The velocity of sound in a gas depends on various factors, including temperature. In general, the velocity of sound in a gas is directly proportional to the square root of the absolute temperature of the gas. The relationship can be expressed by the equation:
v = √(γ * R * T),
where: v is the velocity of sound, γ is the adiabatic index or specific heat ratio of the gas, R is the gas constant, and T is the absolute temperature.
For air, the adiabatic index γ is approximately 1.4 and the gas constant R is approximately 287 m²/s²K.
Let's calculate the velocities at 300 K and 311 K using the given information:
At 300 K: v₁ = √(1.4 * 287 * 300) ≈ 343.2 m/s.
At 311 K: v₂ = √(1.4 * 287 * 311) ≈ 346.7 m/s.
Therefore, the corresponding velocity of sound at 311 K would be approximately 346.7 m/s.