Pressure of oxygen in a vessel with volume V = 4

Let us consider a gas located in a vessel with a volume V = 4 l at a temperature t = 27 °C. The oxygen pressure in the gas is P = 0.5 MPa. It is necessary to determine the total kinetic energy of the translational motion of gas molecules in a vessel after increasing their average thermal speed by 2 times. To solve this problem, we use the formula for calculating the kinetic energy of gas: Ek = (3/2) * n * R * T, where Ek is the kinetic energy of the gas, n is the number of moles of gas, R is the universal gas constant, T is the absolute temperature of the gas . First, let's find the number of moles of gas: n = P * V / (R * T), where P is the gas pressure. Substituting the known values, we get: n = (0.5 MPa * 4 l) / (8.31 J / (mol * K) * (273.15 + 27) K) ≈ 0.060 mol Now we can calculate the kinetic energy of the gas: Ek = (3/2) * 0.060 mol * 8.31 J / (mol * K) * (300 K * 2) ≈ 560 J Thus, after increasing the average thermal speed of gas molecules by 2 times, the total kinetic energy of the translational motion of the molecules gas in the vessel will be approximately 560 J.

Oxygen pressure in the vessel

A digital product that represents the calculation of oxygen pressure parameters in a vessel of a given volume and temperature.

This product allows you to quickly and conveniently determine the oxygen pressure in a vessel with a volume of V = 4 l at a temperature of t = 27 °C, which is P = 0.5 MPa.

You will also be able to calculate the total kinetic energy of the translational motion of gas molecules in a vessel after increasing their average thermal speed by 2 times.

This product is an indispensable tool for everyone involved in science and technology, as well as for students studying physics and chemistry.

What is described in the text is a problem in physics that can be solved by calculating the total kinetic energy of the translational motion of gas molecules in a vessel after increasing their average thermal speed by 2 times. To do this, it is necessary to know the pressure of oxygen in the gas, which is in a vessel with a volume of V = 4 l at a temperature of t = 27 °C. The pressure is P = 0.5 MPa.

This digital product allows you to quickly and conveniently determine the oxygen pressure in a vessel of a given volume and temperature, as well as calculate the total kinetic energy of the translational motion of gas molecules in the vessel after increasing their average thermal speed by 2 times. Such a product can be useful for everyone involved in science and technology, as well as for students studying physics and chemistry.

To solve the problem, it is necessary to use the formula for calculating the kinetic energy of gas: Ek = (3/2) * n * R * T, where Ek is the kinetic energy of the gas, n is the number of moles of gas, R is the universal gas constant, T is the absolute temperature of the gas . First you need to find the number of moles of gas: n = P * V / (R * T), where P is the gas pressure. Substituting the known values, we get: n = (0.5 MPa * 4 l) / (8.31 J / (mol * K) * (273.15 + 27) K) ≈ 0.060 mol.

Now we can calculate the kinetic energy of the gas: Ek = (3/2) * 0.060 mol * 8.31 J / (mol * K) * (300 K * 2) ≈ 560 J. Thus, after increasing the average thermal speed of gas molecules in 2 times, the total kinetic energy of the translational motion of gas molecules in the vessel will be approximately 560 J.

This product offers a solution to the problem with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. The file is presented in image format. If you have questions about solving a problem, you can ask for help.

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Given: Vessel volume V = 4 l = 0.004 m^3 Gas temperature t = 27 °C = 300 K Gas pressure P = 0.5 MPa = 5 * 10^5 Pa

Find: The total kinetic energy of translational motion Ek of gas molecules in a vessel after increasing its average thermal speed by 2 times.

Solution: According to the equation of state of an ideal gas PV = nRT, the amount of gas substance can be found as: n = PV/RT

Here R is the universal gas constant, which is equal to 8.31 J/mol K.

Then the number of gas molecules can be found as: N = n * N_A,

where N_A is Avogadro's constant, which is equal to 6.02 * 10^23 molecules/mol.

The average kinetic energy of gas molecules is expressed in terms of temperature: = (3/2) * k * T,

where k is Boltzmann's constant, which is equal to 1.38 * 10^-23 J/K.

The total kinetic energy of gas molecules is expressed in terms of the number of molecules and the average kinetic energy: Ek = N *

After increasing the average thermal speed of molecules by 2 times, their average kinetic energy will also increase by 2 times: = 2 *

Consequently, the total kinetic energy of gas molecules after increasing the average thermal speed by 2 times is expressed as: Ek' = N * = N * 2 * = 2 * Ek

Thus, the total kinetic energy of gas molecules after increasing the average thermal velocity by 2 times is equal to twice the initial total kinetic energy of gas molecules.

Solution numerically: n = (0.5 MPa * 0.004 m^3) / (8.31 J/(mol K) * 300 K) = 0.000804 mol N = 0.000804 mol * 6.02 * 10^23 molecules/mol = 4.84 * 10^20 molecules = (3/2) * 1.38 * 10^-23 J/K * 300 K = 6.21 * 10^-21 J Ek = 4.84 * 10^20 molecules * 6.21 * 10^-21 J/molecules = 3.00 J

Answer: The total kinetic energy of translational motion Ek of gas molecules in a vessel after increasing its average thermal speed by 2 times is equal to 6 J (twice the initial total kinetic energy of gas molecules).

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