/*! 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 2 a. Convert \(0^{\circ} \mathrm{F... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 2

a. Convert \(0^{\circ} \mathrm{F}\) to degrees Celsius. b. Convert \(212^{\circ} \mathrm{C}\) to degrees Fahrenheit.

Short Answer

Expert verified
a. -17.78掳C; b. 413.6掳F.

Step by step solution

01

Understand the Conversion Formula for Fahrenheit to Celsius

The formula used to convert temperatures from Fahrenheit to Celsius is given by:\[C = \frac{5}{9}(F - 32)\]where \(C\) is the temperature in degrees Celsius and \(F\) is the temperature in degrees Fahrenheit.
02

Substitute 0掳F into the Conversion Formula

We need to convert \(0^{\circ} \mathrm{F}\) to Celsius. Substitute \(F = 0\) into the formula for converting Fahrenheit to Celsius:\[C = \frac{5}{9}(0 - 32)\]
03

Calculate the Celsius Temperature

Evaluate the expression:\[C = \frac{5}{9}(-32) = \frac{-160}{9} \approx -17.78^{\circ} \mathrm{C}\]Thus, \(0^{\circ} \mathrm{F}\) is approximately \(-17.78^{\circ} \mathrm{C}\).
04

Understand the Conversion Formula for Celsius to Fahrenheit

The formula used to convert temperatures from Celsius to Fahrenheit is given by:\[F = \frac{9}{5}C + 32\]where \(F\) is the temperature in degrees Fahrenheit and \(C\) is the temperature in degrees Celsius.
05

Substitute 212掳C into the Conversion Formula

We are now tasked with converting \(212^{\circ} \mathrm{C}\) to Fahrenheit. Substitute \(C = 212\) into the formula above:\[F = \frac{9}{5} \times 212 + 32\]
06

Calculate the Fahrenheit Temperature

Evaluate the expression:\[F = \frac{9}{5} \times 212 + 32 = 381.6 + 32 = 413.6^{\circ} \mathrm{F}\]Thus, \(212^{\circ} \mathrm{C}\) is equivalent to \(413.6^{\circ} \mathrm{F}\).

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 to Celsius Conversion
Converting temperatures from Fahrenheit to Celsius is a straightforward process using a specific formula. To make this conversion, use the formula:
  • \( C = \frac{5}{9}(F - 32) \)
Here, \(C\) represents the temperature in degrees Celsius, and \(F\) is the temperature in degrees Fahrenheit. This formula involves two main steps:
  • Subtract 32 from the Fahrenheit temperature.
  • Multiply the result by \(\frac{5}{9}\).
This process helps in translating the Fahrenheit scale, used mainly in the United States, to the Celsius scale, which is widely used worldwide and in scientific settings.
Celsius to Fahrenheit Conversion
To convert a temperature from Celsius to Fahrenheit, a different formula is used. This gives us insight into how temperature scales vary around the world. The formula is:
  • \( F = \frac{9}{5}C + 32 \)
This equation showcases two key operations:
  • Multiply the Celsius temperature by \(\frac{9}{5}\).
  • Add 32 to the result.
By performing these steps, we translate Celsius temperatures, commonly used in countries other than the United States, into the Fahrenheit scale.
Temperature Calculation
Calculating temperature using these formulas involves substitution and arithmetic operations. Let's look at a step-by-step scenario:
  • Select the correct formula based on the conversion needed.
  • Substitute the known temperature value into the formula.
  • Perform the arithmetic to find the converted temperature.
Take, for example, converting \(0^{\circ} \mathrm{F}\) to Celsius. By plugging \(0\) into the Fahrenheit to Celsius formula, we perform the operations to find \(-17.78^{\circ} \mathrm{C}\). This process involves subtraction and fraction multiplication for precise calculation.
Conversion Formulas
The conversion formulas play an essential role in understanding and calculating temperature changes between Celsius and Fahrenheit. Here's a quick comparison of these formulas:
  • Fahrenheit to Celsius: \( C = \frac{5}{9}(F - 32) \)
  • Celsius to Fahrenheit: \( F = \frac{9}{5}C + 32 \)
Both formulas are designed to adjust for the differences in the degree intervals and starting points of each temperature scale. Fahrenheit to Celsius focuses on subtracting and scaling down, while Celsius to Fahrenheit emphasizes scaling up and offsetting. Mastery of these formulas allows the prediction and understanding of temperature in various scientific, culinary, and everyday applications, ensuring clarity and consistency in temperature-related calculations.

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. Convert \(67.08 \mu \mathrm{L}\) to liters. b. Convert \(56.8 \mathrm{~m}\) to kilometers.

a. What is \(98.6^{\circ} \mathrm{F}\) in degrees Celsius? b. What is \(25.0^{\circ} \mathrm{C}\) in degrees Fahrenheit?

How many milliliters are in \(607.8\) kL?
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

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.