Conceptual Physics

It is important to define what we mean by “system.” Here we define the system as the

engine that includes the container, with its moveable lid, and the gas. When heat flows

into the engine, the gas’s temperature changes, but the container’s temperature is

assumed to stay the same. A rod is attached to the lid. The pressure of the gas pushes

against the lid, and this can force both the rod and the lid upwards. The rod might be

attached to the rest of the engine, such as the drive assembly of an automobile. When

the gas expands, it does work on the rod.

The first law is mandated by the principle of conservation of energy. Conservation of

energy applies to isolated systems, and the system of the engine is not isolated. But the

engine is part of some larger system that is isolated. Heat energy flows into the engine.

This energy must be conserved: Energy can be neither created nor destroyed in the

process. That means the heat flow increases the internal energy of the gas. This

energy, however, can do work, increasing the energy of some object outside of the

engine. Work done by the gas reduces its internal energy.

The work done by the gas equals the force it exerts times how far the lid moves. That

force equals the pressure times the surface area of the lid. Calculating the work done by

the gas is easier when the pressure is constant than when the gas pressure varies.

Although it is not the typical way to analyze engines, you could think of the process

entirely in terms of energy. Let’s further simplify the engine, ignoring the rod and any

forces acting on the lid other than gravity and the gas pressure from inside the engine.

Heat flows in, raising the gas’s internal energy and, if the lid rises, increasing the

potential energy of the disk on top (by mgǻy). The sum of the increase in the gas’s

internal energy and the increase in potential energy of the disk equals the amount of net

heat flow.

The first law applies to any engine process, for any initial and final state of the gas plus

any work done. For instance, in the simulation in the introduction, heat was added and

then the piston was allowed to move, but this could have happened simultaneously, or it

could have happened in a series of steps.

Mathematical signs are important here. A net flow of heat into the engine means Q is

positive; a net flow of heat out of the engine means Q is negative. Work done by the

gas raising the lid is positive, since the force is in the direction of the displacement.

When the lid moves down, the work done by the gas is negative.

The relationship between heat, work and internal energy is illustrated in the example

problem to the right. If 130 J of heat is transferred to an engine and its internal energy

increases by 75 J, the first law of thermodynamics dictates that it must do 55 J of work.

The change in internal energy and the work done by the gas must add up to equal the

net heat transferred.

First law of thermodynamics

Heat transferred to system:

·increases internal energy and/or

·causes system to do work

Q = ǻEint + W

Q = net heat transferred to system

ǻEint = change in internal energy

W = work done by system

The internal energy of the gas

increases 75 J. How much work

is done by the gas?

Q = ǻEint + W

W = QíǻEint

W = 130 J í 75 J

W = 55 J

20.2 - James Joule and the first law

Although it is accepted today as one of the fundamental tenets of science, the proponents of the first law of thermodynamics faced a skeptical

scientific community. Most scientists did not view heat as another form of energy. The prevalent theory in the early 1800s was thecaloric

theory, which proposed that a caloric fluid was added to matter as it was heated. This addition of fluid explained why a metal rod expanded

when it was heated: It expanded because it contained more caloric fluid. One legacy of this belief is that heat still has its own units, the calorie

and the British thermal unit (Btu).

Between 1843 and 1850, the English scientist James Joule performed a series of experiments that showed that heat was another form of

energy. He used equipment similar to the apparatus shown in Concept 1. Rather than using heat to raise the temperature, Joule used

mechanical energy. As the diagram illustrates, a falling weight causes the paddles to rotate, and the work of the paddles on the water causes

its temperature to increase.

Joule applied the work-energy theorem to conclude that the work done by the paddles equaled the amount of change in the potential energy of

the weight. By measuring the change in height and the mass of the weight, he could quantify the change in its PE and so the work done by the

paddles. He also measured the increase in the temperature of the water.

Joule performed his experiment repeatedly. He showed beyond doubt that the change in the potential energy of the weight, which equaled the

(^374) Copyright 2007 Kinetic Books Co. Chapter 20