Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 23: Problem 42

A quantity of ideal gas occupies an initial volume \(V_{0}\) at a pressure \(p_{0}\) and a temperature \(T_{0} .\) It expands to volume \(V_{1}(a)\) at constant pressure, \((b)\) at constant temperature, and \((c)\) adiabatically. Graph each case on a \(p V\) diagram. In which case is \(Q\) greatest? Least? In which case is \(W\) greatest? Least? In which case is \(\Delta E_{\text {int }}\) greatest? Least?

Short Answer

Expert verified
Greatest Q: constant pressure process. Least Q: adiabatic process. Greatest W: adiabatic process. Least W: constant pressure process. Greatest \(\Delta E_{\text{int}}\): adiabatic process. Least \(\Delta E_{\text{int}}\): constant pressure process.

Step by step solution

01

- Understand different gas processes

For all three processes, graph them on a \(pV\) diagram (Pressure-Volume diagram).\n\n(a) For the constant pressure process, the volume \(V_{1}(a)\) increases linearly with temperature because pressure remains constant (from ideal gas law \(pV=nRT\)).\n\n(b) In the constant temperature process, the curve is hyperbolic. This is due to the isothermal condition, which results in volume increasing in an inversely proportional way to pressure decrease (again from ideal gas law).\n\n(c) For the adiabatic process, volume increases more slowly than in the isothermal process. The curve is steeper because there is no heat transfer, thus all the work done is transferred to internal energy of the system.
02

- Determine Q in each process

The heat transferred to the system (\(Q\)) is greatest when constant pressure is applied due to the work done by the system as it expands. It is least in the adiabatic process where no heat is transferred in or out of the system, by definition. For the isothermal process, \(Q\) falls in between these extremes.
03

- Determine W in each process

The work done (\(W\)) is greatest in the adiabatic process because all the work is transferred to internal energy. It is least in the constant pressure process, where the system expands without performing much work. Work done in the isothermal process falls in between these extremes.
04

- Determine \(\Delta E_{\text{int}}\) in each process

The change in internal energy (\(\Delta E_{\text{int}}\)) is greatest in the adiabatic process (where all work done changes to internal energy) and least in the constant pressure process (where the system expands without much work done). For the isothermal process, \(\Delta E_{\text{int}}\) is zero as there is no change in temperature.

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

What mass of steam at \(100^{\circ} \mathrm{C}\) must be mixed with \(150 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\), in a thermally insulated container, to produce liquid water at \(50^{\circ} \mathrm{C}\) ?

Ice has formed on a shallow pond and a steady state has been reached with the air above the ice at \(-5.20^{\circ} \mathrm{C}\) and the bottom of the pond at \(3.98^{\circ} \mathrm{C}\). If the total depth of ice \(+\) water is \(1.42 \mathrm{~m}\), how thick is the ice? (Assume that the thermal conductivities of ice and water are \(1.67\) and \(0.502 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), respectively.)

Calculate the work done by an external agent in compressing \(1.12 \mathrm{~mol}\) of oxygen from a volume of \(22.4 \mathrm{~L}\) and \(1.32\) atm pressure to \(15.3 \mathrm{~L}\) at the same temperature.

An ideal gas experiences an adiabatic compression from \(p=122 \mathrm{kPa}, V=10.7 \mathrm{~m}^{3}, T=-23.0^{\circ} \mathrm{C}\) to \(p=1450 \mathrm{kPa}\) \(V=1.36 \mathrm{~m}^{3} .(a)\) Calculate the value of \(\gamma .(b)\) Find the final temperature. ( \(c\) ) How many moles of gas are present? \((d)\) What is the total translational kinetic energy per mole before and after the compression? (e) Calculate the ratio of the \(\mathrm{rms}\) speed before to that after the compression.

The average rate at which heat flows out through the surface of the Earth in North America is \(54 \mathrm{~mW} / \mathrm{m}^{2}\) and the average thermal conductivity of the near surface rocks is \(2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Assuming a surface temperature of \(10^{\circ} \mathrm{C}\), what should be the temperature at a depth of \(33 \mathrm{~km}\) (near the base of the crust)? Ignore the heat generated by radioactive elements; the curvature of the Earth can also be ignored.
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Rotational Dynamics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Thermodynamics

Read Explanation

Geometrical and Physical 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.

Sign-up for free