Heat and Thermodynamics Problemsets and Solutions

Problem 1:

Two balloons have been filled up with air under atmospheric pressure to volumes V₁ and V₂, respectively.  They are now submerged under water.  A thin string of length L, which is run through a pulley at a fixed depth H, connects the balloons.  (The radii of the pulley and the balloons are much smaller than the length of the string.)  By setting the initial positions of the balloons, one can achieve a state of equilibrium.  Neither balloon is rising or going down.  Determine the difference in the depth of the balloons (in terms of H and L) under those conditions.  The mass of the balloon skins, of the string, and of the air is negligible.  The temperature of the water is constant and equal to the temperature of the air.

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