At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilom has a mass of 32kg.
To find the temperature at which the root-mean-square speed of oxygen molecules is 640 m/s, we can use the following equation:
v(rms) = √(3kT/m)
Where:
- v(rms) is the root-mean-square speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the mass of one molecule in kilograms
Given that the mass of one oxygen molecule (m) is 32 kg, we can substitute these values into the equation and solve for T:
640 = √(3 * 1.38 x 10^-23 * T / 32)
First, square both sides of the equation:
640^2 = (3 * 1.38 x 10^-23 * T / 32)
Next, multiply both sides of the equation by 32:
32 * 640^2 = 3 * 1.38 x 10^-23 * T
Calculate the left side of the equation:
32 * 640^2 ≈ 13.11 x 10^7
Divide both sides of the equation by 3 * 1.38 x 10^-23:
(32 * 640^2) / (3 * 1.38 x 10^-23) ≈ T
T ≈ 2.98 x 10^10 Kelvin
Therefore, the temperature at which the root-mean-square speed of oxygen molecules is 640 m/s is approximately 2.98 x 10^10 Kelvin.