Physical Chemistry Third Edition

2.4 Calculation of Amounts of Heat and Energy Changes 63

Exercise 2.9

The Euler reciprocity relation, Eq. (B-13) of Appendix B, implies that for any system

(

∂^2 U

∂V ∂T

)

n



(

∂^2 U

∂T ∂V

)

n

Show that Eqs. (2.4-11) and (2.4-12) are consistent with this requirement.

The Joule Experiment

The first attempt to determine whether (∂U/∂V)T,nvanishes for real gases was made

by Joule around 1843. His apparatus is schematically depicted in Figure 2.5. A sample

of a gas (the system) was placed in one side of the apparatus and the other side of the

apparatus was evacuated. Mechanical vacuum pumps were not yet invented, so a water

aspirator was used. The system was allowed to equilibrate and the initial temperature

of the apparatus was measured. The stopcock was then opened and the gas expanded

irreversibly into the vacuum.

Because the surroundings were not affected during the expansion into a vacuum,

wwas equal to zero. The gas expanded rapidly so there was little opportunity for

heat to be transferred to or from the surroundings, andqtherefore vanished to a

good approximation. From the first law,∆Uwas equal to zero. If a change in tem-

perature of the gas occurred, heat would be transferred to or from the surround-

ings after the expansion was complete, and the final temperature of the surroundings

Chamber originally containinggas Chamber originally evacuated

Valves

Gas inlet

Thermometer

To vacuum pump

Water bath

Figure 2.5 The Apparatus for the Joule Experiment (Schematic).