a hot air balloon is shaped like a sphere with the radius of

a hot air balloon is shaped like a sphere with the radius of 6m. the temperature of the air outside is 20C and the air inside the ballon is at temperature T. the pressure inside the balloon is 1 atm. the ballon is just able to like a 150kg mass off the ground. what is the temperature inside the ballon?

Solution

here,

radius , r = 6 m

T1 = 20 degree C

density of air at 20 degree C , p = 1.2041 Kg/m^3

let the density inside the ballon is p1

for the balloon to be in equilibrium

Using Archimedes principle

4/3 pi * r^2 * (p - p1) * g = m * g

4/3 * pi * 6^3 * (1.2041 - p1)* 9.8 = 150 * 9.8

solving for p1

p1 = 1.03831 Kg/m^3

Now ,from the table of air density

temperature , T = 70 degree C

the temperature of air inside the balloon is 70 degree C