Plz help me with this PHYSICS question?

2016-06-20 7:58 am
An air bubble of volume 1.0×10^-6 m3 is at a depth of 40 m below the surface of a lake where temperature is 283K. What will be the volume of this air bubble when it just reach the surface of the water where tempertaure is 27°C

回答 (2)

2016-06-20 8:13 am
1 atm = 101000 Pa
Liquid pressure = Density × g × Depth

When the bubble is at a depth of 40 m :
P₁ = (101300 Pa) + (1000 kg/m³) × (9.81 m/s²) × (40 m) = 493700 Pa
V₁ = 1.0 × 10⁻⁶ m³
T₁ = 283 K

When the bubble is at the surface of the water :
P₂ = 101300 Pa
V₂ = ? m³
T₁ = (273 + 27) K = 300 K

For a fixed amount a gas :
P₁V₁/T₁ = P₂V₂/T₂
Then, V₂ = V₁ × (P₁/P₂) × (T₂/T₁)

The volume of the bubble at the surface of the water, V₂
= (1.0 × 10⁻⁶ m³) × (493700/101300) × (300/283)
= 5.2 × 10⁻⁶ m³
2016-06-20 6:12 pm
To determine the new volume, use the following equation.

P1 * V1 ÷ T1 = P2 * V2 ÷ T2

To determine the pressure at a depth of 40 meters, use the following equation.
Pressure = Density * depth * g = 1000 * 40 * 9.8 = 392,000 = 3.92 * 10^5 N/m^2
At the surface of the earth, the pressure is 1.013 * 10^5 N/m^2. Let’s convert the temperature to ˚K.

T = 27 + 273 = 300˚

3.92 * 10^5 * 1 * 10^-6 ÷ 283= 1.013 * 10^5 * V2 ÷ 300
0.392 ÷ 283 = V2 * 337⅔
V2 = (0.392 ÷ 283) ÷ 337⅔

This is approximately 4.1 * 10^-6 m^3
The number that I used for the pressure at the surface of earth came from a table in my physics book.

OR

The volume is directly proportional to the temperature and inversely proportional to the pressure.

Ratio of temperatures = 300:288
Ratio of pressures = 1.013:3.92
300/288 * 3.92/1.013
This ratio is approximately 4.03 to 1.This is why the volume at the surfaces is approximately 4 times the volume at a depth of 40 meters.


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