A uniform steel rod has length l at 0ºC. Now one of its end is kept in ice (0°C) and the other end is kept in steam (100ºC). If the coefficient of thermal expansion of the rod is a, how much is the th

Question

A uniform steel rod has length l at 0ºC. Now one of its end is kept in ice (0°C) and the other end is kept in steam (100ºC). If the coefficient of thermal expansion of the rod is a, how much is the thermal expansion of the rod at steady state?

TestHub · Accepted Answer

The temperature varies linearly along the rod from $0^{\circ} C$ to $10 0^{\circ} C$ . The average temperature of the rod is $(0^{\circ} C + 10 0^{\circ} C) /2 = 5 0^{\circ} C$ .

The thermal expansion $Δ l$ is given by $Δ l = l α Δ T_{a vg}$ .

Here, $Δ T_{a vg} = 5 0^{\circ} C - 0^{\circ} C = 5 0^{\circ} C$ .

So, $Δ l = l α (50) = 50 l α$ .

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