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A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8?
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A balloon contains 14L of air at 760 Torr. What will b the volume of t...
Given:
- Initial volume of air in the balloon = 14L
- Initial pressure of air in the balloon = 760 Torr
- Depth of the swimming pool = 10 ft
- Density of mercury (Hg) = 13.6 g/mL
To Find:
- Final volume of the balloon
Assumptions:
- The temperature of the air and water are equal
- The pressure inside the balloon is equal to the pressure exerted by the water at a depth of 10 ft
Solution:
1. Convert the depth of the swimming pool from feet to cm:
- 1 ft = 30.48 cm
- Depth in cm = 10 ft * 30.48 cm/ft = 304.8 cm
2. Calculate the pressure exerted by the water at a depth of 304.8 cm:
- Pressure = density * g * height
- Density of mercury (Hg) = 13.6 g/mL = 13.6 g/cm^3
- g = acceleration due to gravity = 9.8 m/s^2 = 980 cm/s^2
- Height = 304.8 cm
- Pressure = 13.6 g/cm^3 * 980 cm/s^2 * 304.8 cm
- Pressure ≈ 39882432.768 Torr
3. Apply Boyle's Law to find the final volume of the balloon:
- Boyle's Law states that the product of the initial pressure and volume is equal to the product of the final pressure and volume, assuming constant temperature.
- P1 * V1 = P2 * V2
- P1 = initial pressure = 760 Torr
- V1 = initial volume = 14 L
- P2 = final pressure = 39882432.768 Torr
- V2 = final volume (to be determined)
- 760 Torr * 14 L = 39882432.768 Torr * V2
- V2 = (760 Torr * 14 L) / 39882432.768 Torr
- V2 ≈ 0.266 L
Answer:
The volume of the balloon when it is taken to a depth of 10 ft in a swimming pool is approximately 0.266 L.
- Initial volume of air in the balloon = 14L
- Initial pressure of air in the balloon = 760 Torr
- Depth of the swimming pool = 10 ft
- Density of mercury (Hg) = 13.6 g/mL
To Find:
- Final volume of the balloon
Assumptions:
- The temperature of the air and water are equal
- The pressure inside the balloon is equal to the pressure exerted by the water at a depth of 10 ft
Solution:
1. Convert the depth of the swimming pool from feet to cm:
- 1 ft = 30.48 cm
- Depth in cm = 10 ft * 30.48 cm/ft = 304.8 cm
2. Calculate the pressure exerted by the water at a depth of 304.8 cm:
- Pressure = density * g * height
- Density of mercury (Hg) = 13.6 g/mL = 13.6 g/cm^3
- g = acceleration due to gravity = 9.8 m/s^2 = 980 cm/s^2
- Height = 304.8 cm
- Pressure = 13.6 g/cm^3 * 980 cm/s^2 * 304.8 cm
- Pressure ≈ 39882432.768 Torr
3. Apply Boyle's Law to find the final volume of the balloon:
- Boyle's Law states that the product of the initial pressure and volume is equal to the product of the final pressure and volume, assuming constant temperature.
- P1 * V1 = P2 * V2
- P1 = initial pressure = 760 Torr
- V1 = initial volume = 14 L
- P2 = final pressure = 39882432.768 Torr
- V2 = final volume (to be determined)
- 760 Torr * 14 L = 39882432.768 Torr * V2
- V2 = (760 Torr * 14 L) / 39882432.768 Torr
- V2 ≈ 0.266 L
Answer:
The volume of the balloon when it is taken to a depth of 10 ft in a swimming pool is approximately 0.266 L.
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A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8?
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A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8?.
A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon contains 14L of air at 760 Torr. What will b the volume of the balloon when it is taken to a depth of 10 ft in a swimming pool? Assume that the temperature of the air and water are equal (density of Hg = 13.6g/ml) a) 11 b) 11.3 c) 10 d) 10.8?.
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