Question

an arctic weather balloon is filled with 35.7 l of helium gas inside a prep shed. the temperature inside the shed is 14. °c. the balloon is then taken outside, where the temperature is - 30. °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.

Explanation:

Step1: Convert temperatures to Kelvin

$T_1 = 14 + 273.15=287.15\ K$
$T_2=- 30+273.15 = 243.15\ K$

Step2: Apply Charles's Law ($\frac{V_1}{T_1}=\frac{V_2}{T_2}$)

$V_2=\frac{V_1T_2}{T_1}$
Substitute $V_1 = 35.7\ L$, $T_1 = 287.15\ K$ and $T_2 = 243.15\ K$ into the formula.
$V_2=\frac{35.7\times243.15}{287.15}$
$V_2=\frac{8680.455}{287.15}\approx30.2\ L$

Answer:

$30.2\ L$