Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 58

At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

Short Answer

Expert verified
The numerical reading on a Celsius thermometer equals that on a Fahrenheit thermometer at -40 degrees.

Step by step solution

01

Understand Fahrenheit and Celsius conversions

The Fahrenheit (F) to Celsius (C) conversion formula is \(C = (F - 32) * \frac{5}{9}\). Conversely, the Celsius to Fahrenheit conversion can be written as \(F = C * \frac{9}{5} + 32 \).
02

Set Fahrenheit and Celsius equal

To figure out the temperature at which the Fahrenheit and Celsius scales are the same, we need to set the two formulas equal to each other, resulting in the following equation: \(C = F = C * \frac{9}{5} + 32\).
03

Solve the equation

First, subtract \(C\) from both sides of the equation, resulting in: \( 0 = F - C * \frac{9}{5} + 32\). Next, subtract \(F\) from both sides of the equation: \(-F = -C * \frac{9}{5} + 32\). Finally, Solve the equation for \(F\). This gives: \(C * \frac{9}{5} - F = 32 \).
04

Final computation

Substitute \(F\) with \(C\) in the equation derived from step 3 as the condition is such that \(F = C\) at the specific temperature, thus giving \(C * \frac{9}{5} - C = 32 \). Upon simplification, the equation becomes \(-\frac{4}{5} C = 32 \). Solving this equation gives \(C = -40\). Thus, the numerical readings on both Celsius and Fahrenheit thermometers would be the same at -40.

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

The total volume of seawater is \(1.5 \times 10^{21} \mathrm{~L}\). Assume that seawater contains 3.1 percent sodium chloride by mass and that its density is \(1.03 \mathrm{~g} / \mathrm{mL}\). Calculate the total mass of sodium chloride in kilograms and in tons. \((1\) ton \(=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\).

The thin outer layer of Earth, called the crust, contains only 0.50 percent of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust (27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust. (The mass of Earth is \(5.9 \times 10^{21}\) tons. 1 ton \(=2000 \mathrm{lb}\); \(1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

How many seconds are in a solar year \((365.24\) days \() ?\)

What is the number of significant figures in each of these measured quantities? (a) \(40.2 \mathrm{~g} / \mathrm{cm}^{3}\), (b) \(0.0000003 \mathrm{~cm}\) (c) \(70 \mathrm{~min}\) (d) \(4.6 \times 10^{19}\) atoms.

The price of gold on a certain day in 2004 was \(\$ 315\) per troy ounce. How much did \(1.00 \mathrm{~g}\) of gold cost that day? \((1\) troy ounce \(=31.03 \mathrm{~g} .)\)
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Organic Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

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