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Homework Help: Thermodynamic Processes

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data

    I can't aolve the following question:

    Two moles of an ideal monoatomic gas trebles its initial volume in an isobaric expansion from state A to state B. The gas is then cooled isochorically to state C and finally compressed isothermally until it returns to state A. The molar gas constant is R = 8.314 J mol–1K–1 and Boltzmann's constant is 1.38 × 10–23 JK–1.

    If state B corresponds to a pressure P=8 atm (1 atm = 1.013 × 105 Pa) and temperature T = 552°C, determine the temperature of the gas in state A.

    Correct answer= 275.0K


    2. Relevant equations

    [tex]W=nRT ln \left( \frac{V_i}{V_f} \right)[/tex]

    3. The attempt at a solution

    I know that in an isothermal process the energy transfet [tex]Q[/tex] must be equal to the negative of the work done on the gas; [tex]Q=-W[/tex]. So to find the Temprature I must use the equation

    [tex]W=nRT ln \left( \frac{V_i}{V_f} \right)[/tex]

    I'm told that the amount of gas trebles but I don't know the initial volume of the gas, so I'm not sure if I can use this equation.

    Another approach is maybe to find the change in temprature and then add it to the original temprature. So first I convert 552°C to Kelvins; 552+273.15=825.15 K. Then I want to use the equation [tex]Q=mc \Delta T[/tex]. But again I don't have the mass! What should I do? :confused:

    Is my method even correct?
     
  2. jcsd
  3. Apr 3, 2010 #2

    Andrew Mason

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    The volume at A is 1/3 of that at B. P is the same at A and B. Apply the ideal gas law to find T at A. It has to be 1/3 of the temperature at B.

    AM
     
  4. Apr 4, 2010 #3
    Hi,

    [tex] PV=nRT[/tex]

    [tex]\frac{PV}{T}=nR[/tex]

    [tex]\frac{P_i V_i}{T_i}=\frac{P_fV_f}{T_f}[/tex]

    [tex]\frac{V_i}{T_i}=\frac{V_f}{T_f}[/tex]

    [tex]\frac{v_i}{552}=\frac{3(V_i)}{T_f}[/tex]

    How am I supposed to evaluate Tf now when I don't know what the initial volume is?
     
  5. Apr 4, 2010 #4

    Andrew Mason

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    ?? Divide by Vi - it disappears. (You don't have to find the initial volume. You just need to know Vf/Vi = 3)

    [tex]\frac{V_i}{T_i}=\frac{V_f}{T_f}[/tex]

    [tex]\frac{T_f}{T_i}=\frac{V_f}{V_i} = 3[/tex]

    [tex]T_i = \frac{T_f}{3}[/tex]

    Further hint: temperatures have to be converted to.....

    AM
     
  6. Apr 5, 2010 #5
    Thanks a lot. :smile:
     
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