Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 105

A column of liquid is found to expand linearly on heating. Assume the column rises 5.25 \(\mathrm{cm}\) for a \(10.0^{\circ} \mathrm{F}\) rise in temperature. If the initial temperature of the liquid is \(98.6^{\circ} \mathrm{F}\) , what will the final temperature be in \(^{\circ} \mathrm{C}\) if the liquid has expanded by 18.5 \(\mathrm{cm}\) ?

Short Answer

Expert verified
The final temperature of the liquid in Celsius is \(38.7994\:°C\).

Step by step solution

01

Calculate the rise in temperature in Fahrenheit

First, let's find out the rise in temperature in Fahrenheit when the liquid expands by 18.5 cm. We know that the column rises 5.25 cm for a 10.0°F rise in temperature. Let the rise in temperature in Fahrenheit be x °F, then we can set up a proportion: \(\frac{5.25\:cm}{10.0\:°F} = \frac{18.5\:cm}{x\:°F}\) Now, we will solve for x.
02

Solve the proportion

To solve the proportion, we can cross-multiply and solve for x: \(5.25\:°F * x = 10.0°F * 18.5\:cm\) Divide both sides of the equation by 5.25 °F to isolate x: \(x = \frac{10.0°F * 18.5\:cm}{5.25\:°F}\) Now, calculate the rise in temperature (x): \(x = 35.2381\:°F\) Now we know that the rise in temperature is 35.2381°F.
03

Convert the initial temperature to Celsius

The initial temperature in Fahrenheit is given as \(98.6\:°F\). To convert it to Celsius, we will use the temperature conversion formula: \(°C = (°F - 32) * \frac{5}{9}\) Plug the initial temperature (98.6°F) into the formula: Initial Temperature in Celsius = \((98.6°F - 32) * \frac{5}{9}\) Calculate the initial temperature in Celsius: Initial Temperature in Celsius = \(37\:°C\)
04

Calculate the final temperature in Celsius

Now we have the initial temperature in Celsius and the rise in temperature in Fahrenheit. First, we need to convert the rise in temperature in Fahrenheit to Celsius using the same temperature conversion formula: Rise in temperature in Celsius = \((35.2381°F - 32) * \frac{5}{9}\) Calculate the rise in temperature in Celsius: Rise in Temperature in Celsius = \(1.7994\:°C\) Now add the initial temperature and the rise in temperature to get the final temperature: Final Temperature in Celsius = \(37\:°C + 1.7994\:°C\) Calculate the final temperature: Final Temperature in Celsius = \(38.7994\:°C\) So, the final temperature of the liquid in Celsius is \(38.7994\:°C\).

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 sample containing 33.42 g of metal pellets is poured into a graduated cylinder initially containing 12.7 mL of water, causing the water level in the cylinder to rise to 21.6 mL. Calculate the density of the metal.

Precious metals and gems are measured in troy weights in the English system: $$\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \operatorname{grain} &=0.0648 \mathrm{g} \\ 1 \text { carat } &=0.200 \mathrm{g} \end{aligned}$$ a. The most common English unit of mass is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is 19.3 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

Convert the following Kelvin temperatures to Celsius and Fahrenheit degrees. a. the temperature that registers the same value on both the Fahrenheit and Celsius scales, 233 K b. the boiling point of helium, 4 K c. the temperature at which many chemical quantities are determined, 298 K d. the melting point of tungsten, 3680 K

The U.S. trade deficit at the beginning of 2005 was \(\$ 475,000,000\) . If the wealthiest 1.00\(\%\) of the U.S. population \((297,000,000)\) contributed an equal amount of money to bring the trade deficit to \(\$ 0,\) how many dollars would each person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person living abroad at the time decides to pay in pounds sterling (f). How many pounds sterling does this person contribute (assume a conversion rate of \(1 \mathrm{f}=\$ 1.869\) )?

A copper wire (density \(=8.96 \mathrm{g} / \mathrm{cm}^{3} )\) has a diameter of 0.25 \(\mathrm{mm}\) . If a sample of this copper wire has a mass of 22 \(\mathrm{g}\) , how long is the wire?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

Chemical Reactions

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