Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.1 HEAT, WORK,AND THEFIRSTLAW 60

water

b

m weight

stop

Figure 3.1 System containing an electrical resistor and a paddle wheel immersed in

water. Dashed rectangle: system boundary. Cross-hatched area: removable thermal

insulation.

A process may have more than one kind of work, each with its own work coefficient
and conjugate work coordinate. In this case the work can be expressed as a sum over the
different kinds labeled by the indexi:

∂wD

X

i

YidXi or wD

X

i

ZXi;2

Xi;1

YidXi (3.1.8)

3.1.3 Heat and work as path functions

Consider the apparatus shown in Fig.3.1. Thesystemconsists of the water together with
the immersed parts: stirring paddles attached to a shaft (a paddle wheel) and an electrical
resistor attached to wires. In equilibrium states of this system, the temperature and pressure
are uniform and the paddle wheel is stationary. The system is open to the atmosphere, so
the pressure is constrained to be constant. We may describe the equilibrium states of this
system by a single independent variable, the temperatureT. (The angular position of the
shaft is irrelevant to the state and is not a state function for equilibrium states of this system.)
Here are three experiments with different processes. Each process has the same initial
state defined byT 1 D300:0K, and each has the same final state.

Experiment 1: We surround the system with thermal insulation as shown in the figure and
release the external weight, which is linked mechanically to the paddle wheel. The
resulting paddle-wheel rotation causes turbulent churning of the water and an increase in
its temperature. Assume that after the weight hits the stop and the paddle wheel comes
to rest, the final angular position of the paddle wheel is the same as at the beginning
of the experiment. We can calculate the work done on the system from the difference
between the potential energy lost by the weight and the kinetic energy gained before
it reaches the stop.^7 We wait until the water comes to rest and the system comes to
thermal equilibrium, then measure the final temperature. Assume the final temperature
isT 2 D300:10K, an increase of0:10kelvins.

(^7) This calculation is an example of the procedure mentioned on page 58 in which the change in elevation of an
external weight is used to evaluate work.