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Chapter 36: Problem 9

Why is a white-hot object hotter than a red-hot object?

Short Answer

Expert verified
Answer: A white-hot object is hotter than a red-hot object due to Wien's Law and the relationship between an object's peak wavelength and the colors in the visible light spectrum. As an object's temperature increases, the peak wavelength of its emitted radiation decreases, moving from the red end of the spectrum to the blue-violet end. When an object reaches a certain high temperature, the emitted light appears white, which is a combination of all visible colors.

Step by step solution

01

Understanding Blackbody Radiation

Blackbody radiation is the electromagnetic radiation emitted by an object when it is heated. All objects emit radiation, but the radiation's intensity and wavelength distribution depend on the object's temperature. The color of the light emitted by an object is related to the peak wavelength of the emitted radiation.
02

Explaining Wien's Law

Wien's Law states that the peak wavelength (位_max) of the blackbody radiation is inversely proportional to the object's temperature (T) in Kelvin. The formula for Wien's Law is: 位_max = b / T Where b is Wien's constant, approximately 2.9 x 10^{-3} m K. From this equation, we can see that as the temperature of an object increases, the peak wavelength of its emitted radiation decreases.
03

Relating Temperature to Color

The visible light spectrum consists of various colors ranging from red to violet. The wavelength of these colors ranges from about 700 nm (red) to 400 nm (violet). As an object's temperature increases, the peak wavelength of the emitted radiation decreases and moves from the red end of the spectrum to the violet end. This change in color is a consequence of Wien's Law.
04

Comparing White-Hot and Red-Hot Objects

A red-hot object has a lower temperature than a white-hot object. This difference is because the peak wavelength of a red-hot object is at the red end (longer wavelength) of the spectrum, while that of a white-hot object is at the blue-violet end (shorter wavelength). As the temperature increases, the object's emitted spectrum covers more colors, and when it reaches a certain high temperature, the emitted light appears white, which is a combination of all visible colors. In conclusion, a white-hot object is hotter than a red-hot object due to Wien's Law and the relationship between an object's peak wavelength and the colors in the visible light spectrum.

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