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Homework Help: Change in Vrms, given initial P and V, find energy added.

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data
    One mole of an ideal diatomic gas with [itex]C_{v} = \frac{5R}{2}[/itex] occupies a volume [itex]Vi = 2.14 m^{3}[/itex] at a pressure [itex]P_{i}=1 atm[/itex]. The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process, it is found that the rms speed of the gas molecules has doubled from its initial value. Determine the amount of energy transferred to the gas by heat.

    2. Relevant equations
    ? (If I knew this, I wouldn't be here)

    3. The attempt at a solution
    With some searching, I found the equations [itex]V_{rms} = \sqrt{\frac{3RT}{M}}[/itex] and [itex]Q = MC_{v}\Delta T[/itex]

    Where [itex]Q[/itex] is a change in energy, [itex]V_{rms}[/itex] is the average rms velocity, [itex]T[/itex] is temperature, [itex]M[/itex] is Molar Mass, and [itex] \Delta T[/itex] is change in temperature.

    With some substitution, we eventually found that we can get;
    [itex]Q = M^{2}V_{rms_{initial}}^{2} \frac{5}{2}[/itex]

    Which... Doesn't help at all. So, yeah.

    The question mentions that the pressure is proportional to the volume, but I'm still a bit confused about PV diagrams, and why everything doesn't stay on Isotherms, so I'm really not sure what it means when it says that pressure is proportional to volume. Does it mean [itex]kP = V[/itex] or [itex]\frac{P}{V} = 1[/itex], or what? So... Yeah.
  2. jcsd
  3. Jan 28, 2014 #2
    Problem solved. Got some unexpected help.
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