Single bubble sonoluminescence occurs when sound waves cause a bubble suspended in a fluid to collapse so that the gas trapped inside increases in temperature enough to emit light. The bubble actually undergoes a series of expansions and collapses caused by the sound wave pressure variations.
We now consider a simplified model of a bubble undergoing sonoluminescence. Assume the bubble is originally at atmospheric pressure P_{0}=101 \mathrm{kPa}. When the pressure in the fluid surrounding the bubble is decreased, the bubble expands isothermally to a radius of 36.0 \mu \mathrm{m}. When the pressure increases again, the bubble collapses to a radius of 4.50 \mu \mathrm{m} so quickly that no heat can escape. Between the collapse and subsequent expansion, the bubble undergoes isochoric (constant volume) cooling back to its original pressure and temperature. For a bubble containing a monatomic gas, suspended in water of T=293 \mathrm{~K}, find
a. the number of moles of gas in the bubble,
b. the pressure after the expansion,
c. the pressure after collapse,
d. the temperature after the collapse, and
e. the total work done on the bubble during the whole process.
You may find the following useful: the specific heat capacity at constant volume is C_{V}=3 R / 2 and the ratio of specific heat at constant pressure to constant volume is \gamma=5 / 3 for a monatomic gas.