Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 1

Why do heat \((q)\) and work \((w)\) have positive values when entering a system and negative values when leaving?

Short Answer

Expert verified
Positive values mean energy enters the system; negative means it leaves.

Step by step solution

01

Define the first law of thermodynamics

The first law of thermodynamics states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system: \( \triangle U = q - w \).
02

Understand heat (q) entering and leaving the system

When heat (q) enters a system, it is considered positive because it adds energy to the system. Conversely, when heat leaves the system, it is negative because the system loses energy.
03

Understand work (w) done on and by the system

When work (w) is done on the system, it is positive because external forces are adding energy to the system. When the system itself does work on its surroundings, it is considered negative as the system is losing energy.
04

Summarize the sign convention

Positive values indicate energy entering the system (either as heat or work), increasing the system's internal energy. Negative values indicate energy leaving the system, decreasing its internal energy.

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!

Key Concepts

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

Internal Energy
The internal energy of a system, often denoted by \(\triangle U\), is the total energy contained within the system. It encompasses both the kinetic energy due to the random motion of particles and the potential energy resulting from the interactions between them. Internal energy changes occur due to heat transfer or work done, according to the first law of thermodynamics. Remember: internal energy can't be measured directly; instead, we observe its changes.
Heat Transfer
Heat transfer, represented by \(q\), is the process of energy moving from a hotter object to a cooler one. When heat enters a system, it adds to the system's internal energy and we consider this value positive (\(q > 0\)). Conversely, when heat leaves the system, it reduces the internal energy, making \(q\) negative (\(q < 0\)). It's important to remember that heat naturally flows from hot to cold regions, driving changes in temperature.
Work in Thermodynamics
Work \(w\) in thermodynamics refers to energy transferred when an external force acts upon a system and causes a displacement. Work can be positive or negative depending on the direction of energy transfer. When work is done on the system (e.g., compressing a gas), it's considered positive (\(w > 0\)) because energy is being added to the system. When the system does work on its surroundings (e.g., expanding a gas), the value of work is negative (\(w < 0\)) as the system loses energy. Work and heat transfer are two ways of changing a system's internal energy.
Energy Conservation
The principle of energy conservation is central to the first law of thermodynamics. It asserts that energy cannot be created or destroyed, only transferred or converted from one form to another. In mathematical terms, the first law is expressed as \(\triangle U = q - w\). This equation tells us that any change in the internal energy of a system equals the heat added to the system minus the work done by the system. This ensures that the total energy in the universe remains constant.
Sign Convention in Thermodynamics
Understanding sign conventions in thermodynamics is crucial for analyzing energy changes in a system. Positive values: indicate that energy is entering the system, either in the form of heat (\(q > 0\)) or work (\(w > 0\)). This results in an increase in the system's internal energy. Negative values: indicate that energy is leaving the system, either as heat loss (\(q < 0\)) or work done by the system (\(w < 0\)), resulting in a decrease in internal energy. It’s essential to keep track of these signs to correctly apply the first law of thermodynamics to solve problems.

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 is the difference between the standard enthalpy of formation and the standard enthalpy of reaction?

Kerosene, a common space-heater fuel, is a mixture of hydrocarbons whose "average" formula is \(\mathrm{C}_{12} \mathrm{H}_{26}\) (a) Write a balanced equation, using the simplest whole-number coefficients, for the complete combustion of kerosene to gases. (b) If \(\Delta H_{\mathrm{rn}}^{\circ}=-1.50 \times 10^{4} \mathrm{~kJ}\) for the combustion equation as written in part (a), determine \(\Delta H_{\mathrm{f}}^{\circ}\) of kerosene. (c) Calculate the heat released by combustion of 0.50 gal of kerosene \((d\) of kerosene \(=0.749 \mathrm{~g} / \mathrm{mL})\) (d) How many gallons of kerosene must be burned for a kerosene furnace to produce \(1250 .\) Btu \((1 \mathrm{Btu}=1.055 \mathrm{~kJ}) ?\)

Thermal decomposition of 5.0 metric tons of limestone to lime and carbon dioxide absorbs \(9.0 \times 10^{6} \mathrm{~kJ}\) of heat. Convert this energy to (a) joules; (b) calories; (c) British thermal units.

A 30.5 -g sample of an alloy at \(93.0^{\circ} \mathrm{C}\) is placed into \(50.0 \mathrm{~g}\) of water at \(22.0^{\circ} \mathrm{C}\) in an insulated coffee-cup calorimeter with a heat capacity of \(9.2 \mathrm{~J} / \mathrm{K}\). If the final temperature of the system is \(31.1^{\circ} \mathrm{C},\) what is the specific heat capacity of the alloy?

If you feel warm after exercising, have you increased the internal energy of your body? Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Making Measurements

Read Explanation

Kinetics

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