Agas‑filled weather balloon with a volume of 58.0 l is held at ground level, where the atmospheric pressure is 771 mmhg and the temperature is 24.0 ∘c . the balloon is released and rises to an altitude where the pressure is 0.0571 bar and the temperature is −6.94 ∘c . calculate the weather balloon's volume at the higher altitude.

The balloon's volume at higher altitude is 935.4 L

Explanation:

Step 1: Data given

Volume = 58.0 L

Atmospheric pressure = 771 mmHg = 1.01447 atm

Temperature = 24.0 °C = 297.15 Kelvin

When the balloon is released , it has a pressure of 0.0571 bar (= 0.0563533185 atm)

Temperature = -6.94 °C ( = 266.21 Kelvin)

Step 2: Calculate the volume

P*V=n*R*T   with n and R are constant

(P1*V1)/ T1 = (P2*V2)/ T2

with P1 = 771 mmHg = 1.01447 atm

with V1 = 58.0 L

with T1 = 24.0 °C = 297.15 Kelvin

with P2 = 0.0571 bar (= 0.0563533185 atm)

with V2 = TO BE DETERMINED

with T2 = -6.94 °C ( = 266.21 Kelvin)

V2 = (P1 * V1 * T2 )/( T1 * P2)

V2 = (1.01447 atm * 58.0 L * 266.21 K) / (297.15 K * 0.0563533185 atm)

V2 =935.4 L

The balloon's volume at higher altitude is 935.4 L