Heat and Thermodynamics
Carnot's Theorem
The maximum efficiency of a heat engine depends only on the temperatures of source and sink and for given source and sink temperatures no heat engine can be more efficient than a reversible engine.
P-V diagram for the Carnot cycle:
The Carnot cycle can be represented on a graph of pressure against volume (a P-V diagram) as shown here.
D to A isothermal expansion at 
; work done by the gas
A to B adiabatic expansion; work done by the gas
B to C isothermal compression at 
; work done on the gas
C to D adiabatic compression; work done on the gas
The product of pressure and volume represents a quantity of work. This is represented by the area below a P-V curve.
The area enclosed by the four curves represents the net work done by engine during one cycle.
Coefficient of thermal conductivity:
(i) 
= 
Where K = coefficient of thermal conductivity
A = area of the hotter face
= temperature gradient = 
(ii) Units of K are 
= 
.
(iii) Dimensions of K are 
.
(iv) K denotes thermal conductivity, denotes dimensions of kelvin temperature.
Conducting slabs in series:
(i) Q = 
(ii) Cosider two slabs when 
= 
= x
Q = 
= 
Q = 
Equivalent thermal capacity = K = 
= 
= 
.
K is harmonic mean between 
and 
.
(iii) For two slabs, in general, K = 
Conducitng slabs in parallel:
(i) Q = 
Q = 
(ii) Equivalent thermal capacity = K.
et 
= 
= A
K = 
for two slabs. K is arithmetic mean between 
and 
.
(iii) Generally, for two slabs, K = 
.