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Work done by a heat engine - quick issue with units used in the solution

  1. Jun 3, 2009 #1
    1. The problem statement, all variables and given/known data

    "A gas storage system contains oxygen at a pressure of 5 atmospheres at 300 K.
    (Here, you may assume that oxygen behaves as an ideal gas.) The volume of the
    cylinder is initially 150 L. (State 1.) In a fire the gas is initially heated by 200 K,
    with a safety system keeping the pressure constant (state 2). A sprinkler system
    then reduces the temperature to 280 K but the volume does not change because the
    safety mechanism has jammed (state 3). The gas is then slowly compressed back to
    150 L as the safety mechanism unsticks with the temperature staying constant (state
    4). Finally, the sprinklers stop and the system warms up at constant volume to
    300 K so that it is back in state 1."

    (i) Sketch these processes on a pV diagram showing the numerical values of
    p, V and T in each of the 4 states. {5}
    (ii) What is the net work done by the oxygen? (You may assume that Cp and Cv
    are independent of temperature.) {5}


    2. Relevant equations

    pV=nRT

    equations for work with isothermal processes (don't bother with the constant pressure, it's just the area of the rectangle)

    i.e W = nRT ln (V2/V1)


    3. The attempt at a solution

    Now, i'm happy about the first part (i plotted the diagram correctly). I did forget that i could use the relationships that P1/T1 = P2/T2 etc, but i used the ideal gas equation to work out all the bits individually and they were mostly the same as the answer scheme (only one rounding error - 4.71 calculated against 4.67 exact).

    However, the lecturer does some really funny things on his mark scheme. First and foremost, he uses litres in all his volume calculations.

    I know all the data from state 1 to work out the number of moles of oxygen in the system, so i said that:

    V = 150L = 0.15m^3, P = 5atm = 5*1.01*10^5 Pa, T = 300K given

    Plugging this into the ideal gas equation gives just over 30 moles by my calculation. However, when i went back to mark the exam paper with the supplied solutions, i noticed that the lecturer had used litres in almost all his workings - giving far more moles of oxygen than i got (factor of 1000 roughly). This also meant that the total work done by his calculations was something like 15GJ, which seems ludicrously high. It just seems odd that'd he'd make such a "schoolboy" error, so i wondered whether i was at fault. In theory the results should be the same, regardless of what volume measurement you use (and as far as i understand the volume of a litre of substance doesn't depend on the substance!)?

    Please note that i'm not concerned with the actual answer, i'm confident that my working is sound even if the numbers are off.

    Question: Am i right to say that you must convert to SI units before plugging into the ideal gas equation (i.e. metres rather than litres)?
     
    Last edited: Jun 3, 2009
  2. jcsd
  3. Jun 3, 2009 #2

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes. Everything must be consistent. If everything else is in SI units, your volume should be in SI units. A litre is a cubic decimetre. So you could use litres IF you converted all of your other units to a system that uses a decimetre as the unit of length. Otherwise, no.
     
  4. Jun 3, 2009 #3
    Thanks :)

    Hah i really hope he didn't mark everyone down last year because of that!
     
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