Question

Как изменится давление идеального газа на стенки сосуда,если в данном объеме скорость каждой молекулы удвоилась, а концентрация молекул не изменилась?

Answer 1

$p=1/3*n*m*v^2 p1/p2=v1^2/(2*v1)^2 p2=4p1$

Ответ: увеличилось в 4 раза

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Answer 2

Changes in Pressure of an Ideal Gas

When the speed of each molecule in a given volume of an ideal gas doubles while the concentration of molecules remains unchanged, the pressure exerted by the gas on the walls of the container will also change. To understand this, let's consider the relationship between pressure, volume, and temperature in the ideal gas law.

According to the ideal gas law, the pressure (P) of an ideal gas is directly proportional to the temperature (T) and the number of moles (n) of gas, and inversely proportional to the volume (V) of the gas. The equation can be written as:

P ∝ nT/V

Where: - P is the pressure of the gas - n is the number of moles of gas - T is the temperature of the gas in Kelvin - V is the volume of the gas

In this scenario, the concentration of molecules remains unchanged, which means the number of moles (n) of gas remains constant. Therefore, we can simplify the equation as:

P ∝ T/V

Now, if the speed of each molecule doubles, it means the temperature (T) of the gas will also increase. According to the equation, if the temperature increases while the volume (V) remains constant, the pressure (P) will also increase. This is because the pressure is directly proportional to the temperature.

Therefore, when the speed of each molecule in a given volume of an ideal gas doubles and the concentration of molecules remains unchanged, the pressure exerted by the gas on the walls of the container will increase.

Conclusion

In summary, when the speed of each molecule in a given volume of an ideal gas doubles and the concentration of molecules remains unchanged, the pressure exerted by the gas on the walls of the container will increase. This is because the pressure is directly proportional to the temperature, and an increase in the speed of molecules leads to an increase in temperature.