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Pressure and temperature changes adiabatically for an ideal gas?

  1. Nov 23, 2005 #1
    Question:

    An ideal gas, which is initially at a pressure of 4.05 atm and a temperature of 355 K is permitted to expand adiabatically to 1.51 times its initial volume.

    A.
    Find the final pressure if the gas is monatomic.

    I was thinking [tex]P_i \cdot V_i = P_f \cdot V_f[/tex]. But, I made no use of the information that the gas is monatomic. Later on, a question asks for the final pressure if the gas is diatomic. Well, my starting point wouldn't distinguish between the two, so it's not right.
     
  2. jcsd
  3. Nov 23, 2005 #2

    mezarashi

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    I would suppose you need to use the law for adiabatic expansion of an ideal gas. Of course, the ideal gas law holds as well.

    [tex]PV^\gamma = constant[/tex]

    Being monoatomic, the values for Cv and Cp are [tex]C_v = \frac{3}{2}R, C_p = C_v + R[/tex], which allows you to find gamma, as [tex]\gamma = \frac{C_p}{C_v}[/tex].
     
  4. Nov 23, 2005 #3

    Chi Meson

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    The reason you can't use [tex]P_i \cdot V_i = P_f \cdot V_f[/tex] is becuase the temperature does not remain constant.
     
  5. Nov 23, 2005 #4
    Thanks mezarashi, that is what I needed.

    Chi Meson, thanks for reminding me that temperature is not constant.
     
  6. Apr 25, 2010 #5
    Can someone explain this further? I don't understand what to use for gamma
     
  7. Apr 25, 2010 #6
    mezarashi had it right - gamma is the ratio of Cp / Cv.

    Check your text for Cv of a monatomic ideal gas, and Cv of a diatomic ideal gas, then use the fact that Cp is Cv + R, for an ideal gas.
     
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