A balloon carries a total load of 180 kg at normal pressure and temperature of27°C . What loadwill the balloon carry on rising to a height at which the barometric pressure is 38 cm of Hg and thetemperature is3°C , assuming the volume is constant?
Question
A balloon carries a total load of 180 kg at normal pressure and temperature of27°C . What loadwill the balloon carry on rising to a height at which the barometric pressure is 38 cm of Hg and thetemperature is3°C , assuming the volume is constant?
Solution
To find the load that the balloon will carry at a different height with a constant volume, we can use the ideal gas law equation:
PV = nRT
Where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature
Since the volume is constant, we can rewrite the equation as:
P1/T1 = P2/T2
Where: P1 = initial pressure T1 = initial temperature P2 = final pressure T2 = final temperature
Given: P1 = normal pressure = 1 atm = 76 cm of Hg T1 = normal temperature = 27°C = 300 K P2 = 38 cm of Hg T2 = 3°C = 276 K
Now, we can substitute the values into the equation:
(76 cm of Hg) / (300 K) = (38 cm of Hg) / (276 K)
Simplifying the equation, we get:
(76 cm of Hg) * (276 K) = (38 cm of Hg) * (300 K)
Solving for the final pressure, we find:
Final pressure = (38 cm of Hg) * (300 K) / (276 K)
Final pressure = 41.3 cm of Hg
Therefore, the balloon will carry a load of 41.3 cm of Hg at the given height and temperature.
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