# Baloons

A plastic bag is filled with helium at atmospheric pressure and $22.0^o C$. Assume that the mass of the bag is negligible and take the temperature of the outside air to be $0^o C$. With the help of this “balloon” we want to lift a 43.0 kg girl off her feet. How large a volume of helium (in m3) is required? If hot air is used instead of helium, what is the required volume of the balloon if the air inside can be maintained at $42.0^o C$ ?

density of He at 20 Celsius $\rho(He) =0.1664 kh/m^3$

density of air at 0 Celsius $\rho(air) =1.2922 kg/m^3$

(see http://www.engineeringtoolbox.com/gas-density-d_158.html)

(see http://en.wikipedia.org/wiki/Density_of_air)

$(rho(air)-\rho(He))*V = 43 kg$

$(1.2922 -0.1664)*V = 43$

$V =38.195 m^3$

Density of air at 42 Celsius $rho_1(air) = P/R_s*T$

$T = 273+42 =315 K$

$R_s =287.058 J/(kg*K)$

$P =1 atm =101325 N/m^2$

$rho1(air) =1.1206 kg/m^3$

$(\rho_1(air)-\rho_0(air))*V =43$

$(-1.1206+1.2922)*V =43$

$V =250.529 m^3$