Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.8 ELECTRICALWORK 86

10 cm

b b

A

B

C

D

E

F G

H I

J K

Figure 3.13 Joule’s apparatus for measuring the mechanical equivalent of heat (re-

drawn from a figure in Ref. [ 84 ]).

Key: A—paddle wheel and vessel (see Fig.3.12); B—wood thermal insulator; C—pin

used to engage paddle wheel shaft to roller; D—roller; E—crank used to wind up the

weights; F, G—strings; H, I—pulley wheels; J, K—weights (round lead disks, viewed

here edge-on).

potential energy:wD mgÅhwheremis the combined mass of the two weights. Joule
made corrections for the kinetic energy gained by the weights, the friction in the connecting
strings and pulley bearings, the elasticity of the strings, and the heat gain from the air
surrounding the system.
A typical experiment performed by Joule is described in Prob. 3. 10 on page 99. His
results for the mechanical equivalent of heat, based on 40 such experiments at average
temperatures in the range 13 C– 16 C and expressed as the work needed to increase the
temperature of one gram of water by one kelvin, was4:165J. This value is close to the
modern value of4:1855J for the “ 15 C calorie,” the energy needed to raise the temperature
of one gram of water from14:5C to15:5C.^16

3.8 Electrical Work

The electric potentialat a point in space is defined as the work needed to reversibly move
an infinitesimal test charge from a position infinitely far from other charges to the point of
interest, divided by the value of the test charge. The electrical potential energy of a charge
at this point is the product ofand the charge.

3.8.1 Electrical work in a circuit

Electric current is usually conducted in an electrical circuit. Consider a thermodynamic
system that is part of a circuit: in a given time period electrons enter the system through

(^16) The thermochemical calorie (cal), often used as an energy unit in the older literature, is defined as4:184J.
Thus 1 kcalD4:184kJ.