The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?
Given:
Temperature difference between the ends of the meter stick AB:
ΔT = T2-T1 = 100-0 = 100 °C
Temperature of one end of the rod: T3 = 25 °C
Length of the rod : l = 1 m
Here, C is the point at which the other end of the rod is placed.
Distance between A and C = x
Distance between C and B = 1-x
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.
Now, for zero heat current in the rod, the temperature difference must be zero: ΔT = 0.
Since one end of the rod is maintained at 25 °C, the other end must be maintained at 25 °C.
Hence heat current between A and C must be equal to the heat current between C and B
Here (ΔT)AC and (ΔT)CB is the temperature difference between AC and BC respectively.
∴ 75(1-x) = 25x
∴ 75 -75x = 25x
∴ 75 = 100x
∴ x = 75/100
∴ x = 0.75 m
Hence, in order to have zero heat current through the rod the other end of the rod must be placed at a distance of 0.75 m from the end at 100 ° C.