temperature for a hot air balloon? help plz?

Question

according to contemporary records, the Montgolfier hot air balloon-the first man made flying machine-had a volume of about 2000m^3 and weighed 780kg. on its maiden voyage, it carried two people. estimate the temperature to which the air inside the (rigid) balloon had to be heated in order to achieve lift-off.

any help on this will really be appreciateddd. thnxx

Answer 1

There is some information you need first.

To make it start to lift off the upthrust must counteract the weight

so upthrust = 780kg

from Archimedes principle upthrust = weight of air displaced

so 780kg of air must be displaced

the volume of the air inside the balloon = 2000m^3

normal air has a density of approx 1kg/m^3

so 780m^3 must be displaced

so the air has to expand sufficiently to displace 780m^3.





using gas law PV/T is constant

the volume will have expanded by 780 m^3 at constant pressure



so 2000/T1 = 2780/T2



let T1 be some normal temperature say 20C = 293K

so 2000/293 = 2780/T2

T2 = 2780 x 293/2000 = 407.27K = 134.27C

Answer 2

You need the temperature and density of the air at the launch point ..



Next you look up formula for the relationship between density and temperature of air.



Finally you invoke Archimedes principle.



NB. the comment about 2 people is ASSUMED to be a misdirection (i.e. the 780kg weight given includes passengers) HOWEVER, for completeness, since the wording is ambiguous (perhaps intentionally) I suggest you prepare an answer with a 'passenger' additional component ...



i.e. something like "X degrees PLUS [ (formula) * "weight of passengers not included in the 780kg" ] degrees

Answer 3

Balloons tend to be made up of latex rubber. There are tiny pores interior the form. finding on the scale of the molecules of the gas inflating the balloon the value of diffusion of those molecules throughout the partitions of the balloon will selection. oftentimes a upward push of temperature will advance the diffusion coefficient even whilst different issues proceed to be consistent. it is simply by larger kinetic power of the molecules of the gas at larger temperatures. it particularly is annoyed via extra factors which incorporate larger inner rigidity simply by heating and larger pore length simply by extend of the latex membrane. ordinary, for a given gas, deflation value will advance with increasing temperature.