The ends of a metal bas of constant cross-sectional area are maintained at temperatures T1 and T2 which are both higher than the temperature of the surroundings. If the bar is unlagged, which one of the following sketches best represents the variation of temperature with distance along the bar?
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In an unlagged metal bar with ends at temperatures T1 and T2 (both > Tsurroundings), heat flows along the bar and is also lost to the surroundings from its sides. This lateral heat loss causes the temperature profile to be non-linear, curving downward. The temperature gradient is steeper near the cooler end (T2) because more heat is being conducted to compensate for the lateral losses along the entire length.
The correct sketch shows a concave downward curve, with the temperature decreasing non-linearly from T1 to T2.
Final Answer: The third image (with the concave downward curve).