Experiment with the interactive tool and determine which of the following trends are true or not:
As temperature goes up...
* the peak wavelength goes up.
* stars get bluer and the peak wavelength drops.
* stars get redder.
* the total power output goes up.
True or False
Answer (1)
As temperature increases, peak wavelength decreases: False.
As temperature increases, stars get bluer and peak wavelength drops: True.
As temperature increases, stars get redder: False.
As temperature increases, total power output increases: True.
Explanation
Problem Analysis We need to analyze how changes in temperature affect the peak wavelength, color, and total power output of stars. We'll use Wien's displacement law and the Stefan-Boltzmann law to guide our analysis.
Wien's Displacement Law Wien's displacement law states that the peak wavelength ( λ ma x ) is inversely proportional to the temperature (T): λ ma x = T b , where b is Wien's displacement constant. This means that as the temperature increases, the peak wavelength decreases.
Peak Wavelength and Star Color Based on Wien's law, the statement 'the peak wavelength goes up' is False . As temperature increases, the peak wavelength shifts to shorter wavelengths, which corresponds to bluer colors. Therefore, the statement 'stars get bluer and the peak wavelength drops' is True . The statement 'stars get redder' is False because increasing temperature shifts the color towards blue, not red.
Stefan-Boltzmann Law The Stefan-Boltzmann law states that the total power output (P) of a star is proportional to the fourth power of its temperature (T): P = σ A T 4 , where σ is the Stefan-Boltzmann constant and A is the surface area. This means that as the temperature increases, the total power output increases significantly.
Total Power Output Based on the Stefan-Boltzmann law, the statement 'the total power output goes up' is True .
Final Answer In summary:
'the peak wavelength goes up' is False .
'stars get bluer and the peak wavelength drops' is True .
'stars get redder' is False .
'the total power output goes up' is True .
Examples
Understanding the relationship between temperature and light is crucial in many fields. For example, in astronomy, analyzing the light from distant stars helps us determine their temperature and composition. In everyday life, this principle is used in infrared thermometers to measure body temperature without contact. The hotter an object, the shorter the wavelength of light it emits, and the greater the total energy radiated.
