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!

Homework Help: Final temperature real gas behaving ideally

  1. Mar 2, 2017 #1
    1. The problem statement, all variables and given/known data
    Please consider a mixture of oxygen (1 mole), nitrogen (4 mole), and carbon dioxide (3 mole). The mixture was heated in a well - insulated vessel with 753 kJ.

    Determine the final temperature if the mixture is composed of real gases behaving ideally as described by Eq. 3.48 truncated after the third term.
    Q=753000 J
    O2: α=3.626 β=-1.878 γ=7.055
    N2: α=3.675 β=-1.208 γ=2.324
    CO2: α=2.401 β=8.735 γ=-6.607
    R=8.314 kJ/(kmol*K)
    2. Relevant equations
    EQ 3.48: Q/nR=α(T2-T1)+1/2β(T22-T12)+1/3γ(T23-T13)

    3. The attempt at a solution
    I know all the α,β,γ values for O2, N2, and CO2.
    I know n=8 moles.
    but I don't know the values of α, β, and γ for the mixture.
    I thought of using a molar ratio of each element and multiplying that times each α, β, and γ then adding them all together but I wasn't sure if this was correct
  2. jcsd
  3. Mar 3, 2017 #2
    Yes, that's correct. Approximating the mixture as an ideal gas, the three components behave independently.
  4. Mar 4, 2017 #3

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    You will need to know the initial temperature.

    Just to follow up on Chester's point,

    ##\Delta Q = \Delta U = (n_1C_{v1}+n_2C_{v2}+n_3C_{v3})\Delta T = (n_1+n_2+n_3)C_{vmix}\Delta T##

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted