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Q.

Consider two identical iron spheres A and B, A lies on a thermally insulating plate, whilst B hangs from an insulating thread as shown. Equal amounts of heat are given to the two spheres. Then

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a

Temperature of A is greater than that of B

b

Temperature of B is greater than that of A

c

A and B will have equal temperature

d

None of the above

answer is B.

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Detailed Solution

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As a result of thermal expansion, the size of both spheres increases. The centre of mass of the sphere lying on the plate rises, whilst that of the sphere hanging on the thread sinks. Thus, the potential energy of the first sphere increases, whilst that of the second one decreases as shown in the figure.

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According to the first law of thermodynamics, the heat transferred to the spheres produces not only an increase in internal energy and the small amount of work done in expanding against the atmospheric pressure (this is the same for both spheres), but also a change in gravitational potential energy. The potential energy of the sphere lying on the insulating plate increases a little, therefore its internal energy increases by less than the residual heat transferred. Conversely, the decrease in potential energy of the hanging sphere contributes positively to the increase in its internal energy. In summary, the temperature of the sphere suspended from the thread will be higher.

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