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[Some physicists argue against the use of the concept of relativistic mass and the use of the
Chapter 2
2
The First Law of Thermodynamics formula E mc (where m is the relativistic mass). For opposing viewpoints, see G. Oas,
arxiv.org/abs/physics/0504110; T. R. Sandin, Am. J. Phys., 59, 1032 (1991).]

2.5 ENTHALPY
The enthalpy H of a thermodynamic system whose internal energy, pressure, and vol-
ume are U, P, and V is defined as
H U PV (2.45)*

Since U, P, and V are state functions, H is a state function. Note from dw PdV
rev
that the product of P and V has the dimensions of work and hence of energy. Therefore
it is legitimate to add U and PV. Naturally, H has units of energy.
Of course, we could take any dimensionally correct combination of state functions
3
to define a new state function. Thus, we might define (3U 5PV)/T as the state func-
tion “enwhoopee.” The motivation for giving a special name to the state function U
PV is that this combination of U, P, and V occurs often in thermodynamics. For
example, let q be the heat absorbed in a constant-pressure process in a closed system.
P
The first law U q w [Eq. (2.39)] gives

U U q w q V 2 P dV q P V 2 dV q P1V V 2
2
1
P
P
2
1
V 1 V 1
q U PV U PV 1U P V 2 1U P V 2 H H
1
2
2
P
2
2 2
1
1
2
1
1 1
¢H q const. P, closed syst., P-V work only (2.46)*
P
2
since P P P. In the derivation of (2.46), we used (2.27) (w PdV) for
1 2 rev 1
the work w. Equation (2.27) gives the work associated with a volume change of the
system. Besides a volume change, there are other ways that system and surroundings
can exchange work, but we won’t consider these possibilities until Chapter 7. Thus
(2.46) is valid only when no kind of work other than volume-change work is done. Note
also that (2.27) is for a mechanically reversible process. A constant-pressure process is
mechanically reversible since, if there were unbalanced mechanical forces acting, the
system’s pressure P would not remain constant. Equation (2.46) says that for a closed
system that can do only P-V work, the heat q absorbed in a constant-pressure process
P
equals the system’s enthalpy change.
For any change of state, the enthalpy change is
¢H H H U P V 1U P V 2 ¢U ¢1PV2 (2.47)
1 1
2 2
1
2
1
2
where (PV) (PV) (PV) P V P V . For a constant-pressure process, P
2 1 2 2 1 1 2
P P and (PV) PV PV P V. Therefore
1 2 1
¢H ¢U P ¢V const. P (2.48)
An error students sometimes make is to equate (PV) with P V V P. We have
¢1PV2 P V P V 1P ¢P21V ¢V2 P V
2 2 1 1 1 1 1 1
P ¢V V ¢P ¢P ¢V
1
1
Because of the P V term, (PV)
P V V P.For infinitesimal changes, we
have d(PV) PdV VdP, since d(uv) udv v du [Eq. (1.28)], but the corre-
sponding equation is not true for finite changes. [For an infinitesimal change, the equa-
tion after (2.48) becomes d(PV) PdV VdP dP dV PdV VdP, since the
product of two infinitesimals can be neglected.]