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What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.
Correct answer is '2'. Can you explain this answer?
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Verified Answer
What will be the temperature difference needed in a hot air balloon to...
The correct answer is 2
The solution is as follows:
Δm = mcold − mhot
=[ncold−nhot]M
= PVMR[1T1− 1T2]
Solving we get:
T2−T1 = ΔT = 2
The solution is as follows:
Δm = mcold − mhot
=[ncold−nhot]M
= PVMR[1T1− 1T2]
Solving we get:
T2−T1 = ΔT = 2
Most Upvoted Answer
What will be the temperature difference needed in a hot air balloon to...
Given information:
- Volume of the balloon: 100 m3
- Temperature of the ambient air: 298 K
- Pressure: 1.00 bar
- Air is an ideal gas with an average molar mass of 29 g/mol
To lift 1.00 kg of mass:
Step 1: Calculate the mass of air required:
- The molar mass of air is given as 29 g/mol.
- To find the number of moles, divide the mass of air required (1.00 kg) by the molar mass:
- Mass of air = 1.00 kg = 1000 g
- Number of moles = Mass of air / Molar mass
= 1000 g / 29 g/mol
= 34.48 mol
Step 2: Calculate the number of moles of air in the balloon:
- To find the number of moles of air in the balloon, divide the volume of the balloon by the molar volume at the given temperature and pressure. The molar volume is given by the ideal gas law:
- PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
- Rearranging the equation, we can solve for the number of moles:
- n = PV / RT
- Substituting the given values:
- P = 1.00 bar = 1.00 * 10^5 Pa
- V = 100 m3
- R = 8.314 J/(mol·K)
- T = 298 K
- Calculating the number of moles:
- n = (1.00 * 10^5 Pa * 100 m3) / (8.314 J/(mol·K) * 298 K)
- n ≈ 401.34 mol
Step 3: Calculate the temperature difference:
- The temperature difference needed to lift the mass is the difference between the initial temperature and the final temperature of the air in the balloon.
- To calculate the final temperature, assume ideal gas behavior and use the equation n1T1 = n2T2, where n1 and n2 are the initial and final number of moles, and T1 and T2 are the initial and final temperatures.
- Rearranging the equation, we can solve for the final temperature:
- T2 = (n1T1) / n2
- Substituting the given values:
- n1 = 34.48 mol
- T1 = 298 K
- n2 = 401.34 mol
- Calculating the final temperature:
- T2 = (34.48 mol * 298 K) / 401.34 mol
- T2 ≈ 25.6 K
Step 4: Calculate the temperature difference:
- The temperature difference is the difference between the final temperature and the initial temperature:
- Temperature difference = T2 - T1
= 25.6 K - 298 K
= -272.4 K
Answer:
- The temperature difference needed in a hot
- Volume of the balloon: 100 m3
- Temperature of the ambient air: 298 K
- Pressure: 1.00 bar
- Air is an ideal gas with an average molar mass of 29 g/mol
To lift 1.00 kg of mass:
Step 1: Calculate the mass of air required:
- The molar mass of air is given as 29 g/mol.
- To find the number of moles, divide the mass of air required (1.00 kg) by the molar mass:
- Mass of air = 1.00 kg = 1000 g
- Number of moles = Mass of air / Molar mass
= 1000 g / 29 g/mol
= 34.48 mol
Step 2: Calculate the number of moles of air in the balloon:
- To find the number of moles of air in the balloon, divide the volume of the balloon by the molar volume at the given temperature and pressure. The molar volume is given by the ideal gas law:
- PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
- Rearranging the equation, we can solve for the number of moles:
- n = PV / RT
- Substituting the given values:
- P = 1.00 bar = 1.00 * 10^5 Pa
- V = 100 m3
- R = 8.314 J/(mol·K)
- T = 298 K
- Calculating the number of moles:
- n = (1.00 * 10^5 Pa * 100 m3) / (8.314 J/(mol·K) * 298 K)
- n ≈ 401.34 mol
Step 3: Calculate the temperature difference:
- The temperature difference needed to lift the mass is the difference between the initial temperature and the final temperature of the air in the balloon.
- To calculate the final temperature, assume ideal gas behavior and use the equation n1T1 = n2T2, where n1 and n2 are the initial and final number of moles, and T1 and T2 are the initial and final temperatures.
- Rearranging the equation, we can solve for the final temperature:
- T2 = (n1T1) / n2
- Substituting the given values:
- n1 = 34.48 mol
- T1 = 298 K
- n2 = 401.34 mol
- Calculating the final temperature:
- T2 = (34.48 mol * 298 K) / 401.34 mol
- T2 ≈ 25.6 K
Step 4: Calculate the temperature difference:
- The temperature difference is the difference between the final temperature and the initial temperature:
- Temperature difference = T2 - T1
= 25.6 K - 298 K
= -272.4 K
Answer:
- The temperature difference needed in a hot
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What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer?
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What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer?.
What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the temperature difference needed in a hot air balloon to lift 1.00 kg of mass ? Assume that the volume of the balloon is 100 m3, the temperature of the ambient air is 298 K, the pressure is 1.00 bar, and the air is an ideal gas with average molar mass of 29 g mol-1.Correct answer is '2'. Can you explain this answer?.
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