BioPHYSICAL chemistry

CHAPTER 3 SECOND LAW OF THERMODYNAMICS 65

Since each term has a logarithm, this equation reduces to:

or (db3.11)

Tfinalc Vinitial=Tinitialc Vfinal

If lnx=lnythen ln(x/y) =1 and x=y

For the Carnot cycle, the products are:

VAThotc =VDTcoldc and VCTcoldc =VBThotc (db3.12)

Dividing these two expressions gives:

VAThotc =VDTcoldc and VCTcoldc =VBThotc

(db3.13)

Consequently, we can substitute these volume ratios into the expression for the heat flow
(eqn db3.4):

(db3.14)

VT

VT

VT

VT

Ahot

c

Bhot

c

Dcold

c

Ccold

= c or

VV

V

V

V

A

B

D

C

=

T

T

V

V

nal

initial

c

nal

initial

⎛ 33

⎝

⎜⎜

⎞

⎠

⎟⎟ =

⎛

⎝

⎜⎜

⎞

⎠⎠

⎟⎟

and

or

q

T

q

T

hot

hot

cold

cold

−= 0

q

q

nRT

V

V

nRT

V

V

hot T

cold

hot

b

a

cold

b

a

ln

ln

=

−

=−hhot

Tcold

qnRT

V

V

nRT

V

V

cold cold d nR

c

cold

a

b

==ln ln =− TT

V

cold V

b

a

ln

qnRT

V

hot hot V

b

a

= ln