Calculate the average speed of a water molecule (with a mass of 3.0e-26 kg) on the surface of Venus (730 Kelvin).
To calculate the average speed of a water molecule on the surface of Venus, we can use the root mean square (RMS) speed formula, which is given by:
v = √(3kT / m)
Where:
v = RMS speed of the molecule
k = Boltzmann constant (1.38 × 10^-23 J/K)
T = Temperature in Kelvin
m = Mass of the molecule
Let's plug in the values:
k = 1.38 × 10^-23 J/K
T = 730 K
m = 3.0e-26 kg
v = √(3 * 1.38 × 10^-23 J/K * 730 K / 3.0e-26 kg)
To simplify the calculation, let's divide the numerator and the denominator by 3:
v = √(1.38 × 10^-23 J/K * 730 K / 1.0e-26 kg)
Now, we can solve for v:
v = √(1.38 × 730 / 1.0e-26) m/s
Using a calculator, we can find:
v ≈ 1.52 × 10^3 m/s
Therefore, the average speed of a water molecule on the surface of Venus is approximately 1.52 × 10^3 m/s.