2.3.4 Enthalpy
One of the most important state functions encountered in chemistry is
enthalpy. It is defined by the Equation 2.26:
H = E + PV
(2.26)
The corresponding change in enthalpy is
ΔH = ΔE + Δ PV
ð Þ = ΔE + PΔV + V ΔP
(2.27)
At constant pressure, this equation becomes
ΔH = ΔE + PΔV
(2.28)
Recall that Equation 2.24 describes heat transfer in terms of a change in
internal energy for a constant volume process. There is an analogous
equation describing heat transfer for a process carried out at constant
pressure. The relationship, shown in Equation 2.29, is used to define the
change in enthalpy (ΔH):
q P = ΔH
(2.29)
Thus, enthalpy change is simply the heat transferred in a constant pressure process.
Since the heat capacity is defined as the derivative of q with respect to T
(see Equation 2.19), we have our formal definition of heat capacity at
constant pressure (Equation 2.30):
C P =
∂ H
∂ T
P
(2.30)
Example 2.7 Heat Capacities at Constant Volume and
Pressure
Show that the difference
C P −
C V is equal to the molar gas constant
for an ideal gas at a temperature T.
Solution Start with the fundamental definition of enthalpy:
H = E + PV
For an ideal gas, we can replace PV with nRT. Thus
H = E + nRT
Differentiating with respect to T gives
dH
dT
=
dE
dT
+ nR
CHAPTER 2: Thermodynamics and Nanoscience
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