A perfectly spherical balloon occupied 35°C of neon gas under a pressure of 2 atm. The radius of the balloon is 15 cm. The balloon is then released up in the air until it
reached the temperature of -20°C under 0.3 atm. Determine its volume at that instant.

V₂ =  116126.75 cm³

Explanation:

Given data:

Radius of balloon = 15 cm

Initial pressure = 2 atm

Initial temperature = 35 °C (35 +273 = 308K)

Final temperature = -20°C (-20+273 = 253 K)

Final pressure = 0.3 atm

Final volume = ?

Formula:  

P₁V₁/T₁ = P₂V₂/T₂  

P₁ = Initial pressure

V₁ = Initial volume

T₁ = Initial temperature

P₂ = Final pressure

V₂ = Final volume

T₂ = Final temperature

Solution:

Initial volume of balloon:

V = 4/3πr³

V = 4/3×22/7×(15cm)³

V = 14137.17 cm³

V₂ = P₁V₁ T₂/ T₁ P₂  

V₂ = 2 atm × 14137.17 cm³ × 253 K / 308 K × 0.3 atm

V₂ = 7153408.02 atm .cm³. K / 61.6 K.atm

V₂ =  116126.75 cm³