Please help me with this problem, Please show all work and explanations!! On a s

Question

Please help me with this problem, Please show all work and explanations!!

On a sunny morning in a field, the atmospheric pressure is 10^5N/m^2 and the temperature is 279 K. The film crew has filled a balloon with 1000m^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 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 10^5N/m^2. 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

From the Ideal gas equation

PV=nRT

PVM=mRT ( m/V = rho)

P= rho RT/M

rho=PM/RT

Buoyant force on balloon= 1000*9.8(1.2502-rhoinside air)

weight of balloon mg =240*9.8

1000*9.8(1.2502-rhoinside air)= 240*9.8

rhoinside air= 1.0102

T = PM/Rrhoinside air =345.3K

Q = ncp delT = 40093 ( 3.5 ( 8.314) ( 345.3 K ) = 5.28 * 10^7 J

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