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.

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