/*! 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 23 A monatomic ideal gas expands at... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 18: Problem 23

A monatomic ideal gas expands at constant pressure. Is heat added to the system or taken from the system during this process? (b) Find the heat added to or taken from the gas in part (a) if it expands at a pressure of \(130 \mathrm{kPa}\) from a volume of \(0.76 \mathrm{m}^{3}\) to a volume of \(0.93 \mathrm{m}^{3}\)

Short Answer

Expert verified
Heat is added to the system; the heat added is 22,100 J.

Step by step solution

01

Understand the Process

In this problem, the gas expands at constant pressure. According to the first law of thermodynamics, the change in internal energy is equal to the heat added to the system minus the work done by the system. For a monatomic ideal gas, when it expands at constant pressure, heat is typically added to the system.
02

Relationship Between Work, Heat, and Volume

At constant pressure, the work done by the gas during expansion is given by the formula: \[ W = P \Delta V \]where \(P\) is the pressure, and \(\Delta V\) is the change in volume. The heat added to or removed from the system can be calculated using the specific heat capacity at constant pressure \(C_p\). For a monatomic ideal gas, \(C_p = \frac{5}{2} R\), where \(R\) is the ideal gas constant.
03

Calculate the Change in Volume

The change in volume \(\Delta V\) can be calculated as follows:\[\Delta V = V_{final} - V_{initial} = 0.93 \, \mathrm{m}^{3} - 0.76 \, \mathrm{m}^{3} = 0.17 \, \mathrm{m}^{3}\]
04

Work Done by the System

Using the equation from Step 2, we calculate the work done:\[W = P \Delta V = 130,000 \, \mathrm{Pa} \times 0.17 \, \mathrm{m}^{3} = 22,100 \, \mathrm{J}\]
05

Calculate Heat Added to the Gas

The heat added to the gas \(Q\) is equal to the work done since the internal energy change for an ideal gas at constant pressure is accommodated by adding heat to do work:\[ Q = W = 22,100 \, \mathrm{J} \]
06

Conclusion

The heat added to the system when the gas expands is 22,100 Joules. This confirms that heat is added to a monatomic ideal gas as it expands at constant pressure to perform work against the surrounding pressure.

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.

Monatomic Ideal Gas
A monatomic ideal gas is a theoretical model used to simplify how gases behave under certain conditions. It consists of individual atoms moving in random directions and can be described using simple equations of state. For monatomic gases like helium or neon, intermolecular forces are negligible, allowing us to assume that the gas molecules have no energy except kinetic energy due to their motion.

Some key points about monatomic ideal gases include:
  • They follow the ideal gas law: \( PV = nRT \), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature.
  • Their internal energy depends only on temperature: \( U = \frac{3}{2}nRT \).
  • Specific heat capacities are constant and not dependent on pressure or volume changes.
Understanding monatomic ideal gases helps in predicting how energy transfers within a system as there are changes in conditions like temperature, volume, or pressure.
Constant Pressure Expansion
When a gas undergoes a constant pressure expansion, it means the pressure remains the same while its volume changes. This kind of process is also known as an isobaric process. During expansion, the gas does work on its environment, such as when a gas-filled balloon inflates.

Some important aspects of constant pressure expansion are:
  • The work done by the gas can be calculated simply using \( W = P \Delta V \), where \( \Delta V \) is the change in volume.
  • In this type of process, some energy is transferred out of the system to do work, which requires input of heat to keep the pressure constant while increasing the volume.
  • This type of expansion typically results in an increase in internal energy and temperature for the gas.
This concept is crucial in understanding everyday phenomena like how engines work or how weather balloons rise through the atmosphere.
Work Done by Gas
When a gas expands and does work, it involves a transfer of energy from the gas to its surroundings. This energy is required for the gas to push against the external pressure and create more volume. In the process of constant pressure expansion, the work done by the gas can be straightforwardly calculated.

The formula that gives us the work done is:
\[ W = P \Delta V \]

Where:
  • \( W \) is the work done by the gas.
  • \( P \) is the constant pressure exerted by or on the gas.
  • \( \Delta V \) is the change in volume, \( V_{final} - V_{initial} \).
For example, in the exercise above, the work done during the expansion of the gas from 0.76 m鲁 to 0.93 m鲁 at a constant pressure of 130 kPa was calculated to be 22,100 Joules. This work means that energy is transferred from the gas, reducing its internal energy unless heat is added.
Heat Transfer in Thermodynamics
Heat transfer is a fundamental concept in thermodynamics. It involves the movement of energy between a system and its surroundings, typically due to a temperature difference. When dealing with a gas expansion, heat transfer plays a vital role in furnishing the energy needed for the system to perform work.

Key ideas about heat transfer in this context include:
  • The First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system: \( \Delta U = Q - W \).
  • For a monatomic ideal gas expanding at constant pressure, the heat added compensates for the work done, ensuring the internal energy change relates to the temperature and volume changes.
  • The specific heat capacity at constant pressure, \( C_p \), assists in calculating the precise amount of heat transferred.
Understanding how heat is added or removed during thermodynamic processes such as expansion highlights the core ways energy transforms and moves within physical systems.

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

A basketball player does \(2.43 \times 10^{5}\) J of work during her time in the game, and evaporates \(0.110 \mathrm{kg}\) of water. Assuming a latent heat of \(2.26 \times 10^{6} \mathrm{J} / \mathrm{kg}\) for the perspiration (the same as for water), determine (a) the change in the player's internal energy and (b) the number of nutritional calories the player has converted to work and heat.

An 88 -kg parachutist descends through a vertical height of \(380 \mathrm{m}\) with constant speed. Find the increase in entropy produced by the parachutist, assuming the air temperature is \(21^{\circ} \mathrm{C}\).

An ideal gas doubles its volume in one of three different ways: (i) at constant pressure; (ii) at constant temperature; (iii) adiabatically. Explain your answers to each of the following questions: (a) In which expansion does the gas do the most work? (b) In which expansion does the gas do the least work? (c) Which expansion results in the highest final temperature? (d) Which expansion results in the lowest final temperature?

An inventor claims a new cyclic engine that uses organic grape juice as its working material. According to the claims, the engine absorbs \(1250 \mathrm{J}\) of heat from a \(1010-\mathrm{K}\) reservoir and performs 1120 J of work each cycle. The waste heat is exhausted to the atmosphere at a temperature of \(302 \mathrm{K}\). (a) What is the efficiency that is implied by these claims? (b) What is the efficiency of a reversible engine operating between the same high and low temperatures used by this engine? (Should you invest in this invention?)

A gas is contained in a cylinder with a pressure of \(140 \mathrm{kPa}\) and an initial volume of \(0.66 \mathrm{m}^{3}\). How much work is done by the gas as it (a) expands at constant pressure to twice its initial volume, or (b) is compressed to one-third its initial volume?
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Oscillations

Read Explanation

Fields in Physics

Read Explanation

Measurements

Read Explanation

Energy Physics

Read Explanation

Nuclear Physics

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.