A helium-filled weather balloon has a volume of 512 L at 18.9°C and 756 mmHg. It is released and rises to an altitude of 2.14 km, where the pressure is 639 mmHg and the temperature is 5.9°C.

The volume of the balloon at this altitude is
L.

633.97 L

Explanation:

Well use the combined gas law;

P₁V₁T₁ = P₂V₂T₂

We need to change the temperatures into Kelvin;

18.9°C= 292.05 K

5.9°C = 279.05 K

756 * 512 * 292.05 = 639 * V₂ * 279.05

113,044,377.6 = 178,312.95 V₂

V₂ = 113,044,377.6 / 178,312.95

V₂ = 633.97 L

578.8 L

Explanation:

In order to solve this problem, we can use the equation of state for an ideal gas, which states that:

where

p is the pressure of the gas

V is its volume

n is the number of moles

R is the gas constant

T is the absolute temperature of the gas

The equation can also be rewritten as

For a gas transformation, the term on the right (nR) is constant, so we can write:

where in this problem:

is the initial pressure of the gas

is the initial volume

is the initial temperature

is the final pressure

is the final temperature

Solving for V2, we find the final volume of the balloon: