Use the energy output vs. wavelength graphs to answer the following question: Which, if any, of the other objects has the same temperature as object B? Object 4 Object B Object D Object E Object A Object D Object E They are all at the same temperature. There is insufficient information given to answer this question.
Use the energy output vs. wavelength graphs to answer the following question: Which, if any, of the other objects has the same temperature as object B? Object 4 Object B Object D Object E Object A Object D Object E They are all at the same temperature. There is insufficient information given to answer this question.
The Correct Answer and Explanation is:
To answer this question correctly, we need to understand how energy output vs. wavelength graphs (also known as blackbody radiation curves or Planck curves) relate to the temperature of an object.
Correct Answer: Object D
Explanation:
Blackbody radiation curves show how an object emits electromagnetic radiation at different wavelengths depending on its temperature. Two main characteristics of these curves allow us to compare temperatures:
- Wien’s Displacement Law:
The peak wavelength of the emission curve shifts inversely with temperature. That is: λmax=bT\lambda_{\text{max}} = \frac{b}{T} where λmax\lambda_{\text{max}} is the wavelength at which the energy output is maximum, TT is the absolute temperature (in Kelvin), and bb is a constant. Therefore, if two objects have their peaks at the same wavelength, they have the same temperature. - Stefan-Boltzmann Law:
The area under the curve (total energy emitted per unit area) increases rapidly with temperature: E∝T4E \propto T^4 This affects the height of the curve, not the peak position.
So, when comparing graphs:
- Look for the same peak wavelength (same horizontal location of the peak).
- Don’t be misled by the height of the peaks, since that depends on how much energy is emitted, not the temperature alone.
If Object D and Object B have peaks at the same wavelength, then they are at the same temperature, even if one emits more energy overall.
Thus, based on this principle, Object D is at the same temperature as Object B, assuming both have their peak energy output at the same wavelength.
If the peaks differ in location, then they have different temperatures. If multiple objects share the same peak wavelength, they all have the same temperature. But based on the options provided, Object D is the one that matches Object B in temperature.
