Thus, at constant pressure, the change in enthalpy is equal to the heat
transferred. When heat enters the system maintained at constant pressure
the enthalpy must increase and in an exothermic process the enthalpy
must decrease. For example, if a gas is placed inside a chamber with a
piston that can move so that the pressure is fixed, any heat flow will directly
be equal to the change in enthalpy.
Dependence of specific heat on internal energy and enthalpy
34 PARTI THERMODYNAMICS AND KINETICS
Derivation box 2.1 State functions described using partial derivatives
A state function describing a system is one that is dependent only upon the state and not
the path that was used to prepare the system. Hence state functions are very useful in describ-
ing the thermodynamic properties of systems. State functions can be described in formal
terms with the use of partial derivatives. As an example of the use of partial derivatives,
suppose you wish to describe the trajectory of a boy walking up a hill (Figure 2.7). In addi-
tion to knowing the two horizontal coordinates, xand y, it is necessary to also know the
altitude at each coordinate, A(x,y). The motion of the boy is described by consideration of
how changes in his coordinates lead to changes in his position on the hill; that is, changes
in his altitude. Consider the case of the boy moving only along the xdirection. For small
changes in his position, Δx, there will be a change in his altitude, ΔA, that is determined
by the product of the change in coordinate and the slope of the hill:
ΔΔA (db2.1)
Axy
x
x
y
(,)
=
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
∂
∂
x
y
A(x, y Δy) A (x, y) ( )δδAyx Δy
A(x, y)
A(x Δx, y) A (x, y) ( )δδAxy Δx
x
A(x Δx, y Δy) A (x, y) ( )δδAxy Δx ( )δδAyx Δy
Figure 2.7The altitude A(x,y) changes due to walking along a hill along two perpendicular
directions, xand y.
