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Je m'appelle
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Homework Statement
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.
Homework 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]
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.
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