- #1
rg2004
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I'd just like to check my answer, it seems too big
Air initially at 20◦C is compressed by a factor of 15.
What is the final temperature assuming that the compression is adiabatic and [tex]\gamma[/tex] ≈ 1.4 the value of [tex]\gamma[/tex] for air in the relevant range of temperatures? By what factor does the pressure increase?
PV[tex]\gamma[/tex]=constant
TV[tex]\gamma[/tex]-1=constant
V1/15=V2
T1V1[tex]\gamma[/tex]-1=T2V2[tex]\gamma[/tex]-1
293.15*V1[tex]\gamma[/tex]-1=T2*V1/15
293.15*15[tex]\gamma[/tex]-1=T2
293.15*15.4=T2
T2=866.017 kelvinP1V1[tex]\gamma[/tex]=P2V2[tex]\gamma[/tex]
P1V1[tex]\gamma[/tex]=P2V1/15[tex]\gamma[/tex]
P1*15[tex]\gamma[/tex]=P2
thus P2 increased by a factor of 44.31does it look right?
Homework Statement
Air initially at 20◦C is compressed by a factor of 15.
What is the final temperature assuming that the compression is adiabatic and [tex]\gamma[/tex] ≈ 1.4 the value of [tex]\gamma[/tex] for air in the relevant range of temperatures? By what factor does the pressure increase?
Homework Equations
PV[tex]\gamma[/tex]=constant
TV[tex]\gamma[/tex]-1=constant
The Attempt at a Solution
V1/15=V2
T1V1[tex]\gamma[/tex]-1=T2V2[tex]\gamma[/tex]-1
293.15*V1[tex]\gamma[/tex]-1=T2*V1/15
293.15*15[tex]\gamma[/tex]-1=T2
293.15*15.4=T2
T2=866.017 kelvinP1V1[tex]\gamma[/tex]=P2V2[tex]\gamma[/tex]
P1V1[tex]\gamma[/tex]=P2V1/15[tex]\gamma[/tex]
P1*15[tex]\gamma[/tex]=P2
thus P2 increased by a factor of 44.31does it look right?