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Thermodynamics, Heat transfer question

  1. Nov 22, 2005 #1
    I have done a series of thermodynamics questions covering heat transfer, internal energy, temperature pressure etc. I have a new one but im unsure how to start it, its unlclear whether i know certain things. I can do the question form looking back at pervious questions, if i knew how to start.

    0.36m cubed of air at a pressure of 1.1MN/m2 and 339k is given an energy of 3.4MJ by means of heating at a constant pressure. The air is then allowed to expand to a volume of 1.44m3 according to the law pv power of 12= a constant.

    For each process calculate the final temperature, the work tarnsfer and the change in internal energy.

    I am assuming the question is two parts, and therefore i dont know
    temperature two/final temp or volume 2. thats why im unsure how to get the final volume

    how would i find the final temperature in order to carry out the rest of the question?

    any help whould be great!
     
  2. jcsd
  3. Nov 22, 2005 #2

    mezarashi

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    Could you clarify on the "law pv power of 12 = a constant" part? Does this mean you have

    [tex]PV^1^2 = constant [/tex]
     
  4. Nov 23, 2005 #3
    Yes indeed



    Yes thats it. but i also made a mistake with my phrasing, i want to know the final temperature, not the final volume. The question asks for the final temperature. Im not sure because i dont know temp final but i also dont seem to know v2 either.
     
  5. Nov 23, 2005 #4

    mezarashi

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    I'd just like to note that I've never seen such a high gamma coefficient before :P
    Assume the ideal gas law holds at all times.
    For the first process, which is isobaric, we can write (as we always can):

    [tex]\Delta U = Q - W[/tex]

    Q is given, and [tex]W = \int P dV [/tex]
    where P is constant making it quite easy. The following calorimetric equation also holds at constant pressure [tex]Q = nC_p \Delta T[/tex]

    Using the ideal gas law, you can then find all the other parameters.

    Implicitly stated in the second process is that it is adiabatic, so that:

    [tex] PV^\gamma = constant[/tex]

    Combining with the ideal gas law, you can derive:

    [tex]T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1}[/tex]

    From the previous step you should have the initial temperature and volume. The final volume is given.
     
  6. Nov 23, 2005 #5
    Thanks should help

    Yes those all seem familiar, i have used them in questions but i am still not familiar with the thermodynamics physics enough to tackle any question straight off. i know enough once i get started, so thanks i think that will be fine. I let you know how i get on
     
  7. Nov 24, 2005 #6

    Gokul43201

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    I'm almost certain that "12" is a typo for "1.2"

    [itex]\gamma=12[/itex] is theoretically impossible.

    [tex]\gamma = C_p/C_v = 1 + \frac{R}{C_v} [/tex]

    But the equipartition theorem tells us that [itex]C_v = nR/2 [/itex], where n is an integer denoting the number of degrees of freedom that contribute to the internal energy. So, [itex]R/C_v = 2/n [/itex] and can be at most 2, so [itex]\gamma[/itex] can be no larger than 3.
     
  8. Nov 30, 2005 #7
    I now know that for the first part i need to get final temperature then put it into u=mCVdt dt=(t2-t1) cv=0.718 then Q=U+W I think w is simply the enrgy stated at the start 3.4 MJ = 3400KJ so Q=U+3400KJ then i find change in internal enrgy with:
    can anynone tell me whether this is right. I am still unsure how to get the final temperature for process one too. I am struggling as it seems i dont know v2 for process one or t2, are either of them just the same as the v1 or v2?
     
  9. Nov 30, 2005 #8
    ps yes its right there was a typo its was pv 1.2 not 12
     
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