Question

Which of the following has the higher 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

Understanding black body radiation and Wien's Law

According to black body radiation, the color of a hot object depends on its temperature. As the temperature of an object increases, its peak radiation wavelength decreases. Wien's Law states that the peak wavelength (λ) at which an object emits radiation is inversely proportional to its temperature (T): λ = (b) / T where b is Wien's displacement constant (2.898 x 10^{-3} m K).

Comparing the colors' wavelengths

Knowing that the wavelength decreases as the temperature increases, we can compare the visible light's colors' general wavelength ranges: - Red light: 620 nm to 750 nm - Blue light: 450 nm to 495 nm - White light: a combination of all visible light colors

Determining which color corresponds to the highest temperature

Based on Wien's Law and knowing the colors' general wavelength ranges, we can conclude the order of the colors according to their temperature: - Blue-hot object: shortest wavelength, highest temperature - White-hot object: combination of all colors, intermediate temperature - Red-hot object: longest wavelength, lowest temperature

Conclusion

Therefore, among the given options (a) white-hot object, (c) blue-hot object, and (b) red-hot object, the blue-hot object has the highest temperature.

Key concepts

Understanding Black Body Radiation

Black body radiation is a fundamental concept in physics that describes the emission of electromagnetic radiation from an idealized object which absorbs all incident radiation, called a 'black body.' These objects emit radiation across a spectrum of wavelengths that depends solely on their temperature, which is why they are perfect radiators.

Imagine heating a black body: as it gets hotter, it glows with different colors, shifting from red to white to blue. This shift happens because the temperature of a black body is directly related to the spectrum of light it emits. At lower temperatures, it glows with a red color, being the longer wavelengths of light. As the temperature increases, the color shifts towards blue, which corresponds to shorter wavelengths. This visualization helps in understanding why we associate certain colors with different temperature ranges.

The Significance of Peak Wavelength

The peak wavelength is the particular wavelength in the spectrum of emitted radiation where the intensity of the radiation is at its maximum. It is significant because it tells us the color of light that is most prominently emitted from a hot object.

For instance, when a metal is heated, it starts glowing and its color allows us to estimate its temperature. According to Wien's Law, which can be represented as the equation \( \lambda = \frac{b}{T} \), where \( \lambda \) is the peak wavelength, \( b \) is Wien's displacement constant, and \( T \) is the absolute temperature of the body, the peak wavelength is inversely proportional to the temperature. So, the hotter the object, the shorter the peak wavelength of emitted light. This concept is widely used in thermal imaging and the study of stars and planets to determine their temperatures.

Color Temperature Relationship

The relationship between color and temperature is explained through the color of a black body as it heats up. This relationship, known as color temperature, is commonly used in photography, design, and describing light sources like LEDs or stars.

Color temperature is measured in Kelvins and denotes the hue of the emitted light associated with the temperature of the black body that emits it. For example, a candle flame at around 1,800 K appears reddish, typical household lighting is about 2,700 K and is more yellow, sunlight is around 5,500 K and is considered 'white,' and a clear sky has a blue tone around 10,000 K or higher. Understanding this relationship aids us in realizing why, according to Wien's Law, a blue-hot object has a higher temperature than a white-hot object, which in turn is hotter than a red-hot object.