Question

Calculate the speed of sound in oxygen from the following data. The mass of 22.4 liters of oxygen at STP (T = 273 K and p = 1.0x10⁵ N/m²) is 32 g, the molar heat capacity of oxygen at constant volume is Cᵥ = 2.5 R and that at constant pressure Cₚ = 3.5 R.

Answer 1

Answer ⇒ 313.05 m/s.

Explanation ⇒ Using the formula,

V = √(γP/ρ)

Now γ is the ratio of Cp/Cv.

∴ γ = 3.5/2.5

∴ γ = 35/25

∴ γ = 7/5

P = 10⁵ N/m² = 10⁵ Pa.

ρ = mass/Volume

ρ = 32/22.4 g/L (or kg/m³)

ρ = 1.43 kg/m³.

∴ V = √(7 × 10⁵/5 × 1.43)

∴ V = √(98000)

∴ V = 313.05 m/s.

Hope it helps.

Answer 2

Explanation ⇒ Using the formula,

V = √(γP/ρ)

Now γ is the ratio of Cp/Cv.

∴ γ = 3.5/2.5

∴ γ = 35/25

∴ γ = 7/5

P = 10⁵ N/m² = 10⁵ Pa.

ρ = mass/Volume

ρ = 32/22.4 g/L (or kg/m³)

ρ = 1.43 kg/m³.

∴ V = √(7 × 10⁵/5 × 1.43)

∴ V = √(98000)

∴ V = 313.05 m/s.