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Isothermic compression question. Need help

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data
    The question I am stuck on is "0.253 m of gas is compressed isothermally from a pressure of 1 bar until its volume is 0.0313 m. Calculate the heat energy transfer. "

    2. Relevant equations
    I understand that work done = Heat transfer because it is isothermal but the equation I have to work with is:

    Q=nRT ln V^2/V^1

    I don't want the answer to this because I would like to understand, I just don't know what nRT is and how on earth do I find T if it is not given in the answer.


    3. The attempt at a solution
    I have not attempted to answer yet
     
    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 26, 2011 #2
    What is your question?
    What are your relevant equations?
    Let's see your attempt at solution.
     
  4. Oct 26, 2011 #3
    Sorry about the post being incomplete (don't know what happened). I have now edited the original post.
     
  5. Oct 26, 2011 #4
    Hmm this question is bothering me. I definitely used to know how to do it.

    I know that in an isothermal compression nRT = P1V1 = P2V2 = constant. Maybe thats how you find T, since you know P1V1 is.

    EDIT: I think it is possible that this answer is correct because you're not subbing in a variable PV for NRT, you are subbing in P1V1, which are known, and known to be constant.
     
  6. Oct 30, 2011 #5
    The basic idea that you need to understand is

    W = [itex]\int^{1}_{2} P dv[/itex]


    P*V = n*R*T

    Here n is the number of moles of the gas, R is the Boltzmann gas constant and T is the temperature. For an isothermal gas of fixed mass, n, R, and T are all constants. Therefore

    P = (n*R*T) / V


    [itex]\int^{1}_{2} P dv[/itex]
    = [itex]\int^{1}_{2} (n*R*T) / V dv[/itex]
    = [itex](n*R*T)*\int^{1}_{2} 1 / V dv[/itex]
    = [itex](n*R*T) * ln (v_{2}/v_{1})[/itex]

    Although I am not sure how you can find T, you can surely find n*T as you know the volume pressure and R you can use the equation PV = nRT to get n*T. That value you can use in your equation to find your answer

    And the relationship PV = nRT comes from the ideal gas relationships which state that

    [itex]\frac{P_1*V_1}{T_1} = \frac{P_2*V_2}{T_2}[/itex]

    As this relationship is true we can say for every mole of gas

    [itex]\frac{P_1*V_1}{T_1} = \frac{P_2*V_2}{T_2} = K[/itex]

    This constant K is the Boltzmann gas constant R, and n is the number of moles of the gas.
     
  7. Nov 2, 2011 #6
    Ok thanks for the info guys, I had a go at the question and this is what I came up with. What do you think?

    Q=W=nRT∫_(V_2)^(V_1)▒PdV
    but nRT=PV
    Q=PV∫_(V_2)^(V_1)▒PdV
    During isothermal compression
    P_1 V_1=P_2 V_2⇒PV is a constant

    In this case

    PV=0.253

    ⇒P=PV/V=0.253/V⇒P_2=0.253/V_2 =7.167Bar


    ⇒Q=PV∫_(V_2)^(V_1)▒〖0.253/V dV〗

    ⇒Q=PV[0.253lnV]_0.0313^0.253
    ⇒Q=0.253(0.253ln0.253-0.253ln0.0313)

    ⇒Q=0.253(0.253ln0.253-0.253ln0.0313)
    ⇒Q=0.192
     
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