On a summer morning in a field, the atmospheric pressure is 10^5 N/m^2 and the t
ID: 2222944 • Letter: O
Question
On a summer morning in a field, the atmospheric pressure is 10^5 N/m^2 and the temperature is 279 K. The film crew has filled a balloon with 1000 m^3 of preheated air at atmospheric pressure and a temperature of 300 K. The mass of the empty balloon and its load is 240 kg. Under these conditions, the balloonrises above its burden, but the airship remains grounded. To begin the ascent, the air within the balloon is brought to a higher temperature. It expands but remains at the same pressure of 10^5 N/m^2. No air enter or leaves the balloon. How much heat must be added to the air in the balloon to initiate flight?
Explanation / Answer
PV=nRT
PVM=mRT
P=RT/M
=PM/RT
outside air=1.2502kg/m3
Buoyant force on balloon= 1000*9.8(1.2502-inside air)=weight of balloon=240*9.8
Solving, inside air=1.0102
Temperature of inside air=PM/Rinside air=345.3K
Assuming diatomic gas, Cp=3.5R
n=40093moles
Heat=nCpT=5.285*107J
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