By I. Klotz, R. Rosenberg

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When current is drawn, we can predict that the voltage will be less than the maximum value, but we cannot predict how much less. Similarly, we can calculate the maximum amount of heat that can be transferred from a cold environment into a building by the expenditure of a certain amount of work in a heat pump, but the actual performance will be less satisfactory. Given a nonequilibrium distribution of ions across a cell membrane, we can calculate the minimum work required to maintain such a distribution.

An explicit expression for the potential energy U exists, and this function can be differentiated to give dU, whereas no explicit expression for W that leads to DW can be obtained. The function for the potential energy is a particularly simple one for the gravitational ﬁeld because two of the space coordinates drop out and only the height h remains. That is, U ¼ constant þ mgh (2:15) The symbols m and g have the usual signiﬁcance of mass and acceleration because of gravity, respectively. 3. A third difference between DU and W lies in the values obtained if one uses a cyclic path, as in moving the boulder up the hill and then back down to the 16 MATHEMATICAL PREPARATION FOR THERMODYNAMICS initial point.

5) as W¼ ð State 2 P0 Ajdsj cos u ¼ ð V2 P0 jdVj cos u V1 State 1 For gaseous expansion, cos u ¼ 21 and jdVj ¼ dV; for gaseous compression, cos u ¼ 1, and jdVj ¼ 2dV, so that for both expansion and compression, W ¼À ð V2 P0 dV V1 and dW ¼ ÀP0 dV (3:6) A special case of gaseous expansion, and one that can only be approached but not exactly realized, is that in which the external pressure is adjusted continuously so that it differs only inﬁnitesimally from the pressure of the gas. By an inﬁnitesimal change in the external pressure, the direction can be reversed, hence, the designation reversible.