/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 An incandescent light bulb radia... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 65

An incandescent light bulb radiates at a rate of \(60.0 \mathrm{W}\) when the temperature of its filament is \(2820 \mathrm{K}\). During a brownout (temporary drop in line voltage), the power radiated drops to \(58.0 \mathrm{W} .\) What is the temperature of the filament? Neglect changes in the filament's length and cross-sectional area due to the temperature change. (tutorial: light bulb)

Short Answer

Expert verified
Answer: The approximate temperature of the filament during the brownout is 2790 K.

Step by step solution

01

Write down the Stefan-Boltzmann's Law formula relating power and temperature

We will use the Stefan-Boltzmann's Law formula which relates power and temperature: \(P = \sigma AeT^4\)
02

Find the ratio of the power radiated during the brownout to the original power radiated

Find the ratio of the power radiated during the brownout (\(P_{2} = 58.0 \mathrm{W}\)) to the original power radiated (\(P_{1} = 60.0 \mathrm{W}\)): \(\frac{P_{2}}{P_{1}} = \frac{58.0}{60.0}\)
03

Calculate the ratio of the temperature to the fourth power

Since we are neglecting changes in the filament's length, cross-sectional area, and emissivity, we can express the ratio of temperatures as \(\frac{T_2^4}{T_1^4}\), where \(T_1\) is the initial temperature and \(T_2\) is the temperature during the brownout. Using the ratio of the powers, we can write: \(\frac{T_2^4}{T_1^4} = \frac{P_2}{P_1} = \frac{58.0}{60.0}\)
04

Find the temperature during the brownout

In order to find the temperature of the filament during the brownout (\(T_2\)), we can use the following equation with the known initial temperature (\(T_1 = 2820 \mathrm{K}\)): \(T_2^4 = \frac{58.0}{60.0}T_1^4\) Now, solve for \(T_2\): \(T_2 = \sqrt[4]{\frac{58.0}{60.0}(2820)^4} = 2790 \mathrm{K}\) The temperature of the filament during the brownout is approximately \(2790 \mathrm{K}\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

A copper rod of length \(0.50 \mathrm{m}\) and cross-sectional area \(6.0 \times 10^{-2} \mathrm{cm}^{2}\) is connected to an iron rod with the same cross section and length \(0.25 \mathrm{m} .\) One end of the copper is immersed in boiling water and the other end is at the junction with the iron. If the far end of the iron rod is in an ice bath at \(0^{\circ} \mathrm{C},\) find the rate of heat transfer passing from the boiling water to the ice bath. Assume there is no heat loss to the surrounding air. (tutorial: composite rod)
What is the heat capacity of a system consisting of (a) a \(0.450-\mathrm{kg}\) brass cup filled with \(0.050 \mathrm{kg}\) of water? (b) \(7.5 \mathrm{kg}\) of water in a 0.75 -kg aluminum bucket?

On a very hot summer day, Daphne is off to the park for a picnic. She puts \(0.10 \mathrm{kg}\) of ice at \(0^{\circ} \mathrm{C}\) in a thermos and then adds a grape-flavored drink, which she has mixed from a powder using room temperature water \(\left(25^{\circ} \mathrm{C}\right) .\) How much grape- flavored drink will just melt all the ice?
A blacksmith heats a 0.38 -kg piece of iron to \(498^{\circ} \mathrm{C}\) in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at \(20.0^{\circ} \mathrm{C},\) what minimum amount of water must be in the bucket to cool the iron to \(23.0^{\circ} \mathrm{C} ?\) The water in the bucket should remain in the liquid phase.
A \(0.400-\mathrm{kg}\) aluminum teakettle contains \(2.00 \mathrm{kg}\) of water at \(15.0^{\circ} \mathrm{C} .\) How much heat is required to raise the temperature of the water (and kettle) to \(100.0^{\circ} \mathrm{C} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Electrostatics

Read Explanation

Wave Optics

Read Explanation

Dynamics

Read Explanation

Engineering Physics

Read Explanation

Fundamentals of Physics

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.