Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 46

You decide to establish a new temperature scale on which the melting point of ammonia \(\left(-77.75^{\circ} \mathrm{C}\right)\) is \(0^{\circ}\) A and the boiling point of ammonia \(\left(-33.35^{\circ} \mathrm{C}\right)\) is \(100^{\circ}\) A. What would be (a) the boiling point of water in \(^{\circ}$$\text{A}\); and (b) the temperature of absolute zero in \(^{\circ}$$\text{A}\)?

Short Answer

Expert verified
The boiling point of water and the temperature of absolute zero on the new temperature scale are approximately \(491.4^{\circ}\) A and \(-96708.05^{\circ}\) A, respectively.

Step by step solution

01

Convert Reference Points to Kelvin

The reference points given are in Celsius. Convert these to Kelvin using the formula K \(= ^{\circ}\mathrm{C} + 273.15\). This gives \(0^{\circ}\) A \(= -77.75^{\circ}\mathrm{C} + 273.15 = 195.4 K\) and \(100^{\circ}\) A \(= -33.35^{\circ}\mathrm{C} + 273.15 = 239.8 K\).
02

Formulate the Conversion Formula

The relationship between Kelvin and degree A is linear, which can be described by a linear equation. This equation can be formulated as \(A = aK + b\). To solve this equation two sets of points are substituted \( (195.4, 0) \) and \( (239.8, 100)\) respectively and a system of linear equations is solved to find a and b coefficients.
03

Find the Coefficients a and b

The linear conversion formula uses the equation \(A = aK + b\). Solving the system of linear equations using the given points we get the result \( a = 494.8164908616189 \) and \( b = -96708.04827807982 \). Thus the formula becomes \( A = 494.8164908616189 * K - 96708.04827807982\).
04

Find the Boiling Point of Water in Degree A

First we convert the boiling point of water from Celsius to Kelvin, which gives us \(373.15 K\). We then apply this result into the conversion formula, \( A = 494.8164908616189 * K - 96708.04827807982\), and reach the result \( A = 491.4^{\circ}\) A.
05

Find the Temperature of Absolute Zero in Degree A

Knowing that the absolute zero in Kelvin is \(0 K\) we apply this value into the conversion formula, \( A = 494.8164908616189 * K - 96708.04827807982\), and get the result \( A = -96708.05^{\circ}\) A.

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 15.2 L sample of chloroform at \(20^{\circ} \mathrm{C}\) has a mass of 22.54 kg. What is the density of chloroform at \(20^{\circ} \mathrm{C}\), in grams per milliliter?

Indicate whether each of the following is an exact number or a measured quantity subject to uncertainty. (a) the number of pages in this text (b) the number of days in the month of January (c) the area of a city lot (d) the distance between the centers of the atoms in a gold medal

Compared with its mass on Earth, the mass of the same object on the moon should be (a) less; (b) more; (c) the same; (d) nearly the same, but somewhat less.

The filament in an incandescent light bulb is made from tungsten metal \(\left(d=19.3 \mathrm{g} / \mathrm{cm}^{3}\right)\) that has been drawn into a very thin wire. The diameter of the wire is difficult to measure directly, so it is sometimes estimated by measuring the mass of a fixed length of wire. If a \(0.200 \mathrm{m}\) length of tungsten wire weighs \(42.9 \mathrm{mg}\), then what is the diameter of the wire? Express your answer in millimeters.

State whether the following properties of matter are physical or chemical. (a) An iron nail is attracted to a magnet. (b) A piece of paper spontaneously ignites when its temperature reaches \(451^{\circ} \mathrm{F}\). (c) A bronze statue develops a green coating (patina) over time. (d) A block of wood floats on water.
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

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