A helium-filled balloon escapes a child's hand at sea level and 23.0 C. When it reaches an altitude of 3000 m, where the temperature is 4.4 C and the pressure is only 0.71 atm, how will its volume compare to that at sea level?

Sep 17, 2016

It will be 1.5 times larger.

Explanation:

The altitude itself is irrelevant. The ideal gas law states
$\frac{{P}_{1} \cdot {V}_{1}}{T} _ 1 = \frac{{P}_{2} \cdot {V}_{2}}{T} _ 2$ The temperatures must be in ‘K for the ratio to be correct.

$\frac{1 a t m \cdot {V}_{1}}{296} = \frac{0.71 a t m \cdot {V}_{2}}{277.4}$

${V}_{1} / {V}_{2}$ = 277.4/296 * 0.71 ; ${V}_{1} / {V}_{2}$ = 0.665

Therefore, the volume at 3000m is 1/0.665 = 1.5 times larger than at sea level.