Question

в баллон, содержащий некоторое число атомов гелия, добавляют такое же число молекул водорода, средняя кинетическая энергия поступательного движения которых равна средней кинетической энергии теплового движения атомов гелия. Во сколько раз изменится давление в сосуде?

Answer 1

По закону Дальтона  давление смеси газов равно сумме парциальных давлений. Из условия следует что парциальное давление гелия  такое же как и водорода, а значит давление увеличится в  2 раза

Answer 2

Calculation of Pressure Change in the Vessel

To determine the change in pressure in the vessel, we need to consider the ideal gas law, which states that the pressure of a gas is directly proportional to the number of gas particles and their average kinetic energy.

Let's assume that the initial number of helium atoms in the vessel is N. According to the problem statement, the same number of hydrogen molecules is added to the vessel. The average kinetic energy of the hydrogen molecules is equal to the average kinetic energy of the thermal motion of the helium atoms.

The average kinetic energy of a gas particle can be calculated using the equation:

KE = (3/2) * k * T

Where: - KE is the average kinetic energy of the gas particle - k is the Boltzmann constant (approximately 1.38 x 10^-23 J/K) - T is the temperature in Kelvin

Since the average kinetic energy of the hydrogen molecules is equal to the average kinetic energy of the helium atoms, we can equate their expressions:

(3/2) * k * T_hydrogen = (3/2) * k * T_helium

Simplifying the equation, we find:

T_hydrogen = T_helium

This means that the temperature of the hydrogen molecules is equal to the temperature of the helium atoms.

Now, let's consider the ideal gas law for both the helium atoms and the hydrogen molecules:

PV = nRT

Where: - P is the pressure - V is the volume - n is the number of gas particles - R is the ideal gas constant (approximately 8.314 J/(mol·K)) - T is the temperature in Kelvin

Since the number of helium atoms and hydrogen molecules is the same, we can write:

P_helium * V = P_hydrogen * V

Since the volume is constant, we can cancel it out:

P_helium = P_hydrogen

This means that the pressure of the helium atoms is equal to the pressure of the hydrogen molecules.

Therefore, the change in pressure in the vessel is zero. The pressure remains the same after adding an equal number of hydrogen molecules to the vessel.

Please let me know if you need any further clarification or have any other questions!