Q 59. The ideal gas law states that th... [FREE SOLUTION]

Chapter 12: Q 59. (page 932)

The ideal gas law states that the pressure, P , volume, V, temperature in degrees Kelvin, T, and amount, n, of a gas are related by the equationP = nRT/ V, where R is the universal gas constant. In Exercises 57鈥�60, assume that the amount of the gas is constant and evaluate the specified limits.
If the temperature is held fixed, what is $\lim_{v 鈫� 0} P$ ? Explain why this makes sense

Short Answer

Expert verified

The value of $\lim_{v 鈫� 0} P$ is $鈭�$ . When $T$ is constant.

This makes sense as the gas is extremely compressed, the interaction between the gas particles increases rapidly, causing the pressure to rise infinitely without any bound

Step by step solution

Step 1. Given information.

We have given expression: $\lim_{v 鈫� 0} P$

Evaluate the specified limits. Explain why this makes sense.

$\lim_{v 鈫� 0} P = \lim_{v 鈫� 0} \frac{n R T}{V} = n R T \underset{v 鈫� 0}{l i m} \frac{1}{v} = n R T (\frac{1}{0}) = 鈭�$

The value of $\lim_{v 鈫� 0} P$ is $鈭�$ .When $T$ is constant.

This predicts that when a gas is compressed to 0 volume and kept at constant temperature, the pressure P of the gas approaches infinity.

This makes sense because, when the gas is very compressed, the interaction between the gas particles intensifies rapidly, causing the pressure to climb inexorably.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Step 1. Given information.

Evaluate the specified limits. Explain why this makes sense.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.