Question

Which of the following has the highest temperature? a) a white-hot object c) a blue-hot object b) a red-hot object

Short answer

Answer: The blue-hot object has the highest temperature.

Step-by-step solution

Understand the relationship between color and temperature

An object's color depends on its temperature, and this phenomenon is known as black-body radiation. When an object is heated, it emits electromagnetic radiation in the visible spectrum, causing it to emit a specific color. A cooler object will emit a color towards the red end of the spectrum, while a hotter object will emit a color towards the blue end of the spectrum. This phenomenon is described by Wien's Displacement Law, which states that the black-body radiation curve peaks at a wavelength inversely proportional to the temperature (T): wavelength_peak = b/T where b is Wien's displacement constant (approximately 2.898x10^-3 m.K).

Determine the order of colors based on temperature

Based on Wien's Displacement Law, we know that the peak wavelength of an object depends on its temperature. Since shorter wavelengths correspond to higher frequencies and energies, objects with shorter peak wavelengths are hotter. In the visible spectrum, the order of colors is as follows: Red < Orange < Yellow < Green < Blue < Indigo < Violet Therefore, the temperatures of the listed objects can be ordered as follows: Red-Hot Object < White-Hot Object < Blue-Hot Object

Conclude which of the options has the highest temperature

Using the order established in Step 2, we can conclude that the object with the highest temperature is the blue-hot object, since it has a shorter peak wavelength than the white-hot and red-hot objects.