Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 34

(a) A child has a fever of \(101^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C} ?\) (b) In a desert, the temperature can be as high as \(45^{\circ} \mathrm{C},\) what is the temperature in \({ }^{\circ} \mathrm{F} ?\) (c) During winter, the temperature of the Arctic region can drop below \(-50^{\circ} \mathrm{C}\), what is the temperature in degree Fahrenheit and in Kelvin? (d) The sublimation temperature of dry ice is \(-78.5^{\circ} \mathrm{C}\). Convert this temperature to degree Fahrenheit and Kelvin. (e) Ethanol boils at \(351 \mathrm{~K}\). Convert this temperature to degree Fahrenheit and degree Celsius.

Short Answer

Expert verified
(a) The child's fever is approximately \(38.3^{\circ}C\). (b) The desert temperature is \(113^{\circ}F\). (c) The Arctic winter temperature is \(-58^{\circ}F\) and \(223.15 \mathrm{K}\). (d) The dry ice sublimation temperature is approximately \(-109.3^{\circ}F\) and \(194.65 \mathrm{K}\). (e) The boiling point of ethanol is approximately \(77.85^{\circ}C\) and \(172.13^{\circ}F\).

Step by step solution

01

Use Fahrenheit to Celsius formula

To convert the fever from Fahrenheit to Celsius, use the formula: \(C = \frac{5}{9} (F - 32)\). Substitute the given temperature (101°F) for F and solve for C.
02

Calculate Celsius temperature

Using the formula, we have: \(C = \frac{5}{9} (101 - 32)\) \(C = \frac{5}{9} \times 69\) \(C\approx 38.3^{\circ}C\) (b) Convert a desert high of 45°C to Fahrenheit
03

Use Celsius to Fahrenheit formula

To convert the desert high temperature from Celsius to Fahrenheit, use the formula: \(F = \frac{9}{5} C + 32\). Substitute the given temperature (45°C) for C and solve for F.
04

Calculate Fahrenheit temperature

Using the formula, we have: \(F = \frac{9}{5} \times 45 + 32\) \(F = 81 + 32\) \(F = 113^{\circ}F\) (c) Convert an Arctic winter low of -50°C to Fahrenheit and Kelvin
05

Use Celsius to Fahrenheit formula to find Fahrenheit temperature

Substitute the given temperature (-50°C) for C in the formula: \(F = \frac{9}{5} C + 32\), and solve for F.
06

Calculate Fahrenheit temperature

Using the formula, we have: \(F = \frac{9}{5} \times (-50) + 32\) \(F = -90 + 32\) \(F = -58^{\circ}F\)
07

Use Celsius to Kelvin formula to find Kelvin temperature

Substitute the given temperature (-50°C) for C in the formula: \(K = C + 273.15\), and solve for K.
08

Calculate Kelvin temperature

Using the formula, we have: \(K = -50 + 273.15\) \(K = 223.15 \mathrm{K}\) (d) Convert dry ice sublimation temperature -78.5°C to Fahrenheit and Kelvin
09

Use Celsius to Fahrenheit formula to find Fahrenheit temperature

Substitute the given temperature (-78.5°C) for C in the formula, \(F = \frac{9}{5} C + 32\), and solve for F.
10

Calculate Fahrenheit temperature

Using the formula, we have: \(F = \frac{9}{5} \times (-78.5) + 32\) \(F \approx -109.3^{\circ}F\)
11

Use Celsius to Kelvin formula to find Kelvin temperature

Substitute the given temperature (-78.5°C) for C in the formula, \(K = C + 273.15\), and solve for K.
12

Calculate Kelvin temperature

Using the formula, we have: \(K = -78.5 + 273.15\) \(K \approx 194.65 \mathrm{K}\) (e) Convert boiling point of ethanol 351K to Fahrenheit and Celsius
13

Use Kelvin to Celsius formula to find Celsius temperature

Substitute the given temperature (351K) for K in the formula, \(C = K - 273.15\), and solve for C.
14

Calculate Celsius temperature

Using the formula, we have: \(C = 351 - 273.15\) \(C \approx 77.85^{\circ}C\)
15

Use Celsius to Fahrenheit formula to find Fahrenheit temperature

Substitute the calculated Celsius temperature (77.85°C) for C in the formula, \(F = \frac{9}{5} C + 32\), and solve for F.
16

Calculate Fahrenheit temperature

Using the formula, we have: \(F = \frac{9}{5} \times 77.85 + 32\) \(F \approx 172.13^{\circ}F\)

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.

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

A silvery metal is put inside a beaker of water. Bubbles form on the surface of the metal and it dissolves gradually. (a) Is this an example of a chemical or a physical change? (b) Do you expect the remaining solution to be a pure substance of a mixture?

Musical instruments like trumpets and trombones are made from an alloy called brass. Brass is composed of copper and zinc atoms and appears homogeneous under an optical microscope. The approximate composition of most brass objects is a 2: 1 ratio of copper to zinc atoms, but the exact ratio varies somewhat from one piece of brass to another. (a) Would you classify brass as an element, a compound, a homogeneous mixture, or a heterogeneous mixture? (b) Would it be correct to say that brass is a solution? [Section 1.2\(]\)

Suppose you decide to define your own temperature scale with units of \(\mathrm{O}\), using the freezing point \(\left(13^{\circ} \mathrm{C}\right)\) and boiling point \(\left(360^{\circ} \mathrm{C}\right)\) of oleic acid, the main component of olive oil. If you set the freezing point of oleic acid as \(0^{\circ} \mathrm{O}\) and the boiling point as \(100^{\circ} \mathrm{O},\) what is the freezing point of water on this new scale?

A \(10.0 \mathrm{~g}\) block of gold is hammered into a thin gold sheet which has an area of \(150 \mathrm{~cm}^{2}\). Given the density of gold is $19.3 \mathrm{~g} / \mathrm{cm}^{3}$, what is the approximate thickness of the gold sheet in millimeters?

Convert the following expressions into exponential notation: (a) 3 terameters \((\mathrm{tm})\) (b) 2.5 femtoseconds (fs) (c) 57 micrometers \((\mu m)\) (d) 8.3 megagrams (mg).
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

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