Question

Нижню частину сполучених посудин наповнили ртуттю. У ліве коліно налили гас, а в праве — воду, висота стовпчика якої 16 см. Якої висоти має бути стовпчик гасу, щоб рівень ртуті в посудинах не змінився?

Answer 1

Ответ: 20см

Объяснение:

Дано:

h1=16cм

ρ1=1000кг/м³

ρ2=800кг/м³

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h2-?

h1/h2=ρ2/ρ1

h2=h1*ρ1/ρ2=16*1000/800=20см

Answer 2

To answer your question, we need to consider the principles of Pascal's law, which states that when a fluid is confined in a container, the pressure is transmitted equally in all directions. In this case, we have two vessels connected at the bottom, one filled with mercury and the other with water. The goal is to determine the height of the gas column that would keep the level of mercury unchanged.

According to Pascal's law, the pressure at the bottom of both vessels should be equal in order to maintain the same level of mercury. The pressure at a certain depth in a fluid is given by the equation:

P = ρgh

Where: - P is the pressure - ρ is the density of the fluid - g is the acceleration due to gravity - h is the height of the fluid column

Let's assume that the density of mercury is ρ_m and the density of water is ρ_w. Since the vessels are connected, the pressure at the bottom of both vessels should be equal:

P_m = P_w

Using the equation for pressure, we can write:

ρ_m * g * h_gas = ρ_w * g * h_water

We are given that the height of the water column, h_water, is 16 cm. We need to find the height of the gas column, h_gas, that would maintain the same level of mercury.

To find h_gas, we can rearrange the equation:

h_gas = (ρ_w / ρ_m) * h_water

Now, we need to find the ratio of the densities of water and mercury, (ρ_w / ρ_m). According to the search results, the density of water is approximately 1000 kg/m^3, and the density of mercury is approximately 13546 kg/m^3 [[1]].

ρ_w / ρ_m = 1000 kg/m^3 / 13546 kg/m^3

Calculating this ratio, we find:

ρ_w / ρ_m ≈ 0.0738

Now, we can substitute this value into the equation for h_gas:

h_gas = 0.0738 * 16 cm

Calculating this, we find:

h_gas ≈ 1.18 cm

Therefore, the height of the gas column should be approximately 1.18 cm in order to keep the level of mercury unchanged in the vessels.

I hope this explanation helps! Let me know if you have any further questions.