On a sunny morning in a ?eld, the atmospheric pressure is 10N/m and the temperat

Question

On a sunny morning in a ?eld, the atmospheric pressure is 10N/m and the temperature is 279 K. The ?lm crew has ?lled 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 105 N/m2 . No air enters or leaves the balloon. How much heat must be added to the air in the balloon to initiate the ?ight?

Explanation / Answer

Density of air is 1.293 on the given temperature.
So we have to find out the temperature which will cause so much expansion as the buoyant force will be equal to the whole weight.
The weight of balloon = 240 * 9.81 = 2354.4 N.

at 300 degree celcius and 1 atm pressure the density of air is 0.616 Kg/m3

The air in the balloon weighs 1000 *0.616*9.81 N = 6042.96 N

The buoyant force on the balloon should equal 6042.96+2354.4 N = 8397.36 N

The final volume of the air should be equal to (8397.36 / 1.293) m3 = 6494.5 m3.

Lets say the final temperature of the air in the balloon is T2

P2 V2/T2=P1V1/T1

or, T2= V2*T1*P2/V1

or, T2= 6494.5*(300+273)/1000 = 3721 K

required temperature rise = 3721-573 K = 3148 K

Required Heat = 3362 kJ

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