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Chapter 5: Problem 49

Turn on an electric stove or toaster oven and carefully observe the heating elements as they warm up. Relate your observations to Wien's law and the Stefan-Boltzmann law.

Short Answer

Expert verified
The heating elements of a toaster oven or an electric stove become red hot when they heat up due to black body radiation. When they initially heat up, they emit radiation in the infrared spectrum which is non-visible to the human eye. However, with further heating, the peak wavelength of the radiation shifts into the visible light spectrum, per Wien's law, and we start to see the elements glowing red. As the temperature continues to increase, the elements emit more light, which is seen as increased brightness, as per Stefan-Boltzmann's law.

Step by step solution

01

Observation and Analysis

When the stove or the toaster oven is first turned on, it starts off with room temperature. Observe the heating elements as they warm up. As the appliance begins to heat, the elements will begin to emit light due to blackbody radiation. Initially, the heating elements will emit radiation in the infrared region, which is not visible to the human eye. But the heating elements will turn red as the temperature gets higher since this indicates that the peak wavelength of the radiation has shifted into the visible light spectrum. This demonstrates Wien's Law.
02

Relating to Wien's Law

According to Wien's law, as the temperature of a black body increases, the peak wavelength at which the maximum energy is emitted, decreases. This is demonstrated by the changes in color observed as the temperature of the heating elements increase. Initially, no light is observed because the radiation emitted is in the infrared region. As the elements continue to heat up, they eventually become hot enough to start glowing red, which is at the longer-wavelength, lower-frequency end of the visible light spectrum. This means the peak wavelength has moved from the infrared region into the visible region, indicating an increase in temperature.
03

Relating to Stefan-Boltzmann's Law

According to Stefan-Boltzmann's law, the total energy being radiated per unit area of a black body is proportional to the fourth power of its temperature. Meaning, as the temperature of the heating elements increase, the amount of light (read energy) they emit will increase at a greater rate. This results in an increased brightness observed as the heating elements get hotter.

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