What Temperature Gives Nitrogen Molecules an RMS Speed of 1.5 m/s?

Using the equation and conversion factors, you can easily calculate the temperature. In summary, to find the temperature at which nitrogen molecules have an rms speed of 1.5, you can use the equation V=(3*K_b*T/m)^.5 and the mass of nitrogen (4.677E-26 kg) to calculate the temperature to be 0.0025 kelvin.
  • #1
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Homework Statement



1.5 is a typical walking speed.
At what temperature would nitrogen molecules have an rms speed of 1.5 ?


Homework Equations



V=(3*K_b*T/m)^.5
V is the rms speed
K_b is Boltzmann's constant
T is temp in kelvin
m is mass


The Attempt at a Solution



I am going to make the foolish assumption that when they mean mass, they mean the mass of one nitrogen molecule. So the mass of a proton and a neutron is 1.67E-27kg and the mass of an electron is 9.11E-31kg. One nitrogen atom has 7 protons, 7 neutrons and 7 electrons and multiply that by two because of the second nitrogen atom. So ((1.67E-27)(14)+(7)(9.11E-32))(2)=4.677E-26 kg.

Now I rearrange my equation to solve for T and plug in.

mV^2/(3*K_b)=T

(4.677E-26)(1.5)^2/(3*K_b) = .0025 kelvin

Am I close?

Thanks!
 
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  • #2
Never mind. My answer is correct.
 
  • #3
Good job. For future reference, it may be easier and quicker to look up the mass of nitrogen or other elements in a periodic table.
 

What is the temperature of nitrogen?

The temperature of nitrogen varies depending on its state and the conditions it is under. At standard atmospheric pressure, nitrogen exists as a gas at a temperature of -195.8 degrees Celsius. At lower pressures, it can also exist as a liquid or a solid at much lower temperatures.

What is the coldest temperature nitrogen can reach?

The coldest temperature nitrogen can reach is -210 degrees Celsius, which is the temperature at which it transitions from a gas to a liquid at standard atmospheric pressure. At even lower pressures, nitrogen can reach temperatures as low as -346 degrees Celsius, at which point it transitions from a liquid to a solid.

How does temperature affect the properties of nitrogen?

The properties of nitrogen, such as its density and vapor pressure, are directly affected by temperature. As temperature decreases, the density of nitrogen increases, and its vapor pressure decreases. This is why nitrogen is often used in cryogenic applications, as its properties change significantly at very low temperatures.

What is the relationship between temperature and pressure in nitrogen?

The relationship between temperature and pressure in nitrogen is described by the ideal gas law, which states that at a constant volume, the pressure of a gas is directly proportional to its temperature. This means that as the temperature of nitrogen increases, so does its pressure, and vice versa.

Why is it important to control the temperature of nitrogen in certain applications?

In many industrial and scientific applications, it is crucial to control the temperature of nitrogen. This is because its properties, such as its ability to maintain low temperatures and its inertness, make it useful for various processes, such as cryopreservation, cooling, and inert gas purging. In these applications, precise temperature control ensures the effectiveness and safety of the process.

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