Question

an arctic weather balloon is filled with 14.3 l of helium gas inside a prep shed. the temperature inside the shed is 9. °c. the balloon is then taken outside, where the temperature is 1. °c. calculate the new volume of the balloon.
you may assume the pressure on the balloon stays constant at exactly 1 atm. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Convert temperatures to Kelvin

The formula for Charles's Law is $\frac{V_1}{T_1}=\frac{V_2}{T_2}$. Temperatures must be in Kelvin. $T_1=(9 + 273.15)\text{ K}=282.15\text{ K}$, $T_2=(1 + 273.15)\text{ K}=274.15\text{ K}$, and $V_1 = 14.3\text{ L}$.

Step2: Rearrange Charles's Law to solve for $V_2$

From $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, we get $V_2=\frac{V_1\times T_2}{T_1}$.
Substitute the values: $V_2=\frac{14.3\times274.15}{282.15}$.
Calculate $V_2=\frac{14.3\times274.15}{282.15}\approx14.3\times0.9716\approx13.9$.

Answer:

$13.9\text{ L}$