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Two systems merging, what is final temp?

  1. Nov 2, 2013 #1
    Hi all,

    I just want to see if my work is correct because it's not matching the answer in the book:


    A tank has a volume of 0.1 [itex]m^3[/itex] and is filled with He gas at a pressure of [itex]5x10^6[/itex] Pa. A second tank has a volume of 0.15 [itex]m^3[/itex] and is filled with He gas at a pressure of [itex]6x10^6[/itex] Pa. A valve connecting the two tanks is opened...

    (My problem references this question and asks...)

    If the temperatures within the two tanks before opening the valve, had been T = 300K and 350 K respectively, what would the final temperature be?


    So what I did was utilize this equation:
    [tex]
    U = cNRT
    [/tex]
    to find the energies of each. Based off of the 'adiabatic and rigid' statement given I know no energy is lost to heat flow or work on the walls.

    I get energies for the respective systems of 3741 J and 4365 J. Adding those together I get 8106.
    Now I just plug that number back into the former equation (this time manipulated):
    [tex]
    T = \frac{U}{cNR}
    [/tex]

    And I'm getting a temp of 324.9 K. The book says 330 K. Need some help, am I wrong or is this a misprint?

    Thanks.
     
  2. jcsd
  3. Nov 2, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Using PV = nRT and assuming PV is proportional to the energy content I find that the book's value is reasonable...
     
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