Question

an arctic weather balloon is filled with 2.59 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 9. °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. $T_1=(8 + 273.15)\text{ K}=281.15\text{ K}$, $T_2=(9+ 273.15)\text{ K}=282.15\text{ K}$, and $V_1 = 2.59\text{ L}$.

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

From $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, we get $V_2=\frac{V_1T_2}{T_1}$.
Substitute the values: $V_2=\frac{2.59\times282.15}{281.15}$.
Calculate the numerator: $2.59\times282.15 = 2.59\times(281.15 + 1)=2.59\times281.15+2.59=728.1785+2.59 = 730.7685$.
Then $V_2=\frac{730.7685}{281.15}\approx2.60\text{ L}$.

Answer:

$2.60\text{ L}$