Heat capacities of a gas mixture.

[Je m'appelle]

Homework Statement

1 gram of Hydrogen H_2 and 1 gram of Helium He 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 C_v and C_p, as well as \gamma = \frac{C_p}{C_v} of this gas mixture.

Homework Equations

n = \frac{m}{M_{molar}}

PV = nRT

For a monoatomic gas

C_v = \frac{3}{2}R

For a diatomic gas

C_v = \frac{5}{2}R

For both monoatomic and diatomic gas

C_p = C_v + R

\gamma = \frac{C_p}{C_v}

R = 8,31 \frac{J}{K.mol}

T_{kelvin} = T_{celsius} + 273

The Attempt at a Solution

(a)

P = \frac{nRT}{V}

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?

n_{He} = \frac{1}{4} = 0.25

n_{H_2} = \frac{1}{1} = 1

n_{mixture} = n_{He} + n_{H_2}

So,

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

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?

C_v (He) + C_v (H_2) = C_v (Mixture)

C_p (He) + C_p (H_2) = C_p (Mixture)

\gamma_{mixture} = \frac{C_p (He) + C_p (H_2)}{C_v (He) + C_v (H_2)}

Is this correct?

Thanks in advance.

 

[aim1732]

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 C_p and C_v for the mixture and then γ.