Page 184 - Physical chemistry understanding our chemical world
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THE EFFECT OF PRESSURE ON THERMODYNAMIC VARIABLES      151

             and
                                           ∂G                             These two equations
                                     −S =                         (4.38)  are known as the
                                           ∂T
                                                                          Maxwell relations.
               Equations (4.37) and (4.38) are known as the Maxwell relations.
             The second Maxwell relation (Equation (4.38)) may remind us of
             the form of the Clausius equality (see p. 142). Although the first Maxwell relation
             (Equation (4.37)) is not intuitively obvious, it will be of enormous help later when
             we look at the changes in G as a function of pressure.



              Why does a vacuum ‘suck’?

             The value of G as a function of pressure

             Consider two flasks of gas connected by a small tube. Imagine also that a tap separates
             them, as seen by the schematic illustration in Figure 4.4. One flask contains hydrogen
             gas at high pressure p, for example at 2 atm. The other has such a low pressure of
             hydrogen that it will be called a vacuum.
               As soon as the tap is opened, molecules of hydrogen move spon-
             taneously from the high-pressure flask to the vacuum flask. The
                                                                          The old dictum, ‘nature
             movement of gas is usually so rapid that it makes a ‘slurp’ sound,  abhors a vacuum’ is not
             which is why we often say the vacuum ‘sucks’.                just an old wives tale, it
               Redistributing the hydrogen gas between the two flasks is essen-  is also a manifestation
             tially the same phenomenon as a dye diffusing, as we discussed  of the second law of
             at the start of this chapter: the redistribution is thermodynamically  thermodynamics.
             favourable because it increases the entropy, so  S is positive.
               We see how the spontaneous movement of gas always occurs
             from high pressure to low pressure, and also explains why a balloon  Gases move spon-
             will deflate or pop on its own, but work is needed to blow up  taneously from high
             the balloon or inflate a bicycle tyre (i.e. inflating a tyre is not  pressure to low.
             spontaneous).



                                                              Before






                                                              After


             Figure 4.4 Two flasks are connected by a tap. One contains gas at high pressure. As soon as the
             tap separating the two flasks is opened, molecules of gas move spontaneously from the flask under
             higher pressure to the flask at lower pressure. (The intensity of the shading represents the pressure
             of the gas)
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