The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I — Fall 2008
September 8, 2008
Lecture 3: Heat capacity, working with the first law, U&H
References
1. Levine, Physical Chemistry, Sections 2.4–2.6, 2.8–2.9
Key Concepts
•We defined the heat capacity,Cas the response of a system to heat flow:
C=δq
dT
Since heat flow is path dependent, heat capacities must be defined for specific conditions, for example
constant pressure (Cp) versus constant volume (Cv).
•For ideal gases:
Cp−Cv=R
The constant pressure heat capacity is larger due to the fact that “extra” work is done in expanding
the gas as it is heated under constant pressure. At constant volume, no P dV work is done, therefore
all the heat goes into raising the temperature. For a monatomic ideal gas, Cv=3
2Rand for a diatomic
ideal gas, Cv=5
2R.
•The amount of heat and work exchanged with the surroundings is dependent on the path from state 1
to state 2, but the change in internal energy must be the same since Uis a state function.
•If we heat a system at constant volume, we can write:
dU =δqv−P dV =δqv
∆U=qv
So to measure ∆U, we can measure the heat flow into or out of the system at constant volume. This
is sometimes know as bomb calorimetry.
•At constant pressure we can define a new thermodynamic potential or energy, enthalpy (H):
H≡U+P V
∆H=qp
where qPis the heat flow at constant pressure. Enthalpy is also a state function and is therefore
path independent. Enthalpy is a useful function because it is a function of pressure, not volume and
is therefore more useful in terms of doing work in the constant pressure world we work in. We can
measure changes in enthalpy by measuring heat flow at constant pressure. It seems like this definition
is quite arbitrary, but the actual mathematical justification will be discussed shortly.
Related Exercises in Levine
Exercises 2.9, 2.12, (you can try 2.10, as per question in class today)
