Q25 of 67 Page 98

Figure shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20 cm and area of cross-section 0.20 cm2. The junction is maintained at a constant temperature 40°C and the two ends are maintained at 80°C. Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivities are KAl = 200 W m–1°C–1andKCu = 400 W m–1 °C–1.



Given –


Length of each rod of 20 cm = 0.2m



Area of cross-section 0.20 cm2


= 2 × 10-5 m2


Junction temperature = 40°C


End temperature = 80°C


The conductivities of Aluminum and copper,KAl=200 W m–1 °C–1


And KCu = 400 W m–1 °C–1.


Now ,total heat drawn per second –


= Heat drawn due to copper rod + heat drawn due to Aluminium rod


= QAl + QCu


We know, rate of heat absorption by the rod of length l, area A is given by


Q =


Where is the change in temperature


= +


⇒ Q = 2.4 J


Heat drawn in 1 minute = 2.4 × 60 = 144J


Hence, amount of heat taken out from the cold junction in one minute after the steady state is reached is 144J


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23

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross-sectional area. The free end of the copper rod is kept at 0°C and that of the steel rod is kept at 100°C. Find the temperature at the junction of the rods. Conductivity of copper = 390 W m–1 °C–1 and that of steel = 46 W m–1 °C–1.


 24

An aluminium rod and a copper rod of equal length 1.0 m and cross-sectional area 1 cm2 are welded together as shown in figure. One end is kept at a temperature of 20°C and the other at 60°C. Calculate the amount of heat taken out per second from the hot end. Thermal conductivity of aluminium = 200 Wm–1 °C–1 and of copper = 390 Wm–1 °C–1.


 26

Consider the situation shown in figure. The frame is made of the same material and has a uniform cross-sectional are everywhere. Calculate the amount of heat flowing per second through a cross-section of the bent part if the total heat taken out per second from the end at 100°C is 130J.


 27

Suppose the bent part of the frame of the previous problem has a thermal conductivity of 780 J s–1m–1 °C–1, whereas it is 390 J s–1m–1°C–1for the straight part. Calculate the ratio of the rate of hat flow through the bent part to the rate of heat flow through the straight part.