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2.13 SUMMARY Further Reading
The work done on a closed system when it undergoes a mechanically reversible infin-
itesimal volume change is dw rev PdV.
2
The line integral P(T, V) dV (which equals w ) is defined to be the sum of
1
rev
the infinitesimal quantities P(T, V) dV for the process from state 1 to state 2. In gen-
eral, the value of a line integral depends on the path from state 1 to state 2.
The heat transferred to a body of constant composition when it undergoes a tem-
perature change dT at constant pressure is dq C dT, where C is the body’s heat
P
P
P
capacity at constant pressure.
The first law of thermodynamics expresses the conservation of the total energy of
system plus surroundings. For a closed system at rest in the absence of fields, the total
energy equals the internal energy U, and the change in U in a process is U q w,
where q and w are the heat flowing into and the work done on the system in the
process. U is a state function, but q and w are not state functions. The internal energy
U is energy that exists at the molecular level and includes molecular kinetic and
potential energies.
The state function enthalpy H is defined by H U PV. For a constant-pressure
process, H q in a closed system with P-V work only.
P
The heat capacities at constant pressure and constant volume are C dq /dT
P
P
( H/ T) and C dq /dT ( U/ T) .
V
P
V
V
The Joule and Joule–Thomson experiments measure ( T/ V) and ( T/ P) ;
U
H
these derivatives are closely related to ( U/ V) and ( H/ P) .
T
T
A perfect gas obeys PV nRT and ( U/ V) 0. The changes in thermodynamic
T
properties for a perfect gas are readily calculated for reversible isothermal and re-
versible adiabatic processes.
The methods used to calculate q, w, U, and H for various kinds of thermody-
namic processes were summarized in Sec. 2.9.
2
The line integral db is independent of the path from state 1 to state 2 if and
L 1
only if b is a state function. The line integral db is zero for every cyclic process if
and only if b is a state function.
The molecular interpretation of internal energy in terms of intramolecular and
intermolecular energies was discussed in Sec. 2.11.
Important kinds of calculations dealt with in this chapter include calculations of
q, w, U, and H for
• Phase changes (for example, melting).
• Heating a substance at constant pressure.
• Heating at constant volume.
• An isothermal reversible process in a perfect gas.
• An adiabatic reversible process in a perfect gas with C constant.
V
• An adiabatic expansion of a perfect gas into vacuum.
• A constant-pressure reversible process in a perfect gas.
• A constant-volume reversible process in a perfect gas.