Question

Объём баскетбольного мяча в результате погружения в воду уменьшился в 2 раза. Температура воздуха и воды соответственно равны 20 °С и 7 °С. Определите давление воздуха в мяче после погружения. Атмосферное давление – 760 мм рт. ст.

Answer 1

Ответ:

Объяснение:

Дано:

V₂

V₂ = V₁ / 2

t₁ = 20°C ;  T₁ = 273 + 20 = 293 K

t₂ =   7°C ;  T₂ = 273 +   7 =  280 K

p₀ = 760 мм.рт.ст.

_________________

p₂ - ?

По основному уравнению:

p₁·V ₁ / T₁ = p₂·V₂ / T₂

p₁·V₁ / 293 = p₂·V₁ / (2·290)

p₁ /293 = p₂ / 580

p₂ = (580/293)·p₁

p₂ ≈ 2·p₁

Давление увеличилось в 2 раза.

Answer 2

Calculation of the Pressure in the Basketball after Submersion

To determine the pressure in the basketball after submersion, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. The equation for the ideal gas law is:

P1 * V1 / T1 = P2 * V2 / T2

Where: - P1 is the initial pressure of the gas (in this case, the atmospheric pressure) - V1 is the initial volume of the gas (the volume of the basketball before submersion) - T1 is the initial temperature of the gas (the temperature of the air) - P2 is the final pressure of the gas (the pressure in the basketball after submersion) - V2 is the final volume of the gas (the volume of the basketball after submersion) - T2 is the final temperature of the gas (the temperature of the water)

Given: - Atmospheric pressure (P1) = 760 mmHg - Initial volume of the basketball (V1) = ? - Initial temperature of the air (T1) = 20 °C = 293.15 K - Final volume of the basketball (V2) = V1 / 2 (since the volume decreased by 2 times) - Final temperature of the gas (T2) = 7 °C = 280.15 K

To find the initial volume of the basketball (V1), we need to solve for it using the ideal gas law equation.

P1 * V1 / T1 = P2 * V2 / T2

Substituting the given values: 760 mmHg * V1 / 293.15 K = P2 * (V1 / 2) / 280.15 K

Simplifying the equation: 2 * 760 mmHg * V1 = P2 * V1 * 293.15 K / 280.15 K

Canceling out V1: 2 * 760 mmHg = P2 * 293.15 K / 280.15 K

Simplifying further: P2 = (2 * 760 mmHg * 280.15 K) / 293.15 K

Calculating the value: P2 = 1450.07 mmHg

Therefore, the pressure in the basketball after submersion is approximately 1450.07 mmHg.

Please note that the above calculation assumes that the basketball behaves as an ideal gas and that there are no other factors affecting the pressure change.