/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 34 Show that pressure has the units... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 34

Show that pressure has the units of energy density.

Short Answer

Expert verified
Both pressure and energy density have the same units and are dimensionally equivalent, which is Pascal (Pa) or N/m^2 (Newton per square meter)

Step by step solution

01

Understand the units of Pressure, Energy and Density

Pressure (P) is defined as Force (F) per unit area (A), so its units are N/m^2 or Pa (Pascal). Energy (E) is the ability to do work and its derived SI unit is Joule (J), which can be defined as Newton meter (N.m). Density (蟻) is mass (m) per unit volume (V), so its units are kg/m^3
02

Establish the formula for Energy Density

Energy Density (u) is defined as the Energy per unit Volume, Hence its SI units become J/m^3 or N.m/m^3 or N.m^(-2).m or N/m^2 which are the units of pressure.
03

Validate the equivalence using dimensional analysis

The dimensional formula for pressure is [M L^(-1) T^(-2)] and for Energy Density is [M L^(-1) T^(-2)]. Hence, they are dimensionally equivalent therefore we conclude they have the same units

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

Most popular questions from this chapter

Assuming normal atmospheric pressure, how massive an object can a 5.0 -cm- diameter suction cup support on a vertical wall, if the coefficient of friction between cup and wall is \(0.72 ?\)

The pressure unit torr is defined as the pressure that will support a column of mercury \(1 \mathrm{mm}\) high. Meteorologists often give barometric pressure in inches of mercury, defined analogously. Express each of these in SI units. (Hint: Mercury's density is \(\left.1.36 \times 10^{4} \mathrm{kg} / \mathrm{m}^{3} .\right)\)

It's not possible to breathe through a snorkel from a depth greater than a meter or so. Why not?

When a couple with total mass \(120 \mathrm{kg}\) lies on a water bed, pressure in the bed increases by \(4700 \mathrm{Pa}\). What surface area of the two bodies is in contact with the bed?

Why are dams thicker at the bottom than at the top?
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Nuclear Physics

Read Explanation

Turning Points in Physics

Read Explanation

Space Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Wave Optics

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.