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A tiny particle of mass 1.38 x 10-11 kg is floating in air at 3000C. Ignoring gravity, its rms speed (in μm/sec) due to random collisions with air molecules will be closest to ______.
Correct answer is '41.46'. Can you explain this answer?
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A tiny particle of mass 1.38 x 10-11 kg is floating in air at 3000C. I...
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Order to find the root mean square (rms) speed of the particle, we can use the equation:
v = sqrt((3 * k * T) / m)
where:
v = rms speed
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature in kelvin (K)
m = mass of the particle
First, let's convert the temperature from Celsius to Kelvin:
T = 3000C + 273.15 = 3273.15 K
Now we can plug in the values into the equation:
v = sqrt((3 * (1.38 x 10^-23 J/K) * (3273.15 K)) / (1.38 x 10^-11 kg))
Calculating this expression gives us:
v ≈ 1457.91 m/s
Therefore, the rms speed of the particle is approximately 1457.91 m/s.
v = sqrt((3 * k * T) / m)
where:
v = rms speed
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature in kelvin (K)
m = mass of the particle
First, let's convert the temperature from Celsius to Kelvin:
T = 3000C + 273.15 = 3273.15 K
Now we can plug in the values into the equation:
v = sqrt((3 * (1.38 x 10^-23 J/K) * (3273.15 K)) / (1.38 x 10^-11 kg))
Calculating this expression gives us:
v ≈ 1457.91 m/s
Therefore, the rms speed of the particle is approximately 1457.91 m/s.
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A tiny particle of mass 1.38 x 10-11 kg is floating in air at 3000C. Ignoring gravity, its rms speed (inμm/sec) due to random collisions with air molecules will be closest to ______.Correct answer is '41.46'. Can you explain this answer?
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