how do the wavelengths of radiant energy vary with the temperature of the radiating source? How does this affect solar and terrestrial radiation?
The wavelengths of radiant energy can vary with the temperature of the radiating source. This relationship is described by Wien's Law, which states that as the temperature of a radiating object increases, the peak wavelength of its emitted radiation decreases.
To understand this further, you can follow these steps to apply Wien's Law:
Step 1: Convert the temperature to Kelvin
The temperature needs to be converted to the Kelvin scale by adding 273.15 degrees to the Celsius temperature. This is because the Kelvin scale starts from absolute zero.
Step 2: Use Wien's displacement law formula
The formula for Wien's displacement law is given by:
λ(max) = (b / T)
where λ(max) is the peak wavelength, b is a constant equal to approximately 2.898 x 10^-3 meters-Kelvin, and T is the temperature in Kelvin.
Step 3: Calculate the peak wavelength
Plug in the temperature in Kelvin into the formula to calculate the peak wavelength. The result will be the wavelength at which the radiating object emits the maximum intensity of radiation.
Now, let's discuss the implications for solar and terrestrial radiation:
Solar Radiation:
The Sun is a very hot object, with a surface temperature of about 5,500 degrees Celsius (5,773 Kelvin). Using Wien's Law, we can calculate that the peak wavelength of solar radiation is around 501 nanometers, which falls within the visible range of the electromagnetic spectrum. This is why we see sunlight as white light, which is a mixture of different colors.
Terrestrial Radiation:
Terrestrial (Earth) radiation refers to the emission of heat energy from the Earth's surface. Since the average temperature of the Earth's surface is much lower than that of the Sun, the peak wavelength of terrestrial radiation is longer. In the infrared region of the spectrum, the Earth emits longer wavelength radiation, typically between 8 and 14 micrometers.
This difference in peak wavelength between solar and terrestrial radiation has important consequences for processes like greenhouse effect and heat transfer. Greenhouse gases in the Earth's atmosphere, such as CO2 and water vapor, are particularly good at absorbing and re-emitting longer wavelength terrestrial radiation. This results in the greenhouse effect, which helps to maintain Earth's temperature at levels suitable for life.
In summary, as the temperature of a radiating source increases, the peak wavelength of its emitted radiation decreases. Solar radiation, emitted from the hot Sun, has a shorter peak wavelength in the visible range, while terrestrial radiation, emitted from the cooler Earth, has a longer peak wavelength in the infrared range.