energy in watt-hours as:
Total energy = Energy / 3600
Total energy = 20,900,000 J / 3600
Total energy ≈ 5805.6 Wh/day
b) To determine the collector area required, we need to consider the efficiency of the system and the available irradiance.
The formula to calculate the collector area is:
Collector area = (Total energy required) / (Efficiency × Irradiance × Sun hours)
Using the given values:
Collector area = 5805.6 Wh/day / (0.7 × 1000 W/m2 × 3 hours)
Simplifying the calculation:
Collector area = 5805.6 Wh/day / (2100 W/m2 × 3 hours)
Collector area ≈ 0.923 m2
c) If only half of the hot water needed has to be stored, we need to find out how much water is required to meet that demand.
The formula to calculate the amount of water required is:
Amount of water = (Total hot water demand) / (2)
Using the given hot water demand of 100L/day:
Amount of water = 100L / 2
Amount of water = 50L
Hence, the storage tank should be at least 50L in size.