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kpw1
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An explosive liquid at temperature 300 K contains a spherical bubble of radius 5 mm, full of its vapour. When a mechanical shock to the liquid causes adiabatic compression of the bubble, what radius of the bubble is required for combustion of the vapour, given that the vapour ignites spontaneously at 1100 degrees C? That ratio of CV/(n*R) is 3.0 for the vapour.
I'm going to combine relevant equations and attempt at solution together because I'm not sure if the equations I'm using are the relevant ones to begin with.
So for reversible adiabatic changes in an ideal gas,
PV[tex]^{\gamma}[/tex] = constant
And if we put P = nRT/V into that equation, we get
TV[tex]^{\gamma-1}[/tex] = constant
The problem is, how am I supposed to know the n of the gas (how many particles)? I'm guessing I have to use the ratio CV/(n*R) somehow to also find [tex]\gamma[/tex]:
CV/nR = 3 (from above)
So
CV = 3nR
and
CP = CV + R
So
CP = 3nR + R
= (3n + 1)R
[tex]\gamma[/tex] = CP/CV
= [tex]\frac{(3n + 1)R}{3nR}[/tex]
= [tex]\frac{3n+1}{3n}[/tex]
And now I'm stuck again because I still don't know n
Any help/guidance would be appreciated. Thanks.
Also, this problem is from Introductory Statistical Mechanics 2nd ed. by Roger Bowley and Mariana Sanchez, Chapter 1, Problem 8
I'm going to combine relevant equations and attempt at solution together because I'm not sure if the equations I'm using are the relevant ones to begin with.
So for reversible adiabatic changes in an ideal gas,
PV[tex]^{\gamma}[/tex] = constant
And if we put P = nRT/V into that equation, we get
TV[tex]^{\gamma-1}[/tex] = constant
The problem is, how am I supposed to know the n of the gas (how many particles)? I'm guessing I have to use the ratio CV/(n*R) somehow to also find [tex]\gamma[/tex]:
CV/nR = 3 (from above)
So
CV = 3nR
and
CP = CV + R
So
CP = 3nR + R
= (3n + 1)R
[tex]\gamma[/tex] = CP/CV
= [tex]\frac{(3n + 1)R}{3nR}[/tex]
= [tex]\frac{3n+1}{3n}[/tex]
And now I'm stuck again because I still don't know n
Any help/guidance would be appreciated. Thanks.
Also, this problem is from Introductory Statistical Mechanics 2nd ed. by Roger Bowley and Mariana Sanchez, Chapter 1, Problem 8