Page 65 - Physical Chemistry

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If we wait long enough, the piston’s kinetic energy will be dissipated by the internal friction
Chapter 2
The First Law of Thermodynamics (viscosity—see Sec. 15.3) in the gas. The gas will be heated, and the piston will eventually
come to rest (perhaps after undergoing oscillations). Once the piston has come to rest, we
have K pist 0 0 0, since the piston started and ended at rest. We then have w irrev
2
P dV. Hence we can find w irrev after the piston has come to rest. If, however, part of the
ext
1
piston’s kinetic energy is transferred to some other body in the surroundings before the piston
comes to rest, then thermodynamics cannot calculate the work exchanged between system and
surroundings. For further discussion, see D. Kivelson and I. Oppenheim, J. Chem. Educ., 43,
233 (1966); G. L. Bertrand, ibid., 82, 874 (2005); E. A. Gislason and N. C. Craig, ibid., 84,
499 (2007).

Summary
For now, we shall deal only with work done due to a volume change. The work done
on a closed system in an infinitesimal mechanically reversible process is dw
rev
2
PdV. The work w PdV depends on the path (the process) used to go from
rev 1
the initial state 1 to the final state 2.

2.3 HEAT
When two bodies at unequal temperatures are placed in contact, they eventually reach
thermal equilibrium at a common intermediate temperature. We say that heat has
flowed from the hotter body to the colder one. Let bodies 1 and 2 have masses m and
1
m and initial temperatures T and T , with T T ; let T be the final equilibrium tem-
2 1 2 2 1 f
perature. Provided the two bodies are isolated from the rest of the universe and no
phase change or chemical reaction occurs, one experimentally observes the following
equation to be satisfied for all values of T and T :
1 2
m c 1T T 2 m c 1T T 2 q (2.30)
1
1 1
f
f
2
2 2
where c and c are constants (evaluated experimentally) that depend on the composi-
1 2
tion of bodies 1 and 2. We call c the specific heat capacity (or specific heat) of body
1
1. We define q, the amount of heat that flowed from body 2 to body 1, as equal to
m c (T T ).
2 2 2 f
The unit of heat commonly used in the nineteenth and early twentieth centuries
was the calorie (cal), defined as the quantity of heat needed to raise one gram of
water from 14.5°C to 15.5°C at 1 atm pressure. (This definition is no longer used,
as we shall see in Sec. 2.4.) By definition, c H 2 O 1.00 cal/(g °C) at 15°C and 1 atm.
Once the specific heat capacity of water has been defined, the specific heat capacity
c of any other substance can be found from (2.30) by using water as substance 1.
2
When specific heats are known, the heat q transferred in a process can then be cal-
culated from (2.30).
Actually, (2.30) does not hold exactly, because the specific heat capacities of sub-
stances are functions of temperature and pressure. When an infinitesimal amount of
heat dq flows at constant pressure P into a body of mass m and specific heat capac-
P
ity at constant pressure c , the body’s temperature is raised by dT and
P
dq mc dT (2.31)
P
P
where c is a function of T and P. Summing up the infinitesimal flows of heat, we get
P
the total heat that flowed as a definite integral:
T 2
q m c 1T2 dT closed syst., P const. (2.32)
P
P
T 1