Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 8

An ideal gas is in contact with a heat reservoir so that it remains at a constant temperature of \(300.0 \mathrm{K}\). The gas is compressed from a volume of \(24.0 \mathrm{L}\) to a volume of 14.0 L. During the process, the mechanical device pushing the piston to compress the gas is found to expend \(5.00 \mathrm{kJ}\) of energy. How much heat flows between the heat reservoir and the gas and in what direction does the heat flow occur?

Short Answer

Expert verified
Answer: The heat transfer between the gas and the heat reservoir is -5000 J, and the direction of the heat flow is from the gas into the heat reservoir.

Step by step solution

01

Write the First Law of Thermodynamics equation for the given problem

Since we know that the change in internal energy (\(\Delta U\)) is zero, we can rewrite the First Law of Thermodynamics equation as: $$Q = -W$$
02

Convert the work done into Joules

We are given the work done by the mechanical device as \(5.00 \mathrm{kJ}\). To be consistent with the units, we need to convert this value into Joules. We know that \(1 \mathrm{kJ} = 1000 \mathrm{J}\), so the work done is: $$W = 5.00 \times 1000 = 5000 \mathrm{J}$$
03

Calculate the heat transfer

Using the equation we derived in Step 1, we can now calculate the heat transfer as: $$Q = -W$$ $$Q = -5000 \mathrm{J}$$
04

Determine the direction of heat flow

Since the calculated heat transfer (\(Q\)) is negative, this means that the heat is flowing out of the gas and into the heat reservoir. In conclusion, the heat flows between the heat reservoir and the gas is \(-5000 \mathrm{J}\), and the direction of the heat flow is from the gas into the heat reservoir.

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

If the pressure on a fish increases from 1.1 to 1.2 atm, its swim bladder decreases in volume from \(8.16 \mathrm{mL}\) to \(7.48 \mathrm{mL}\) while the temperature of the air inside remains constant. How much work is done on the air in the bladder?
A balloon contains \(200.0 \mathrm{L}\) of nitrogen gas at $20.0^{\circ} \mathrm{C}$ and at atmospheric pressure. How much energy must be added to raise the temperature of the nitrogen to \(40.0^{\circ} \mathrm{C}\) while allowing the balloon to expand at atmospheric pressure?
A heat engine takes in \(125 \mathrm{kJ}\) of heat from a reservoir at $815 \mathrm{K}\( and exhausts \)82 \mathrm{kJ}\( to a reservoir at \)293 \mathrm{K}$ (a) What is the efficiency of the engine? (b) What is the efficiency of an ideal engine operating between the same two reservoirs?
The efficiency of a muscle during weight lifting is equal to the work done in lifting the weight divided by the total energy output of the muscle (work done plus internal energy dissipated in the muscle). Determine the efficiency of a muscle that lifts a \(161-\mathrm{N}\) weight through a vertical displacement of \(0.577 \mathrm{m}\) and dissipates \(139 \mathrm{J}\) in the process.
Within an insulated system, \(418.6 \mathrm{kJ}\) of heat is conducted through a copper rod from a hot reservoir at \(+200.0^{\circ} \mathrm{C}\) to a cold reservoir at \(+100.0^{\circ} \mathrm{C} .\) (The reservoirs are so big that this heat exchange does not change their temperatures appreciably.) What is the net change in entropy of the system, in \(\mathrm{kJ} / \mathrm{K} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Famous Physicists

Read Explanation

Engineering Physics

Read Explanation

Kinematics Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Physics of Motion

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