Physical Chemistry Third Edition

56 2 Work, Heat, and Energy: The First Law of Thermodynamics

Thermometer

Cord wound on drum

Pulley

Weight

Stirrer

Figure 2.4 Joule’s Apparatus for Determining the Mechanical Equivalent of Heat

(Schematic).

qC∆T(4.18JK−^1 g−^1 )(100.0g)∆T418JK−^1 −∆V

∆T

39 .2J

418JK−^1

 0 .0937 K

Joule found that there was no detectable difference in the final state of the system

whether its temperature was raised by doing work on it or by heating it. This shows

that heat and work are two different means of changing a single property of the system.

Since energy is defined as the capacity to do work, the work done on the sample of

water must have increased its energy. Therefore the heat transferred must also have

increased its energy. Joule’s sample of water could have kinetic energy if its center

of mass were moving, and it could have gravitational potential energy. The work and

heat that Joule added to his system did not change either of these forms of energy, so

there must be an additional form of energy, which we call theinternal energyor the

thermodynamic energyand denote byU. If the system is close to the surface of the

earth, the total energy of the system is

Etotal

1

2

mv^2 c+Mgzc+U (2.3-1)