Heating up
Consider two identical homogeneous balls, A and B, with the same initial temperatures. One of them is at rest on a horizontal plane, while the second one hangs on a thread (Fig). The same quantities of heat have been supplied to both balls.The final temperatures of which ball is more? (All kinds of heat losses are negligible.
Hint: The dimensions of the balls may change while heating.
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When the balls are warmed up, their mass centers are moving as the radii of the balls are changing. The mass center of the ball A goes down, while the mass center of the ball B goes up. It is shown in figure. Displacement of the mass center corresponds to a change of the potential energy of the ball in the gravitational field. In case of the ball A the potential energy decreases. From the 1st principle of thermodynamics it corresponds to additional heating of the ball. In case of the ball B the potential energy increases. From the 1st principle of thermodynamics it corresponds to some “losses of the heat provided” for performing a mechanical work necessary to rise the ball. The net result is that the final temperature of the ball B should be lower than the final temperature of the ball A