/*! 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 18 During an isothermal compression... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 18

During an isothermal compression of an ideal gas, 335 \(\mathrm{J}\) of heat must be removed from the gas to maintain constant temperature. How much work is done by the gas during the process?

Short Answer

Expert verified
The work done by the gas is -335 J.

Step by step solution

01

Understand the Process

In an isothermal compression process, the temperature (T) of the gas remains constant. For an ideal gas, this means the internal energy change (\( \Delta U \)) is zero. So, according to the first law of thermodynamics, \( \Delta U = Q - W = 0 \), where \( Q \) is the heat exchanged and \( W \) is the work done by the gas.
02

Apply the First Law of Thermodynamics

From the first law, since \( \Delta U = 0 \), we have \( Q = W \). Therefore, the work done by the gas equals the heat removed. Given that 335 \( \mathrm{J} \) of heat is removed, thus \( W = Q = 335 \mathrm{J} \) , but since the work is done on the gas during compression, \( W = -335 \mathrm{J} \).
03

Conclude the Calculation

Since we are calculating the work \( W \) done by the gas and it has a negative value because it is compression, the work done by the gas is \(-335 \mathrm{J} \). This negative sign indicates that work is done on the gas, not by the gas.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ideal Gas
An ideal gas is a hypothetical concept that simplifies the study of gases by assuming certain conditions. These conditions include:
  • The gas consists of a large number of tiny particles (molecules) that are in constant random motion.
  • The particles are so small that their volume is negligible compared to the total volume of the gas.
  • There are no interactions between the particles except during elastic collisions.
These assumptions make it easier to apply mathematical models to predict the behavior of gases. One of the key equations used for ideal gases is the Ideal Gas Law: \[ PV = nRT \]where:
  • \( P \) is the pressure,
  • \( V \) is the volume,
  • \( n \) is the number of moles,
  • \( R \) is the ideal gas constant,
  • \( T \) is the temperature in Kelvin.
This equation helps us understand how changes in volume, pressure, and temperature relate when dealing with an ideal gas, especially during processes like isothermal compression.
First Law of Thermodynamics
The first law of thermodynamics is a foundational principle in physics that deals with the conservation of energy. It can be stated as:\[ \Delta U = Q - W \]Here:
  • \( \Delta U \) is the change in internal energy of a system,
  • \( Q \) is the heat added to the system,
  • \( W \) is the work done by the system.
In the context of an isothermal process, where the temperature of an ideal gas remains constant, the change in internal energy \( \Delta U \) is zero. This simplifies the equation to \( Q = W \), meaning the heat exchanged is equal to the work done. In the case of isothermal compression, if heat is removed, it indicates work is done on the gas. If 335 J of heat is removed, the work done is \( -335 \) J, illustrating energy balance.
Work and Heat Transfer
Understanding work and heat transfer is crucial when analyzing thermodynamic processes: - **Work** is the energy transferred when a force is applied over a distance. For a gas, work is associated with volume change during processes. In the case of compression, work is done on the gas, often resulting in a decrease in volume. - **Heat Transfer** occurs when thermal energy is exchanged between a system and its surroundings. Heat can be absorbed or released depending on whether the system is heated or cooled. For isothermal compression of an ideal gas:
  • Heat is removed to maintain a constant temperature.
  • The work done on the gas results is energy being transferred out of the gas.
This illustrates the interdependence of work and heat transfer, demonstrating how energy changes form but is conserved according to the first law of thermodynamics.

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

An air pump has a cylinder 0.250 \(\mathrm{m}\) long with a mov- able piston. The pump is used to compress air from the atmosphere (at absolute pressure \(1.01 \times 10^{5}\) Pa) into a very large tank at \(4.20 \times 10^{5}\) Pa gauge pressure. (For air, \(C_{V}=20.8 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\) ) (a) The piston begins the compression stroke at the open end of the cylinder. How far down the length of the cylinder has the piston moved when air first begins to flow from the cylinder into the tank? Assume that the compression is adiabatic. (b) If the air is taken into the pump at \(27.0^{\circ} \mathrm{C}\) , what is the temperature of the compressed air? (c) How much work does the pump do in putting 20.0 mol of air into the tank?

CALC A cylinder with a frictionless, movable piston like that shown in Fig. 19.5 contains a quantity of helium gas. Initially the gas is at a pressure of \(1.00 \times 10^{5}\) Pa, has a temperature of 300 \(\mathrm{K}\) , and occupies a volume of 1.50 \(\mathrm{L}\) . The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature equal to 300 \(\mathrm{K}\) . This continues until the pressure reaches \(2.50 \times 10^{4}\) Pa. In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50 L. Assume that the gas may be treated as ideal. (a) In a \(p V\) -diagram, show both processes. (b) Find th volume of the gas at the end of the first process, and find the pressure and temperature at the end of the second process. (c) Fin the total work done by the gas during both processes. (d) Final would you have to do to the gas to return it to its original pres sure and temperature?

A cylinder contains 0.250 mol of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) gas at a temperature of \(27.0^{\circ} \mathrm{C}\) . The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 Atm on the gas. The gas is heated until its temperature increases to \(127.0^{\circ} \mathrm{C}\) . Assume that the \(\mathrm{CO}_{2}\) may be treated as an ideal gas. (a) Draw a \(p V\) -diagram for this process. (b) How much work is done by the gas in this process? (c) On what is this work done? (d) What is the change in internal energy of the gas? (e) How much heat was supplied to the gas? (f) How much work would have been done if the pressure had been 0.50 atm?

Nitrogen gas in an expandable container is cooled from \(50.0^{\circ} \mathrm{C}\) to \(10.0^{\circ} \mathrm{C}\) with the pressure held constant at \(3.00 \times 10^{3}\) Pa. The total heat liberated by the gas is \(2.50 \times 10^{4}\) . Assume that the gas may be treated as ideal. (a) Find the number of moles of gas. (b) Find the change in internal energy of the gas. (c) Find the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?

Starting with 2.50 mol of \(\mathrm{N}_{2}\) gas (assumed to be ideal) in a cylinder at 1.00 atm and \(20.0^{\circ} \mathrm{C},\) a chemist first heats the gas at constant volume, adding \(1.52 \times 10^{4} \mathrm{J}\) of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume. (a) Calculate the final temperature of the gas. (b) Calculate the amount of work done by the gas. (c) Calculate the amount of heat added to the gas while it was expanding. (d) Calculate the change in internal energy of the gas for the whole process.
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Magnetism

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Geometrical and Physical Optics

Read Explanation

Turning Points in Physics

Read Explanation

Electric Charge Field and Potential

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.