2011 Semifinal Exam Part A 3 Part A Question Al 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 bub- ble is originally at atmospheric pressure Po =101 kPa.When the pressure in the fluid surrounding the bubble is decreased,the bubble expands isothermally to a radius of 36.0 um.When the pressure increases again,the bubble collapses to a radius of 4.50 um 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 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 Cy =3R/2 and the ratio of specific heat at constant pressure to constant volume is y=5/3 for a monatomic gas. Solution We consider the bubble to be filled with an ideal monatomic gas,so originally:PoVo =nRTo. The bubble undergoes 3 processes:1)isothermal expansion,2)adiabatic collapse (no heat escapes),and 3)isochoric (constant volume)cooling.The final process is isochoric,so we know that the bubble's collapsed volume is equal to its original volume,so 2=%, and PoVo=PoV2 nRTo. Rearranging, PoV2 n= RTo 乃π3 n= RTo 0量·新~(4.50×10-6m3 101,000 3.86×10-11 n= moles 8.31m0K293K 2430 Copyright C2011 American Association of Physics Teachers2011 Semifinal Exam Part A 3 Part A Question A1 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 bub￾ble is originally at atmospheric pressure P0 = 101 kPa. When the pressure in the fluid surrounding the bubble is decreased, the bubble expands isothermally to a radius of 36.0 µm. When the pressure increases again, the bubble collapses to a radius of 4.50 µm 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 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 CV = 3R/2 and the ratio of specific heat at constant pressure to constant volume is γ = 5/3 for a monatomic gas. Solution We consider the bubble to be filled with an ideal monatomic gas, so originally: P0V0 = nRT0. The bubble undergoes 3 processes: 1) isothermal expansion, 2) adiabatic collapse (no heat escapes), and 3) isochoric (constant volume) cooling. The final process is isochoric, so we know that the bubble’s collapsed volume is equal to its original volume, so V2 = V0, and P0V0 = P0V2 = nRT0. Rearranging, n = P0V2 RT0 n = P0 4 3 πr3 2 RT0 n = 101, 000 N m2 · 4 3 π · (4.50 × 10−6 m)3 8.31 J mol·K · 293 K = 3.86 × 10−11 2430 moles Copyright c 2011 American Association of Physics Teachers