Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.8 ELECTRICALWORK 88

liquid

L

C

R

 e

Figure 3.14 System containing an electrical resistor immersed in a liquid. The

dashed rectangle indicates the system boundary.

and positive if electrons leave there. This relation provides an alternative form of Eq.3.8.1:

∂welDIÅdt (3.8.3)

(electrical work in a circuit)

Equations3.8.1and3.8.3are general equations for electrical work in a system that is
part of a circuit. The electric potential differenceÅwhich appears in these equations may
have its source in the surroundings, as for electrical heating with a resistor discussed in the
next section, or in the system, as in the case of a galvanic cell (Sec.3.8.3).

3.8.2 Electrical heating

Figure3.14shows an electrical resistor immersed in a liquid. We will begin by defining
the system to include both the resistor and the liquid. An external voltage source provides
an electric potential differenceÅacross the wires. When electrons flow in the circuit, the
resistor becomes warmer due to the ohmic resistance of the resistor. This phenomenon is
variously called electrical heating, Joule heating, ohmic heating, or resistive heating. The
heating is caused by inelastic collisions of the moving electrons with the stationary atoms of
the resistor, a type of friction. If the resistor becomes warmer than the surrounding liquid,
there will be a transfer of thermal energy from the resistor to the liquid.
The electrical work performed on this system is given by the expressions∂wel D
Å ∂Qsysand∂welDIÅdt(Eqs.3.8.1and3.8.3). The portion of the electrical circuit
inside the system has an electric resistance given byRelDÅ=I(Ohm’s law). Making the
substitutionÅDIRelin the work expressions gives two new expressions for electrical
work in this system:
∂welDIRel∂Qsys (3.8.4)
∂welDI^2 Reldt (3.8.5)
The integrated form of Eq.3.8.4whenIandRelare constant iswelDIRelQsys. When
the source of the electric potential difference is in the surroundings, as it is here,I and
Qsyshave the same sign, sowelis positive for finite current and zero when there is no
current. Figure3.15on the next page shows graphically how the work of electrical heating
is positive for both positive and negative changes of the work coordinateQsysand vanishes
asI, the rate of change of the work coordinate, approaches zero. These are characteristic