Question

An arctic weather balloon is filled with 24.9 L of helium gas inside a prep shed. The temperature inside the shed is 8. °C. The balloon is then taken outside, where the temperature is -31. °C. Calculate the new volume of the balloon.

You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits.

Answer 1

21.4 L

Step-by-step explanation:

You want the volume of a balloon at -31 °C if it is 24.9 L at 8 °C at the same pressure.

Volume

Volume the volume of the gas in the balloon is proportional to the absolute temperature, other things remaining the same.

V2/V1 = T2/T1

V2 = V2·T2/T1 = (24.9 L)(-31 +273.15)/(8 +273.15) ≈ 21.4 L

The new volume of the balloon is about 21.4 liters.

__

Additional comment

Adding 273.15 to the temperature in °C converts it to a Kelvin temperature, referenced to absolute zero.