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?

d) The cost per m2 of collector is estimated as 120 Euros, and the extra costs for water tank and piping are 6 Euros per L of storage. How much will the whole system cost?

e) However, Mr Smith has read an article in the newspaper in which it was claimed that at the moment it is more expensive to install a solar thermal system for water heating than directly using the PV electricity to heat up water. Therefore, he wants to make some calculations to check such assessement. If the price for Wp of a PV panel is 1 Euro and the external costs are 400 Euros, and considering an efficiency of electricity to heat conversion of 85%, how much (in Euros) will it cost to cover the same amount of energy with PV technology?

f) Assume that the lifetime of both systems is 20 years and the maintenance costs are also equal for both cases. Which will be the better choice for water heating?

1)Solar thermal system
2)Photovoltaic system
3)Both systems are equally good

a:5805.36

b:2.76
c:50
d:631.2

e: 2674.5

f) Solar thermal system

Someone know the answer or at least the explanation of e?

Thanx, Can you also give out the rest??

a) To calculate the total energy needed to heat the water, we can use the equation:

Energy = mass * specific heat capacity * temperature difference

First, we need to convert the volume of water from liters to grams by multiplying by the density of water (1g/ml).

Mass = volume * density = 100 L * 1000 ml/L * 1 g/ml = 100,000 g

Next, we calculate the temperature difference:

Temperature difference = final temperature - initial temperature = (60°C - 10°C) = 50°C

Now we can calculate the total energy:

Energy = 100,000 g * 4.18 J/gK * 50°C = 20,900,000 J

To convert this energy to Wh, we divide by 3,600 (since there are 3,600 Joules in 1 Wh):

Energy (Wh) = 20,900,000 J / 3,600 = 5,805.56 Wh/day

Therefore, the system will need to supply approximately 5,805.56 Wh/day to cover the warm water demand.

b) The collector area needed can be calculated using the equation:

Collector area = Energy demand / (efficiency * irradiance * sun hours)

First, we need to convert the irradiance from W/m2 to Wh/m2, considering 3 equivalent sun hours:

Irradiance (Wh/m2) = 1000 W/m2 * 3 h = 3000 Wh/m2

Now we can calculate the collector area:

Collector area = 5,805.56 Wh/day / (0.70 * 3000 Wh/m2) = 2.616 m2

Therefore, approximately 2.616 m2 of collector area will be needed to cover the demand.

c) To determine the size of the storage tank, we need to calculate half of the hot water needed:

Half of hot water needed = 100 L / 2 = 50 L

Therefore, the storage tank should be at least 50 liters in size.

d) To calculate the cost of the system, we need to consider the cost per m2 of the collector, the extra costs for the water tank and piping, and the collector area needed.

Cost of collector = collector area * cost per m2 = 2.616 m2 * 120 Euros/m2 = 313.92 Euros

Cost of water tank and piping = storage tank size * extra cost per liter = 50 L * 6 Euros/L = 300 Euros

Total cost of the system = cost of collector + cost of water tank and piping = 313.92 Euros + 300 Euros = 613.92 Euros

Therefore, the whole system will cost approximately 613.92 Euros.

e) To calculate the cost of covering the same amount of energy with PV technology, we need to determine the energy demand and the conversion efficiency.

Energy demand = 5,805.56 Wh/day

Conversion efficiency = 85%

First, we need to convert the energy demand to Wp:

Energy demand (Wp) = Energy demand / conversion efficiency = 5,805.56 Wh/day / 0.85 = 6,829.42 Wp

Next, we multiply the Wp by the price per Wp and add the external costs:

Cost of PV system = (6,829.42 Wp * 1 Euro/Wp) + 400 Euros = 7,229.42 Euros

Therefore, it will cost approximately 7,229.42 Euros to cover the same amount of energy with PV technology.

f) To determine the better choice for water heating, we need to compare the costs and consider the lifetime of both systems.

The solar thermal system costs 613.92 Euros and the PV system costs 7,229.42 Euros.

Assuming the maintenance costs are equal, we can compare the costs over the lifetime of 20 years.

Total cost of solar thermal system = 613.92 Euros * 20 years = 12,278.4 Euros

Total cost of PV system = 7,229.42 Euros * 20 years = 144,588.4 Euros

Based on cost alone, the solar thermal system is the better choice for water heating. It is significantly cheaper compared to the PV system over the lifetime of the systems.

Therefore, the better choice for water heating would be the solar thermal system (option 1).

a)900