Question

an arctic weather balloon is filled with 31.5 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 2. °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

$T_1 = 8^\circ\text{C} + 273.15 = 281.15\ \text{K}$, $T_2 = 2^\circ\text{C} + 273.15 = 275.15\ \text{K}$

Step2: Apply Charles's Law

$\frac{V_1}{T_1} = \frac{V_2}{T_2} \implies V_2 = V_1 \times \frac{T_2}{T_1}$
$V_2 = 31.5\ \text{L} \times \frac{275.15}{281.15}$

Step3: Calculate and round

$V_2 \approx 31.5 \times 0.9786 \approx 30.8\ \text{L}$

Answer:

30.8 L