Hi I am struggling answering this question, please try to answer my question ste
ID: 1817485 • Letter: H
Question
Hi
I am struggling answering this question, please try to answer my question step by step
with complete calculation and assumptions as fast as possaible. please make it fully detalied.
thank you so much
Appreciate it
qustion:
A 2 mm diameter, spherical air bubble is suspended in an insulating fluid . with a focused laser, the bubble is heated so that the bubble radius increases by 90% . For spherical bubble the pressure difference between the bubble and surrounding fluid is given by delta P = 2s/r , where s is the interfacial tension and r is the radius of the bubble . assuming the interfacial tension is constant at 0.70 N/m, the initial bubble temperature is 300K, and the surrounding fluid has a pressure of 100 kPa calculate (a) the mass of the bubble , (b) the final temperature of the bubble ,(c) the work done by the gas , and(d) the laser energy required to perform the expansion.
Additionally , is this is a realistic scenario?? Why? What assumption are most likely to fail? Note the volume of the bubble is related to the radius by V=(4/3)pr3
Explanation / Answer
initial pressure =100*1000+ 2*0.7/0.001 = 101400 Pa, n= no of moles = PV/RT =101400*(4/3 *pi*0.001^3)/8.314*300 = 1.703*10^-7
a) therefore mass of air inside bubble = ( 1.703*10^-7 ) * 29 = 4.938*10^-6 g = 4.938 micro gram
b)final radius = 0.001*1.9 = 0.0019 m
final P= 100*1000 + 2*0.7/0.0019 = 100736.842 Pa
therefore temperature = PV/nR = 100736.842 * (4/3 * pi * 0.0019^3) / 1.703*10^-7 * 8.314 = 2044.15 K
c) work done by the gas = P* delta V = (100*1000)(4/3*pi)(0.0019^3 - 0.001^3) = 2.45 mJ
d) as from first law of thermodynamics , change in internal energy = -work done by gas + heat given,
here change in internal energy = m*cp*delta T , here cp = air specific heat capacity (at 1200 K )= 1.173 KJ/kg-K, hence change in internal energy = 4.938*10^-6 * 1.173 *1000*(2044.15 - 300) = 10.1025 J , hence heat given = 10.1025 + 2.45 *10^-3 = 10.105J
d) This doesn't seem to be realistic scenario, because at such a higer temperature ( around 2000 K ) bubble would definitely burst off, here assumption for "surface tension to be constatnt" is making it unrealistic.