/*! 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 22 How much energy becomes unavaila... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 22

How much energy becomes unavailable for work in an isothermal process at \(425 \mathrm{~K}\) if the entropy increase is \(40 \mathrm{~J} / \mathrm{K}\) ?

Short Answer

Expert verified
The energy that becomes unavailable for work during the isothermal process is 17000J.

Step by step solution

01

Understanding given values

We are given the absolute temperature of the isothermal process as \(425 K\) and the process has an entropy increase of \(40 J/K\).
02

Calculation of energy unavailable for work

The formula that relates heat, entropy and temperature in an isothermal process is \(\Delta S = \Delta Q / T\). Therefore, the heat energy which is becoming unavailable for work, denoted as \(\Delta Q_u\), can be calculated by rearranging the formula: \(\Delta Q_u = \Delta S \times T\). By replacing the values, we get \(\Delta Q_u = 40 J/K \times 425 K = 17000 J\)
03

Conclusion

Hence, the amount of energy becoming unavailable for work during the isothermal process amounts to 17000 joules.

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.

Entropy
Entropy is a fundamental concept in thermodynamics, and it reflects the level of disorder or randomness in a system. The increase in entropy is an indication of a system moving towards equilibrium, which means that energy is spreading out or dispersing.
In an isothermal process, which occurs at a constant temperature, the entropy change can be directly associated with heat transfer. According to the second law of thermodynamics, entropy will naturally increase when heat is added to a system.
  • The formula used in isothermal processes is \( \Delta S = \Delta Q / T \), where \( \Delta S \) is the change in entropy, \( \Delta Q \) is the heat added, and \( T \) is the absolute temperature.
  • In scenarios where entropy increases, it often signifies that the energy in the system is less usable for doing work. This is critical in understanding why certain processes cannot be completely efficient.
Understanding entropy helps in calculating the amount of energy unavailable for useful work in many thermodynamic processes including isothermal ones.
Heat Energy
Heat energy, or thermal energy, is the energy that comes from the movement of particles within a substance. Heat is a form of energy transfer and is crucial in thermodynamic processes like the isothermal process.
In the context of the isothermal process, heat energy plays a significant role because it is exchanged without changing the temperature of the system.
  • In isothermal conditions, any heat energy transferred to a system is completely converted to work or into increasing entropy.
  • When dealing with heat energy in calculations, it is often expressed as \( \Delta Q \) and is calculated based on the entropy change and isothermal temperature using the formula \( \Delta Q = \Delta S \times T \).
By understanding how heat energy operates, especially in processes like isothermal ones, we can determine how much of this energy becomes unavailable for doing useful work.
Temperature
Temperature is a measure of the average kinetic energy of the particles in a substance. It is a critical factor in thermodynamics and plays a vital role in dictating the direction of heat transfer.
In an isothermal process, temperature remains constant throughout the process. This influences how the system exchanges heat with its surroundings.
  • Maintaining a constant temperature in an isothermal process means that any heat added to the system is perfectly balanced by heat leaving the system, preserving its internal energy.
  • The temperature is crucial in the equation \( \Delta Q = \Delta S \times T \), since it directly affects the amount of heat energy involved when there's an entropy change.
Grasping the concept of temperature, especially in relation to isothermal processes, allows us to calculate changes in entropy and heat energy efficiently and to comprehend the flow and transformation of energy within a system.

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

In an alternative universe, you've got the impossible: an infinite heat reservoir, containing infinite energy at temperature \(T_{h^{*}}\). But you've only got a finite cool reservoir, with initial temperature \(T_{c 0}\) and heat capacity \(C\). Find an expression for the maximum work you can extract if you operate an engine between these two reservoirs.

You operate a store that's heated by a gas furnace that supplies \(24.4 \mathrm{kWh}\) of heat from every hundred cubic feet (CCF) of gas. The gas costs you \(\$ 1.28\) per CCF. You're considering switching to a heat-pump system powered by electricity that costs \(14.6 \%\) per \(\mathrm{kWh}\). Find the minimum heat-pump COP that will reduce your heating costs.

Your power company claims that electric heat is \(100 \%\) efficient. Discuss.

Toyota's Mirai fuel-cell car stores its hydrogen \(\left(\mathrm{H}_{2}\right)\) fuel in tanks that hold \(5.0 \mathrm{~kg}\) of hydrogen at \(70 \mathrm{MPa}\) pressure. During a test one of these tanks leaks its hydrogen into the surrounding test chamber, whose volume is \(955 \mathrm{~m}^{3}\) and which is essentially at vacuum. The hydrogen stays at a constant \(293-\mathrm{K}\) temperature during this process. If the energy that becomes unavailable to do work is \(54.6 \mathrm{MJ}\), what's the fuel tank's volume? Note: The unavailable energy here is not the energy that would have been released on reacting the hydrogen in the vehicle's fuel cell; rather, it's the much lower energy that could have been recovered by using the pressurized gas to turn a turbine.

Ocean thermal-energy conversion (OTEC) is an energy-producing scheme that uses the temperature difference between warm ocean surface waters in the tropics and cooler water several hundred meters down. Find the Carnot efficiency for an OTEC plant operating between \(25^{\circ} \mathrm{C}\) surface water and \(5^{\circ} \mathrm{C}\) deep water. Your answer may seem low, but remember that OTEC's "fuel" is free.
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Wave Optics

Read Explanation

Energy Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Measurements

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.