Lesson Three : Activities and Quizzes
Advanced Activity 4: Wien’s Law and the Stefan-Boltzmann LawPrecisely stated, the Stefan-Boltzmann Law tells us the total energy given off per second by a hot source is directly proportional to the temperature to the fourth power (T4 = T × T × T × T). That is, as temperature increases, the object gets very hot, very quickly. The exact relationship between energy and temperature in an object emitting thermal radiation, as given by the Stefan-Boltzmann law, is stated below:
Itotal = Etotal / (t × A)
Itotal = σ * T4
Where I is the total intensity in Joules/second*meter2, E is the total energy in Joules, t is the time (in seconds), A is the surface area in square meters (meter2), T is the temperature in Kelvin, and σ is a constant equal to 5.67 × 10-8.
According to Wien's Displacement Law, the wavelength of the emitted radiation is inversely proportional the the temperature:
λ = b/T
Where λ is the wavelength of the emitted radiation. T is the temperature in Kelvins, and b is a constant equal to 2.90 × 10-3.
To convert from Kelvin to degrees Celsius, use the following conversion:
TK - 273.15 = TC
Where TK is the temperature in Kelvin and TC is the temperature in degrees Celsius.
Answer the following question using a calculator. Round your answers to 3 significant digits.
- Consider our sun, with a surface temperature of 5,800 K (5,530 degrees Celsius).
- Use the Stefan-Boltzmann Law to determine the total intensity of the sun. Express your answer in J/ s*m2.
- The surface area of the sun is 6.08 × 108 m2. How much energy does the sun emit in one day?
- Use the Stefan-Boltzmann Law to determine the total intensity of the sun. Express your answer in J/ s*m2.
- Consider the human body, with a surface temperature of about 98.5 degrees Fahrenheit (or 310 K).
- What is the wavelength at which the human body emits the most radiation?
- What part of the spectrum in this wavelength in? Hint: Review the wavelengths of the various sections in the electromagnetic spectrum.
- What is the wavelength at which the human body emits the most radiation?
- By knowing the color of a star, we can predict the temperature at its surface.
- Consider a violet star, with a wavelength of 4 × 10-7 m. Use Wien's Law to determine the temperature at the surface of this star. Compare this temperature to the temperature at the surface of the sun.
- Consider a red star, with a wavelength of 7 × 10-7 m. Use Wien's Law to determine the temperature at the surface of this star. Compare this temperature to the temperature at the surface of the sun.
- Consider a violet star, with a wavelength of 4 × 10-7 m. Use Wien's Law to determine the temperature at the surface of this star. Compare this temperature to the temperature at the surface of the sun.