Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 167

where is thehydrostatic pressure ( is the height of the water). We

disregard anyeffects due to the finitesize of thebubblesincethey are

small After merging, thepressureinside thenew bubblewill not

change. This is due to the fact that the temperature is constant, and since

the jar is closed and water is incompressible,the total volumealsowill not

change. The new radius isgiven by

Writing(S.4.61.1) for the newbubble, we obtain

where we disregard any small change in hydrostatic pressure. From

(S.4.61.1) and (S.4.61.3) we findthat thechange ofpressure inside the

jaris

4.62 Soap Bubble Coalescence (Moscow Phys-Tech)

Assumethat, during thecoalescence, thetotal mass of airinside the bubbles

and the temperature do not change. So,

where are themasses of airinsidebubbles respec-
tively. By theideal gaslaw,

where is themass, is thepressure, and is the volume in

theithbubble, and is the molar mass of thetrapped air. The equilibrium

condition for a bubble is