The cp/cv ratio for a gas mixture consisting of 4g of helium and 32 g of oxygen

To find the cp/cv ratio for a gas mixture, we need to know the individual cp/cv ratios for each gas component and their respective mass fractions.

1. Calculate the moles of helium (He) and oxygen (O2) in the mixture:

   • Moles of He = mass of He / molar mass of He
   • Moles of O2 = mass of O2 / molar mass of O2

2. Determine the individual cp/cv ratios for helium and oxygen:

   • The cp/cv ratio for helium (γ_He) is approximately 5/3 or 1.67.
   • The cp/cv ratio for oxygen (γ_O2) is approximately 7/5 or 1.4.

3. Calculate the mass fractions of helium (X_He) and oxygen (X_O2) in the mixture:

   • Mass fraction of He = mass of He / total mass of the mixture
   • Mass fraction of O2 = mass of O2 / total mass of the mixture

4. Calculate the weighted average cp/cv ratio for the gas mixture:

   • cp/cv ratio of the mixture (γ_mixture) = (γ_He * X_He) + (γ_O2 * X_O2)

Now, let's calculate the cp/cv ratio for the given gas mixture consisting of 4g of helium and 32g of oxygen:

1. Calculate the moles of helium and oxygen:

   • Moles of He = 4g / molar mass of He
   • Moles of O2 = 32g / molar mass of O2

2. Determine the individual cp/cv ratios for helium and oxygen:

   • γ_He = 1.67
   • γ_O2 = 1.4

3. Calculate the mass fractions of helium and oxygen:

   • Mass fraction of He = 4g / (4g + 32g)
   • Mass fraction of O2 = 32g / (4g + 32g)

4. Calculate the weighted average cp/cv ratio for the gas mixture:

   • γ_mixture = (1.67 * Mass fraction of He) + (1.4 * Mass fraction of O2)

By substituting the values, we can find the cp/cv ratio for the given gas mixture.