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: 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?

    but nRT=PV
    During isothermal compression
    P_1 V_1=P_2 V_2⇒PV is a constant

    In this case


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

    ⇒Q=PV∫_(V_2)^(V_1)▒〖0.253/V dV〗


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