Physics - Thermodynamics | Question and Answer

Contents
Question 1..................................................................................................................................1
Part A.....................................................................................................................................1
Part B......................................................................................................................................2
Part C......................................................................................................................................2
Part D.....................................................................................................................................3
Question 2..................................................................................................................................4
Part A.....................................................................................................................................4
Part B......................................................................................................................................5
Question 3..................................................................................................................................5
Part A.....................................................................................................................................5
Part B......................................................................................................................................6
Part C......................................................................................................................................6
Question 4..................................................................................................................................7
Part A.....................................................................................................................................7
References..................................................................................................................................8

Question 1
Part A
Heat transfer occurs from higher temperature to lower temperature. Thus heat flow direction
is from the surface at which temperature is T2 to the surface at which temperature is T1. ‘k’
is the thermal conductivity of the material, ‘A’ is the area perpendicular to the direction of
heat transfer and ‘dx’ is the thickness of the solid body.
According to Fourier law of heat conduction heat transfer by conduction is expressed as
Q = -kA ∆ T
∆ x and ∆ T = T1-T2
Part B
Thermal resistance is the resistance to heat flow. The thermal resistance can be compared
with electrical resistance. The modification of the Fourier law can be written as
Q = -
∆ T
( ∆ x
kA ) . Thus the heat transfer is written as the ratio of driving force and thermal
resistance. Comparing with electrical resistance current is the ratio of voltage and electric
resistance. Thue thermal resistance is written as
R_thermal = ( ∆ x
kA )
Part C

The total thermal resistance of the following system is
∑ Rthermal=∑ Rconduction+∑ Rconvection
∑ Rthermal = 1
h1 A1
+ L1
k1 A1
+ L2
k2 A2
+ 1
h2 A2
Since the area is the same
∑ Rthermal = 1
h1
+ L1
k1
+ L2
k2
+ 1
h2
Part D
The thermal resistance of the whole system is expressed as
R1 = ∆ x
kA = 0.01/2.5/0.12 = 0.033 C/W
R2 = ∆ x
kA = 0.05/18/0.04 = 0.156 C/W
R3 = ∆ x
kA = 0.05/7/0.04 = 0.1785 C/W