1. Limited time only! Sign up for a free 30min personal 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 process

  1. Jul 28, 2012 #1
    1. The problem statement, all variables and given/known data
    In a diesel engine, the piston compresses the air-fuel mixture from an initial volume of 630 cm^3 to a final volume of 30cm^3. If the initial temperature of the air-fuel mixture is 45 degrees C and the process is occurring adiabatically, determine the final temperature. Comment on the significance of the result.


    2. Relevant equations
    V(initial) = 6.3x10^-4 m^3
    V(final = 3.0x10^-5 m^3
    T(initial) = 318.15 K
    T(final) = ?
    y = 1.4

    T(final) = T(initial)*(V(initial)/V(final))^y-1

    3. The attempt at a solution

    T(final) = 318.15(6.3x10^-4/3.0x10^-5)^0.4
    T(final) = 1075.28 K or 802.13 degrees C


    Is that on the right track? I found the equation online but I am a little confused how the equation is actually formed from T(f) = P(f)*V(f) / nR which I have in my textbook.
     
  2. jcsd
  3. Jul 29, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    During an adiabatic process, no heat exchange occurs, so the change of internal energy is do to the work alone: dU=-PdV. PV=nRT is valid but the temperature and pressure changes during the process: [itex]P=nRT/V[/itex]. For an ideal gas, the internal energy is [itex]U=nC_vT[/itex], [itex]dU=nC_vdT[/itex], so [itex]nC_vdT=-(nRT/V) dV[/itex]. n cancels. Collect the like terms and integrate

    [tex]\int{\frac{dT}{T}}=\int{-\frac{R}{C_v}\frac{dV}{V}}[/tex]

    [tex] \ln(T)=-\frac{R}{C_v} \ln(V) +const[/tex].

    R/Cv can be written in terms of γ=Cp/Cv: [itex]\frac{R}{C_v}=\gamma -1[/itex].

    You can rewrite the equation as [tex] \ln(TV^{\gamma-1})=const [/tex],

    that is [tex]TV^{\gamma-1}=const[/tex] .

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Adiabatic process
  1. Adiabatic process (Replies: 2)

  2. Adiabatic Process (Replies: 1)

  3. Adiabatic process (Replies: 8)

Loading...