Thanks to GPT-4:
In general, the temperature of the sheet can be approximated by the following equation:
T = Ta + (Q / A) / ρc
where T is the temperature of the sheet, Ta is the ambient temperature, Q is the heat flux (in watts) absorbed by the sheet, A is the area of the sheet, ρ is the density of the sheet, and c is the specific heat capacity of the sheet.
Assuming an ambient temperature of 35°C (95°F), a solar radiation intensity of 1000 W/m^2, a density of 8000 kg/m^3, and a specific heat capacity of 500 J/kg-K, the temperature rise of the sheet can be estimated as follows:
Q = A * α * I
where α is the absorptivity of the sheet and I is the solar radiation intensity. Assuming an absorptivity of 0.4 (typical for stainless steel), we get:
Q = (1 m x 1 m) x 0.4 x 1000 W/m^2 = 400 W
Substituting the values into the equation above, we get:
T = 35 + (400 / (1 m x 1 m x 0.003 m) / (8000 kg/m^3 x 500 J/kg-K) = 81.25°C
Therefore, the stainless steel sheet could reach a temperature of around 81.25°C (178°F) on a hot summer day in the sun under the assumptions made.
Here's a table of approximate surface temperatures for different car paint colors in direct sunlight:
Paint Color | Surface Temperature Range (°C) | Surface Temperature Range (°F) |
---|
White | 27-52°C | 81-126°F |
Silver | 35-55°C | 95-131°F |
Gray | 43-68°C | 109-154°F |
Red | 46-71°C | 115-160°F |
Blue | 50-75°C | 122-167°F |
Green | 52-77°C | 126-171°F |
Black | 57-84°C | 135-183°F |
Note that the temperature ranges provided are approximate and can vary depending on a number of factors, including the specific shade and type of paint, the angle and intensity of the sun's rays, the air temperature, and local weather conditions. Additionally, the surface temperature of a car can vary depending on the specific surface being measured (e.g. roof, hood, trunk), with darker surfaces tending to be hotter than lighter surfaces.
It's important to take precautions to avoid exposure to high temperatures in cars parked in direct sunlight, regardless of the color of the paint. This can include using sunshades or car covers, parking in shaded areas, and avoiding leaving people or pets inside the car for extended periods of time.