Question

Плотность одного газа при давлении 400 кПа равна 1,6 кг/м3. Второй газ массой 2 кг занимает объем 10 м3 при давлении 200 кПа. Во сколько раз средняя квадратичная скорость молекул второго газа больше, чем первого?

Answer 1

V2/v1 = корень (3*R*T2/m2) / корень (3*R*T1/m1)

p*V = (m/M)*R*T. Отсюда R*T/M = p*V/m

v2/v1 = корень (3*p2*V2/m2) / корень (3*p1*V1/m1) =
= корень ((p2*V2/m2) / (p1/ро1)) = корень (p2*v2*ро1/p1*m2) =
= корень (200*10*1,6 / 400*2) = корень (4) = 2
Ответ: в 2 раза

Answer 2

Calculation of Gas Densities

To determine the ratio of the average square velocities of the two gases, we first need to calculate the densities of the gases.

The density of the first gas is given as 1.6 kg/m^3 at a pressure of 400 kPa. The density of a gas can be calculated using the ideal gas law equation:

Density = (Pressure * Molecular Mass) / (Gas Constant * Temperature)

Since the temperature is not provided, we can assume it to be constant for both gases.

Let's calculate the density of the first gas:

Density of first gas = (400 kPa * Molecular Mass of first gas) / (Gas Constant * Temperature)

Unfortunately, the molecular mass and gas constant are not provided in the given information. Therefore, we cannot calculate the exact density of the first gas.

Moving on to the second gas, we are given its mass as 2 kg and volume as 10 m^3 at a pressure of 200 kPa. To calculate the density of the second gas, we can use the formula:

Density = Mass / Volume

Let's calculate the density of the second gas:

Density of second gas = 2 kg / 10 m^3 = 0.2 kg/m^3.

Calculation of Average Square Velocities

To find the ratio of the average square velocities of the two gases, we need to use the formula:

Ratio = (Average Square Velocity of second gas) / (Average Square Velocity of first gas)

The average square velocity of a gas can be calculated using the formula:

Average Square Velocity = (3 * Pressure) / (Density)

Let's calculate the average square velocities of both gases:

For the first gas, we don't have the density, so we cannot calculate its average square velocity.

For the second gas, we have the density as 0.2 kg/m^3 and the pressure as 200 kPa. Let's calculate its average square velocity:

Average Square Velocity of second gas = (3 * 200 kPa) / (0.2 kg/m^3) = 3000 m^2/s^2.

Since we don't have the average square velocity of the first gas, we cannot determine the exact ratio of the two velocities.

In conclusion, we cannot determine the exact ratio of the average square velocities of the two gases without the molecular mass and gas constant of the first gas.