Question

Баллон вместимостью V1=0,02 м^3, содержащий воздух под давлением p=4*10^5 соединяют с баkлоном вместимостью V2=0?06m^3 из которого воздух выкачан. найти давление p, установившееся в сосудах T=const

Answer 1

После соединения сосудов газ занимает весь предоставленный ему объем
V=V1+V2
так как T = соnst   по закону Бойля-Мариотта
P1*V1=P2*(V1+V2)
P=P1*V1/(V1+V2)=100000 Па=100кПа

Answer 2

Calculation of the Final Pressure

To find the final pressure in the vessels when they are connected, we can use the principle of conservation of mass and the ideal gas law. According to the principle of conservation of mass, the total mass of air in the system remains constant. Therefore, the initial mass of air in the first vessel is equal to the final mass of air in both vessels.

The ideal gas law relates the pressure, volume, and temperature of a gas. It can be expressed as:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of the gas - R is the ideal gas constant - T is the temperature of the gas

Since the number of moles and the temperature remain constant in this case (T = const), we can rewrite the ideal gas law as:

P1V1 = P2V2

Where: - P1 is the initial pressure in the first vessel - V1 is the initial volume of the first vessel - P2 is the final pressure in both vessels (which we need to find) - V2 is the final volume of the second vessel

Given the values: - V1 = 0.02 m^3 - P1 = 4 * 10^5 Pa - V2 = 0.06 m^3

We can substitute these values into the equation to find the final pressure:

P1V1 = P2V2

4 * 10^5 * 0.02 = P2 * 0.06

Simplifying the equation:

P2 = (4 * 10^5 * 0.02) / 0.06

Calculating the value:

P2 = 1.33 * 10^5 Pa

Therefore, the pressure that will be established in the vessels when they are connected is 1.33 * 10^5 Pa.