Cool air at 20.0ºC is forced into a hot-air balloon with an operating volume of 2500 m^3 using a fan. If the air in the hot-air balloon reaches a maximum operating temperature of 120ºC, what volume of air at 20.0ºC must be forced into the balloon to fill the balloon to its operating volume of 2500 m^3?

1864.11 m³

Explanation:

Let's suppose the gas is acting ideally, then according to Charles's Law, "The volume of a fixed mass of gas at constant pressure is directly proportional to the absolute temperature". Mathematically for initial and final states the relation is as follow,

V₁ / T₁ = V₂ / T₂

Data Given;

V₁ = ?

T₁ = 20 °C = 293.15 K

V₂ = 2500 m³

T₂ = 120 °C = 393.15 K

Solving equation for V₁,

V₁ = V₂ T₁ / T₂

Putting values,

V₁ = (2500 m³ * 293.15 K) : 393.15 K

V₁ = 1864.11 m³

Result:

When 1864.11 m³ volume of gas at 20 °C is allowed to enter a balloon at 120 °C, then the volume will increase to 2500 m³.