Question

A balloon has a volume of 4.0 L when at sea level (1.0 atm) at a room temperature of
28 °C. What will be its volume when inflated with the same amount of gas at an elevation
where the atmospheric pressure is 200 mm Hg at 28°C?

Answer 1

The balloon has a volume of 4.0 L when at sea level (1.0 atm) at a room temperature of 28 °C.

So, pressure, P1 = 1.0 atm

   Temperature = 28°C 

               = (28+273)K

               = 301 K

           T2 = 301 K

   Volume, V1 = 4 L

    

where the atmospheric pressure is 200 mm Hg at 28°C, let there volume will be, V2 L

Pressure, = 200 mmHg

         = (200/76) atm

  So, P2 = (200/76) atm

Temperature = 28°C

            = (273+28) K

            = 301 K

          T2 = 302 K

We know,  

  P1×V1/T1 = P2×V2/T2

 Or, V2 = (P1×V1×T2)/(T1×P2)

       = (1×4×301)/{301×(200/76)}

       = 1.52 

Hence, the volume = 1.52 L, where the atmospheric pressure is 200 mm Hg at 28°C.