Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 12

Using Wien's law and the Stefan-Boltzmann law, explain the color and intensity changes that are observed as the temperature of a hot, glowing object increases.

Short Answer

Expert verified
When the temperature of a hot, glowing object increases, it appears bluer and brighter due to Wien's law, which causes the peak wavelength to decrease (shifting the color towards blue), and the Stefan-Boltzmann law, which leads to an increase in the total radiated energy, making the object appear brighter.

Step by step solution

01

Understand Wien's Law

Wien's law states that the peak wavelength of a blackbody's radiation is inversely proportional to its temperature. The formula for Wien's law is \(λ_{max} = \frac{b}{T}\) where \(λ_{max}\) is the peak wavelength, b is Wien's constant (\(2.898 × 10^{-3} mK\)), and T is the temperature (in Kelvin). Thus, as the temperature of an object increases, the peak wavelength decreases, causing the color of black body radiation to shift towards shorter wavelengths or towards the blue end of the visible spectrum.
02

Understand the Stefan-Boltzmann Law

The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. The formula for Stefan-Boltzmann law is \(E = σT^4\) where E is the energy radiated per unit time per unit surface area, σ is the Stefan-Boltzmann constant (\(5.67 × 10^{-8} W/m^2K^4\)), and T is the temperature (in Kelvin). Hence, as the temperature increases, the radiated energy (intensity of light) also increases.
03

Combining the Two Laws to Explain Observed Changes

As the temperature of an object increases, the color shifts towards the blue end of the spectrum due capitalizing on Wien's law, while the intensity of the light increases due to the Stefan-Boltzmann law. Therefore, as the temperature of a hot, glowing object increases, the object will appear to be bluer and brighter.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How did Newton show that a prism breaks white light into its component colors, but does not add any color to the light?

Instruments on board balloons and spacecraft detect \(511-\mathrm{keV}\) photons coming from the direction of the center of our Galaxy. (The prefix \(\mathrm{k}\) means kilo, or thousand, so \(1 \mathrm{keV}=\) \(10^{3} \mathrm{eV}\).) What is the wavelength of these photons? To what part of the electromagnetic spectrum do these photons belong?

(a) Can a hydrogen atom in the ground state absorb an \(\mathrm{H}\)-alpha \(\left(\mathrm{H}_{\alpha}\right)\) photon? Explain why or why not. (b) Can a hydrogen atom in the \(n=2\) state absorb a Lyman-alpha \(\left(\mathrm{L}_{a}\right)\) photon? Explain why or why not.

The wavelength of \(\mathrm{H}_{\beta}\) in the spectrum of the star Megrez in the Big Dipper (part of the constellation Ursa Major, the Great Bear) is \(486.112 \mathrm{~nm}\). Laboratory measurements demonstrate that the normal wavelength of this spectral line is \(486.133 \mathrm{~nm}\). Is the star coming toward us or moving away from us? At what speed?

When Jupiter is undergoing retrograde motion as seen from Earth, would you expect the eclipses of Jupiter's moons to occur several minutes early, several minutes late, or neither? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Electricity and Magnetism

Read Explanation

Thermodynamics

Read Explanation

Modern Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free