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Question

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of 1000C while the other one is kept at 00C. If the two are brought into contact, then, assuming no heat loss to the environment, the final temperature that they will reach is

A
500C
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B
Less than 500C
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C
More than 500C
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D
00C
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Solution

The correct option is C More than 500C
Let θ be the final common temperature.
Further, let sc and sh be the average heat capacities of the cold and hot (initially) bodies respectively (where sc < sh given)
From, principle of calorimetry,
heat lost = heat gained
sh(100°C θ )= scθθ=shsh+sc×100°C =100°C1+scsh1+scsh <2 (scsh<1)θ >100°C2 or θ >50°C

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