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Heat capacities of a gas mixture.

  1. Jun 25, 2010 #1
    1. The problem statement, all variables and given/known data

    1 gram of Hydrogen [tex]H_2[/tex] and 1 gram of Helium [tex]He[/tex] are put together into a container of 10 L in volume and at a temperature of 27°C.

    (a) Find the pressure

    (b) Find the molar specific heat capacities [tex]C_v[/tex] and [tex]C_p[/tex], as well as [tex]\gamma = \frac{C_p}{C_v} [/tex] of this gas mixture.

    2. Relevant equations

    [tex]n = \frac{m}{M_{molar}}[/tex]

    [tex]PV = nRT [/tex]

    For a monoatomic gas

    [tex]C_v = \frac{3}{2}R [/tex]

    For a diatomic gas

    [tex]C_v = \frac{5}{2}R [/tex]

    For both monoatomic and diatomic gas

    [tex]C_p = C_v + R[/tex]

    [tex]\gamma = \frac{C_p}{C_v} [/tex]

    [tex]R = 8,31 \frac{J}{K.mol}[/tex]

    [tex]T_{kelvin} = T_{celsius} + 273 [/tex]


    3. The attempt at a solution

    (a)

    [tex]P = \frac{nRT}{V} [/tex]

    Now, the problem here is to find 'n' for the mixture, can I simply find the number of mols of each gas separately and then sum them up?

    [tex]n_{He} = \frac{1}{4} = 0.25 [/tex]

    [tex]n_{H_2} = \frac{1}{1} = 1 [/tex]

    [tex]n_{mixture} = n_{He} + n_{H_2} [/tex]

    So,

    [tex]P = \frac{1,25 \times 8,31 \times 300}{10} = 311,625[/tex]

    Is this correct?

    (b)

    In order to find out the molar heat capacity for the mixture, can I proceed just as before and work out them separately and them add them up?

    [tex]C_v (He) + C_v (H_2) = C_v (Mixture) [/tex]

    [tex]C_p (He) + C_p (H_2) = C_p (Mixture) [/tex]

    [tex]\gamma_{mixture} = \frac{C_p (He) + C_p (H_2)}{C_v (He) + C_v (H_2)} [/tex]

    Is this correct?

    Thanks in advance.
     
    Last edited: Jun 25, 2010
  2. jcsd
  3. Jun 26, 2010 #2
    No the value of γ is not correct.
    The best way to find it is to calculate heat capacity (as opposed to specific heat capacity) - the heat required to raise temperature of whole mixture by 1° C - for the mixture. Then divide it by the no. of moles present in the mixture.
    This way you find Cp and Cv for the mixture and then γ.
     
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