Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 31

Hint: K is the boiling temperature of liquid nitrogen at

atmospheric pressure.Oxygenboils at a higher temperature.

4.61 Air Bubble Coalescence (Moscow Phys-Tech)

A tightly closed jar is completely filled with water. On the bottom of the

jar are two small air bubbles (see Figure P.4.61a) which sidle up to each

other and become one bubble (see Figure P.4.61b). The pressure at the top

of the jar is the radius ofeachoriginal bubble is and the coefficient

of surface tension is Consider the process to be isothermal. Evaluate

the change of pressure inside the jar upon merging of the two bubbles.

4.62 Soap Bubble Coalescence (Moscow Phys-Tech)

Two soap bubbles and of radii and become one bubble of

radius Find the surface tension coefficient for the soap solution. The

ambient pressure is

4.63 Soap Bubbles in Equilibrium (Moscow

Phys-Tech)

Two soapbubbles ofradius areconnected by a thin“straw” of negli-
gible volume compared to the volume of the bubbles (see Figure P.4.63).
The ambient pressure is the temperature is and the surfacetension
coefficient is

Is this system in stableequilibrium?What is the finalstate?

Calculate the entropychange between thefinal-stateconfiguration

and the configuration in FigureP.4.63.Assume

a)

b)