Question

In Vancouver where the air pressure is 98kPa, a child is given a 2.7 L ballon. The family then drives to Banff which is 1386 m above sea level and the air pressure is only 85 kPa. If the temperature is the same in both places, what is the volume of the baloon in Banff?.

Answer 1

The volume of the balloon in Banff is 3.113 liters.

According to the equation of state for ideal gases, the pressure ($P$), in kilopascals, is inversely proportional to the volume ($V$), in liters. The final volume of the balloon is found by the following relationship:

$V_{2} = \frac{P_{1}\cdot V_{1}}{P_{2}}$ (1)

Where:

• $V_{1}$ - Initial volume, in liters.
• $V_{2}$ - Final volume, in liters.
• $P_{1}$ - Initial pressure, in kilopascals.
• $P_{2}$ - Final pressure, in kilopascals.

If we know that $P_{1} = 98\,kPa$, $P_{2} = 85\,kPa$ and $V_{1} = 2.7\,L$, then the final volume of the balloon is:

$V_{2} = 2.7\,L\times \frac{98\,kPa}{85\,kPa}$

$V_{2} = 3.113\,L$

The volume of the balloon in Banff is 3.113 liters.

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