Question
Following 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 conductivites are KAt = 200 W m−1°C−1 and KCu = 400 W m−1°C−1.
Solution
Area of cross section, A = 0.20 cm2 = 0.2 × 10–4 m2
Thermal conductivity of aluminium, KAl = 200 W/m °C
Thermal conductivity of copper, KCu = 400 W/m°C
Total heat flowing per second = qAl + qCu
`= (K_{AI}xxAxx(80xx40))/l +(K_{cu}xxAxx(80xx40))/l`
`=(200xx0.2xx10^-4xx40)/0.2 + (400xx0.2xx 10^-40)/0.2`
`= 8 xx 10^_1 + 16xx10^_1`
`=24xx10^_1`
`=2.4 ` J/s
Heat drawn in 1 minute = 2.4 × 60 = 144 J
