A hot air balloon achieves itsbuoyant lift by heating the air inside the balloon

Question

A hot air balloon achieves itsbuoyant lift by heating the air inside the balloon, which makes itless dense than the air outside.  

Suppose the volume ofa balloon is 1800m3and the required lift is 2700N. Calculate the temperature of the air inside the balloon which willproduce the required lift. Assume that the outside airtemperature is 0*C and that air is an ideal gas under theseconditions. What factors limit the maximum altitudeattainable by this method for a given load? (Neglect variables likewind.)

Explanation / Answer

Since PV=nRT P1V1/T1=nR and P2V2/T2=nR then P1V1/T1 =P2V2/T2 also P1=P2 we have V1/T1 =V2/T2 T2=(V2 /V1)T1   we hav eto find therelationship between V1 and V2 V= V2 - V1 V= V2 - V1 since air= 1.27 kg/m3 V= W / (gair ) =V2 - V1 V2 = W / (gair ) +V1 = V2 = 2700 / (9.81 x 1.27) + 1800 = V2 =2017 m3 Finally since T2=(V2 /V1)T1   T2=(2017 / 1800)(273 + 0) T2= 306 K or ˜ 33 C and What factors limit the maximum altitudeattainable by this method for a given load? and What factors limit the maximum altitudeattainable by this method for a given load? 1. Air density 2. Displacement volume of the balloon 3. Temperature maintance ( the temperature deminishes withaltitude) Solar heating may aid a bit ;-). Please let me know if you have any questions

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