1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Adiabatic compression of air

  1. Sep 6, 2010 #1
    I'd just like to check my answer, it seems too big

    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations

    PV[tex]\gamma[/tex]=constant
    TV[tex]\gamma[/tex]-1=constant

    3. 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 kelvin


    P1V1[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 44.31


    does it look right?
     
  2. jcsd
  3. Sep 6, 2010 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Looks right. You can also use the ideal gas law to find final pressure:

    [tex]nR = P_1V_1/T_1 = P_2V_2/T_2[/tex]

    [tex]P_2/P_1 = T_2V_1/T_1V_2 = \frac{866*15}{293} = 44.3[/tex]

    AM
     
  4. Sep 6, 2010 #3
    Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Adiabatic compression of air
Loading...