Q30 of 67 Page 98

The three rods shown in figure have identical geometrical dimensions. Heat flows from the hot end at a rate of 40 W in the arrangement

(a) Find the rates of heat flow when the rods are joined as in arrangement (b) and in (c). Thermal conductivities of alumimium and copper are 200 W m–1 °C–1 and 400 W m–1 °C–1 respectively.



(a).Let’s redraw the diagram


w10.png


Since all rods are connected in series,


Req = RAl + RCu + RAl


Given -


Temperature of the hot end ,T1 = 100°C


cold end ,T2 = 0°C


Substitution for Req –


Req =


Given Thermal conductivities of aluminium =200 W m–1 °C–1


Copper = 400 W m–1 °C–1


Therefore


Req = + + ) =


Now rate of flow of heat,


=


= (1)


Given rate of flow of heat


From (1)


40 = 80 × 100 ×


⇒ (2)


(b) Lets redraw the diagram –


w11.png


The equivalent circuit in terms of thermal resistances becomes-


w12.PNG


Req = RAl +


= ++


=


=


Now rate of flow of heat,


=


= (3)


From (2)


Substituting in (3)


=


= 75 W


(c) Lets redraw the diagram-


w13.PNG


Since the thermal resistors are connected in parallel.


= + +


⇒ =


⇒ = (Al + Al +Cu ) = (200+200+400)


⇒ = *(800)


⇒ =


From (2)


⇒ =


⇒ = 400W


More from this chapter

All 67 →
28

A room has a window fitted with a single 1.0 m × 2.0 m glass of thickness 2 mm.

(a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32°C and that outside is 10°C.


(b) The glass is now replaced by two glass panes, each having a thickness of 1 mm and separated by a distance of 1 mm.


Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J s–1m–1 °C–1and that of air = 0.025 J s–1m–1 °C–1.


 29

The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.


 31

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length cross-sectional area and thermal conductivity of each rod are ℓ, A and K respectively. The ends A, E and F are maintained at temperatures T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, final the temperature at B.


 32

Seven rods A, B, C, D, E, F and G are joined as shown in figure. All the rods have equal cross-sectional area A and length ℓ. The thermal conductivities of the rods are KA = KC = KD, KD = 2KD, KE = 3KD, KF = 4KD and KD = 5KD. The rod E is kept at a constant temperature T1 and the rod G is kept at a constant temperature T2(T2> T1).

(a) Show that the rod F ahs a uniform temperature T = (T1 + 2T2)/3.


(b) Find the rate of heat flowing from the source which maintains the temperature T2.