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A heavy piston supported by a spring inside a vertical cylindrical container is in equilibrium with only a tiny gap above the container bottom after all air is pumped out (Diagram 1). When gas at temperature T is introduced under the piston, it rises to height h (Diagram 2). If the gas is then heated to temperature 2T, what is the new height of the piston above the container bottom?

1. h
2. 2h
3. 3h
4. 4h

Correct answer: 3h

Solution

In vacuum, spring supports piston: k*x0 = Mg (spring compressed by x0 from natural length, pushing piston up). When gas at T is added and piston rises by h: gas pressure P1*A = Mg + k*delta where delta is additional spring compression or extension. Using ideal gas law and force balance, heating to 2T gives height 3h.

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