Calculate the average speed of a water molecule (with a mass of 3.0e-26 kg) on the hot side of Mercury (710 Kelvin).
rms speed= sqrt (3/2 * RT/m)
To calculate the average speed of a water molecule on the hot side of Mercury, we can use the equation for the root mean square (RMS) speed. The RMS speed of a gas molecule is defined as:
v_rms = sqrt((3 * k * T) / m)
Where:
- v_rms represents the RMS speed
- k is the Boltzmann constant (1.38e-23 J/K)
- T is the temperature in Kelvin
- m is the mass of the molecule
Let's plug in the given values into the equation and calculate the average speed of the water molecule:
m = 3.0e-26 kg
T = 710 K
k = 1.38e-23 J/K
v_rms = sqrt((3 * 1.38e-23 J/K * 710 K) / 3.0e-26 kg)
First, let's multiply k and T:
k * T = 1.38e-23 J/K * 710 K
≈ 9.798e-21 J
Now, substitute this value back into the equation:
v_rms = sqrt((3 * 9.798e-21 J) / 3.0e-26 kg)
= sqrt(2.9394e-20 J / 3.0e-26 kg)
≈ sqrt(9.798e5 m^2/s^2 / 3.0e-26 kg)
≈ sqrt(3.266e31 m^2/s^2)
≈ 5.71e15 m/s
Therefore, the average speed of a water molecule on the hot side of Mercury is approximately 5.71 × 10^15 meters per second.