Marandsnoteschapter3thesecondlawofthermodynamics 123

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Unformatted text preview: ce
between
temperatures
TA
and
TB
is
accompanied
by
a
 change
in
entropy
ΔSm.
 ΔSm = TB ∫ TA T T B BC δqP dHm Pm ( T) =∫ =∫ dT 
 T T T T T A A where
Cpm
is
the
molar
heat
capacity
at
constant
pressure
of
that
 € substance.
Obviously,
the
above
equation
is
only
valid
if
that
substance
 does
not
exhibit
a
phase
change
between
the
temperatures
TA
and
TB.

The
 above
equation
can
be
generalized
to
describe
the
change
in
entropy
for
 Marand’s
Notes:
Chapter
3
‐
The
Second
Law
of
Thermodynamics
 111
 one
mole
of
a
pure
substance,
when
it
is
heated
at
constant
pressure
 between
0
K
and
a
temperature
T.
If
we
assume
that
at
temperature
T
the
 substance
is
in
the
vapor
phase,
then
the
change
in
entropy
between
0
K
 and
T
is
given
at
the
standard
pressure
by:
 ΔS∅ m = S∅ m (T) − S∅ m Tfus (0) = ∫ 0 C S ( T) Pm T Tb CL ( T) Δ fusH∅ dT + + ∫ Pm dT Tfus T T fus T ∅ + Δ vapH Tb + ∫ Tb C V Pm ( T) T 
 dT where
Tfus
and
Tb
are
respectively
the
melting
(fusion)
temperature
of
the
 € substance
in
the
solid
state
and
the
boiling
(vaporization)
temperature
of
 the
substance
in
the
liquid
state
at
the
standard
pressure,
PØ.
In
the
above
 equation,
the
quantities
CPmS,
CPmL
and
CPmV
are
the
molar
heat
capacities
at
 constant
pressure
(P
Ø)
for
the
solid,
liquid
and
vapor
phases,
respectively.

 Calorimetric
measurements
allow
us
to
measure
specific
heat
capacities
as
 a
function
of
temperature
(for
temperatures
above
a
few
kelvins)
as
well
as
 latent
heats
of
phase
transformation
(standard
enthalpy
of
fusion
and
 va...
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