Chapter 12: Q. 68 (page 945)

$The pressure P of an ideal gas is given by P (n, T, V) = \frac{n R T}{V}, where n is the amount of the gas, R is a constant, T is the temperature of the gas in degrees Kelvin, and V is the volume of the gas . Find \frac{鈭� P}{鈭� n}, \frac{鈭� P}{鈭� V}, and \frac{鈭� P}{鈭� T} . What are the physical interpretations of these partial derivatives ?$

Short Answer

Expert verified

$\frac{鈭� P}{鈭� n} = \frac{R T}{V} This tells us how fast the pressure changes with a unit change in the amount of the gas . \frac{鈭� P}{鈭� V} = - \frac{n R T}{V^{2}} This tells us how fast the pressure changes with a unit change in the volume of the gas . \frac{鈭� P}{鈭� T} = \frac{n R}{V} This tells us how fast the pressure changes with a unit change in the temperature of the gas .$

Step by step solution

Step 1. Given information

The pressure of a ideal gas is given by, $P (n, T, V) = \frac{n R T}{V}$

Step 2. Finding the partial derivatives and physical interpretation of them

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

Step 2. Finding the partial derivatives and physical interpretation of them

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Calculus

Mechanics Maths

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

ThepressurePofanidealgasisgivenbyP(n,T,V)=nRTV,wherenistheamountofthegas,Risaconstant,TisthetemperatureofthegasindegreesKelvin,andVisthevolumeofthegas.Find鈭�P鈭�n,鈭�P鈭�V,and鈭�P鈭�T.Whatarethephysicalinterpretationsofthesepartialderivatives?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the partial derivatives and physical interpretation of them

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Calculus

Mechanics Maths

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.