/*! 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 5 (a) At what temperature do the F... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 5

(a) At what temperature do the Fahrenheit and Celsius scales give the same reading? (b) Is there any temperature at which the Kelvin and Celsius scales coincide?

Short Answer

Expert verified
(a) -40 degrees is the temperature where Fahrenheit and Celsius are the same. (b) No temperature allows Kelvin and Celsius to have the same reading.

Step by step solution

01

Understanding the Problem

The question asks us to find temperatures where two different temperature scales read the same value. First, we'll solve for where Fahrenheit equals Celsius, and then we'll determine if such a temperature exists for Kelvin and Celsius.
02

Equate Fahrenheit to Celsius

The relationship between Fahrenheit and Celsius is given by the formula: \[ F = \frac{9}{5}C + 32 \]We need to find the value of temperature 'T' where C = F. So, set C to F and solve for 'T'.\[ T = \frac{9}{5}T + 32 \]
03

Solve the Equation

To solve \( T = \frac{9}{5}T + 32 \), start by subtracting \( \frac{9}{5}T \) from both sides:\[ T - \frac{9}{5}T = 32 \]Simplify the left side by combining like terms:\[ \left(1 - \frac{9}{5}\right)T = 32 \]\[ -\frac{4}{5}T = 32 \]Multiply both sides by \(-\frac{5}{4}\) to isolate T:\[ T = -40 \]
04

Evaluate Kelvin and Celsius

The Kelvin scale is related to the Celsius scale by the formula:\[ K = C + 273.15 \]To find if a temperature exists where Kelvin equals Celsius, set K equal to C:\[ T = T + 273.15 \]This equation results in 0 = 273.15, which is not possible. Therefore, no temperature exists where Kelvin equals Celsius.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fahrenheit and Celsius equivalence
Understanding when Fahrenheit and Celsius scales cross paths is a neat curiosity in temperature measurement. The formula to convert Celsius to Fahrenheit is \( F = \frac{9}{5}C + 32 \). To find a temperature where these scales are equal, we equate Celsius (C) to Fahrenheit (F). Thus, solving for \( T \), our equation becomes:
  • Set \( C = F \)
  • Resulting equation: \( T = \frac{9}{5}T + 32 \)
When solving this, we subtract \( \frac{9}{5}T \) from both sides giving \( T - \frac{9}{5}T = 32 \). Combining terms we find:
  • \( \left(1 - \frac{9}{5}\right)T = 32 \)
  • Simplifying yields \( -\frac{4}{5}T = 32 \)
To isolate \( T \), multiply both sides by \(-\frac{5}{4}\), resulting in \( T = -40 \). So, at \(-40\) degrees, Fahrenheit and Celsius read the same.
Kelvin and Celsius difference
Kelvin and Celsius scales have a consistent difference and cannot be equivalent at any point. The relationship here is linear: \( K = C + 273.15 \). Kelvin is an absolute scale and always 273.15 units more than Celsius.
Setting these two scales to be equal results in the equation \( T = T + 273.15 \), which simplifies to \( 0 = 273.15 \), an impossibility. This shows that there isn't any temperature at which they coincide.
  • Kelvin scale starts at absolute zero, with \( 0 \) Kelvin being the coldest possible temperature.
  • Celsius scale starts at water鈥檚 freezing point, 0掳C.
Thus, no overlap can occur as they are inherently offset by 273.15 degrees.
Temperature scale relationships
Understanding how different temperature scales relate provides a strong foundational grasp of their applications. Here's how the scales interrelate:
  • Fahrenheit to Celsius: Utilize \( F = \frac{9}{5}C + 32 \). This indicates that Fahrenheit is an extended scale where water freezes at 32掳F and boils at 212掳F.
  • Celsius to Kelvin: Simply shift by 273.15 using \( K = C + 273.15 \). This shows Kelvin is an absolute measure starting from absolute zero.
  • The Kelvin scale is used primarily in scientific scenarios because it expresses temperature directly relative to absolute zero.
Each of these scales has its unique application based on regional or scientific needs. They help in diverse fields such as meteorology, physics, and engineering, adapting to situational relevance.

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 physicist uses a cylindrical metal can \(0.250 \mathrm{~m}\) high and \(0.090 \mathrm{~m}\) in diameter to store liquid helium at \(4.22 \mathrm{~K} ;\) at that temperature the heat of vaporization of helium is \(2.09 \times 10^{4} \mathrm{~J} / \mathrm{kg} .\) Completely surrounding the metal can are walls maintained at the temperature of liquid nitrogen, \(77.3 \mathrm{~K},\) with vacuum between the can and the surrounding walls. How much helium is lost per hour? The emissivity of the metal can is 0.200 . The only heat transfer between the metal can and the surrounding walls is by radiation.

A carpenter builds an exterior house wall with a layer of wood \(3.0 \mathrm{~cm}\) thick on the outside and a layer of Styrofoam insulation \(2.2 \mathrm{~cm}\) thick on the inside wall surface. The wood has a thermal conductivity of \(0.080 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}),\) and the Styrofoam has a thermal conductivity of \(0.010 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})\). The interior surface temperature is \(19.0^{\circ} \mathrm{C}\). and the exterior surface temperature is \(-10.0^{\circ} \mathrm{C}\). (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

Maintaining body temperature. While running, a \(70 \mathrm{~kg}\) student generates thermal energy at a rate of \(1200 \mathrm{~W}\). To maintain a constant body temperature of \(37^{\circ} \mathrm{C},\) this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the heat could not flow out of the student's body, for what amount of time could a student run before irreversible body damage occurred? (Protein structures in the body are damaged irreversibly if the body temperature rises to \(44^{\circ} \mathrm{C}\) or above. The specific heat of a typical human body is \(3480 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K}),\) slightly less than that of water. The difference is due to the presence of protein, fat, and minerals, which have lower specific heats.)

A \(5.00 \mathrm{~kg}\) lead sphere is dropped from the top of a \(60.0-\mathrm{m}\) -tall building. If all of its kinetic energy is converted into heat when it hits the sidewalk, how much will its temperature rise? (Ignore air resistance.)

The emissivity of tungsten is \(0.35 .\) A tungsten sphere with a radius of \(1.50 \mathrm{~cm}\) is suspended within a large evacuated enclosure whose walls are at \(290 \mathrm{~K}\). What power input is required to maintain the sphere at a temperature of \(3000 \mathrm{~K}\) if heat conduction along the supports is negligible?
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Linear Momentum

Read Explanation

Quantum Physics

Read Explanation

Physics of Motion

Read Explanation

Medical Physics

Read Explanation

Further Mechanics and Thermal 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.