On a sunny morning in a field, the atmospheric pressure is 105N/m2 and the tempe

Question

On a sunny morning in a field, the atmospheric pressure is 105N/m2 and the temperature is 279 K. The film crew has filled a balloon with 1000m3 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 balloon rises 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 pressure of 105N/m2 . No air enters or leaves the balloon. How much heat must be added to the air in the balloon to initiate the 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/R?inside air=345.3K

Assuming diatomic gas, Cp=3.5R

n=40093moles

Heat=nCp?T=5.285*107J

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