Nitrogen is at temperature T = 300 K. Find the average

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Using our calculator, you can easily and quickly determine the average kinetic energy of the rotational motion of one gas molecule and the total kinetic energy of all gas molecules.

For example, if nitrogen is in a vessel at a temperature T = 300 K, and its mass is 0.7 kg, then our calculator will allow you to easily determine the total kinetic energy of all gas molecules.

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Our new product, a unique calculator for calculating the kinetic energy of gases, allows you to easily and quickly determine the average kinetic energy of the rotational motion of one gas molecule and the total kinetic energy of all gas molecules.

To solve a problem in which nitrogen is at a temperature T = 300 K and its mass is 0.7 kg, you can use the formulas for the kinetic energy of a gas molecule:

Ek = (3/2)kT

where Ek is the kinetic energy of the molecule, k is Boltzmann’s constant, T is the gas temperature.

To find the total kinetic energy of all gas molecules, it is necessary to multiply the kinetic energy of one molecule by the number of molecules in the gas:

Eк = N * (3/2)kT

where N is the number of gas molecules.

Substituting the values ​​into the formulas, we get:

Ek(one molecule) = (3/2) * 1.38 * 10^-23 J/K * 300 K = 6.21 * 10^-21 J

N = m/M

where m is the gas mass in kg, M is the molar mass of gas in kg/mol.

M(nitrogen) = 28 g/mol = 0.028 kg/mol

N = 0.7 kg / 0.028 kg/mol = 25 mol

Ek (all molecules) = 25 mol * 6.21 * 10^-21 J/mol = 1.55 * 10^-19 J

Thus, the average kinetic energy of the rotational motion of one nitrogen molecule at a temperature T = 300 K is equal to 6.21 * 10^-21 J, and the total kinetic energy of all nitrogen molecules in a vessel weighing 0.7 kg is 1.55 * 10^-19 J.

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This product is not a physical product, but rather a problem to solve.

To solve the problem, it is necessary to use the relationship between the kinetic energy of the rotational motion of the molecule and its moment of inertia:

Ek = (1/2)Iω²,

where Ek is the kinetic energy of the rotational motion of the molecule, I is the moment of inertia of the molecule, ω is the angular velocity of rotation of the molecule.

It is also necessary to use the relationship between the moment of inertia of the molecule, its mass and dimensions:

I = (2/5)mR²,

where m is the mass of the molecule, R is its radius.

The average kinetic energy of rotational motion of one molecule is calculated by the formula:

= (1/2)kT,

where k is Boltzmann's constant, T is the gas temperature.

The total kinetic energy of all gas molecules is calculated by the formula:

Eк = (3/2)kT*N,

where N is the number of gas molecules.

Thus, to solve this problem, it is necessary to know the mass of nitrogen in the vessel, the gas temperature and Boltzmann's constant. From these data, it is possible to calculate the average kinetic energy of the rotational motion of one molecule and the total kinetic energy of all gas molecules.

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