Final answer:
To heat 250 kg of water from 15°C to 30°C in one hour using a solar panel with an efficiency of 0.30 and an intensity of 680 W m⁻², the minimum area required for the solar panel is approximately 21.51 m². Estimating the temperature of the roof tiles without specific calculations is less precise, but given that solar panels get 30-40°C hotter than their surroundings, roof tiles would likely be cooler than solar panels but warmer than the ambient temperature.
Step-by-step explanation:
To determine the minimum area of the solar heating panel required to increase the temperature of all the water in the tank to 30°C from an initial temperature of 15°C in 1.0 hour, we need to calculate the energy required using the specific heat equation and then relate this to the power provided by the solar radiation.
The energy required (Q) can be calculated by the specific heat equation, Q = mcΔT, where:
m = Mass of the water = 250 kg
c = Specific heat capacity of water = 4200 J kg⁻¹ K⁻¹
ΔT = Change in temperature = (30 - 15)°C = 15°C
Plugging the values into the equation we get:
Q = (250 kg)(4200 J kg⁻¹ K⁻¹)(15 K) = 15,750,000 J
Since the overall efficiency of the heating system is 0.30, the total energy that needs to be incident on the panel is:
Q' = Q / Efficiency = 15,750,000 J / 0.30 = 52,500,000 J
Given that the intensity of solar radiation is 680 W m⁻² and the amount of time is 1.0 hour (3600 seconds), the energy provided by the solar panel is related to its area (A) by:
Power = Intensity × Area = Energy / Time
Area = Energy / (Intensity × Time) = 52,500,000 J / (680 W m⁻² × 3600 s) ≈ 21.51 m²
Therefore, the minimum area required for the solar heating panel is approximately 21.51 m².
Due to the complexity of the factors involved, including the heat capacity of the tiles, the intensity of the sunlight, the distribution of heat over the tiles, and the reflection and emissivity properties of the tiles, it is difficult to provide an exact temperature estimate without more detailed information and a specific calculation method. However, it is known that solar panels can operate at temperatures 30-40°C above ambient temperature in strong sunlight, according to the information provided in the question background.
Using this, we might infer that roof tiles, which are not designed to absorb heat as efficiently as solar panels and have a certain albedo (reflectivity), would likely be cooler than the solar panel but warmer than ambient temperature on a sunny day.