40
2 Macroscopic Thermodynamics
We have earlier employed a quantity that we referred to as the heat capacity at
constant volume, C V , and defined as
C V ≡
∂U
∂T
V
= lim
T →0
(δQ) V
T
,
(2.2.15c)
with the final step above representing the experimental operational definition of
C V . The experimental determination of the isochoric heat capacity thus consists
of supplying a series of accurately known, but sequentially decreasing, quantities
of energy δQ into a system of fixed volume, measuring the attendent temperature
increases T , and extrapolating the ratio δQ//T to T = 0 to obtain the
experimental value of C V .
2.3 New Thermodynamic State Functions
As many more chemical processes take place under constant pressure, rather than at
constant volume, it would be both convenient and useful to define a thermodynamic
state function H that, in analogy with Eq. (2.2.15b), gives
Q P = H ≡ H f − H i
(2.3.1a)
directly as the difference between its values in the initial and final thermodynamic
states connected by an isobaric process. To determine the form taken by this new
thermodynamic state function, we may begin again with the first law expression
δQ = dU + P dV ,
which becomes
δQ = d(U + P V ) − V dP ,
upon adding and subtracting V dP on its right-hand side. It is clear from this expression that the heat added to a thermodynamic system for which the pressure is fixed
will be given via expression (2.3.1a) as the difference H in the thermodynamic
state function H , given by U + P V , between the initial and final thermodynamic
states. By analogy with Eq. (2.2.15a) the differential heat supplied in a constant
pressure (isobaric) measurement is given as
(δQ) P = dH
(2.3.1b)
which, by analogy with the heat capacity at constant volume, may be defined via the
sequence of equalities
2 Macroscopic Thermodynamics
We have earlier employed a quantity that we referred to as the heat capacity at
constant volume, C V , and defined as
C V ≡
∂U
∂T
V
= lim
T →0
(δQ) V
T
,
(2.2.15c)
with the final step above representing the experimental operational definition of
C V . The experimental determination of the isochoric heat capacity thus consists
of supplying a series of accurately known, but sequentially decreasing, quantities
of energy δQ into a system of fixed volume, measuring the attendent temperature
increases T , and extrapolating the ratio δQ//T to T = 0 to obtain the
experimental value of C V .
2.3 New Thermodynamic State Functions
As many more chemical processes take place under constant pressure, rather than at
constant volume, it would be both convenient and useful to define a thermodynamic
state function H that, in analogy with Eq. (2.2.15b), gives
Q P = H ≡ H f − H i
(2.3.1a)
directly as the difference between its values in the initial and final thermodynamic
states connected by an isobaric process. To determine the form taken by this new
thermodynamic state function, we may begin again with the first law expression
δQ = dU + P dV ,
which becomes
δQ = d(U + P V ) − V dP ,
upon adding and subtracting V dP on its right-hand side. It is clear from this expression that the heat added to a thermodynamic system for which the pressure is fixed
will be given via expression (2.3.1a) as the difference H in the thermodynamic
state function H , given by U + P V , between the initial and final thermodynamic
states. By analogy with Eq. (2.2.15a) the differential heat supplied in a constant
pressure (isobaric) measurement is given as
(δQ) P = dH
(2.3.1b)
which, by analogy with the heat capacity at constant volume, may be defined via the
sequence of equalities