Q. 10

The left end of a copper rod (length = 20 cm, area of cross-section = 0.20 cm2) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation, find

(a) the temperature at a point 11 cm from the left end and

(b) the heat current through the rod. Thermal conductivity of copper = 385 W m–1 °C–1.

Answer :

Length of the rod: x = 20 cm =0.2 m
Area of cross section of the rod: A = 0.2 cm2 = 0.2× 10-4 m2.
Temperature at left end : T2 = 20° C
Temperature at right end : T1 = 80° C
Thermal conductivity of copper: K = 385 W m–1 °C–1.

Distance of point C from left end : x’ = 11cm = 0.11 m
Formula used:
Rate of amount of heat flowing or heat current is given as:

Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness or length of the material.
Transfer of heat due to entire rod is,

Hence, heat current in the rod is 2.31 J/s
Let T be the temperature at point C.
T>T2 as heat flows from High temperature to low temperature.
Substituting we get,

Hence, temperature at a distance of 11 cm from the left end is 53 °C.

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