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Variation of Kinetic Energy with temperature

  1. Jun 14, 2012 #1
    Question:

    Find the total kinetic energy per unit volume in a monoatomic gas at standard temperature and pressure and deduce an expression for the variation of this kinetic energy with temperature if the pressure is maintained constant. [Standard pressure = 1.01E5 Pa]

    Attempt:

    Pressure of a gas
    [itex]pV= \dfrac{N_A m <c>^2}{3V}V[/itex]
    [itex]\dfrac{M<c>^2}{2} = 3pV/2[/itex]
    where M = NAm
    [itex]E_k /V = 3p/2[/itex]
    [itex]E_k /V = 1.52x10^5 J/m^3[/itex]

    Variation of this Ek with temperature is pressure is maintained constant:
    [itex]E_k = 3pV/2[/itex]
    [itex]E_k = 3(nRT)/2[/itex].

    Comments: For the "Variation of this Ek with temperature is pressure is maintained constant", is that all that I should show? What other comments should I include to make my working more accurate?

    The guide mentioned:
    How so? can anyone please explain the bold sentence to me? Thank you!
     
  2. jcsd
  3. Jun 15, 2012 #2
    Kinetic energy given by 3kNT/2 is for one mole of the gas at a given volume. So, I think that refers to the expansion of gas with the rise in temperature. The number of molecules per unit volume at a temperature T1 will be lesser that the number of molecules per unit volume at temperature T2 < T1.
     
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