Question

an arctic weather balloon is filled with 10.7 l of helium gas inside a prep shed. the temperature inside the shed is 5. °c. the balloon is then taken outside, where the temperature is -17. °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 temps to Kelvin

$T_1 = 5^\circ\text{C} + 273.15 = 278.15\ \text{K}$, $T_2 = -17^\circ\text{C} + 273.15 = 256.15\ \text{K}$

Step2: Apply Charles's Law

$\frac{V_1}{T_1} = \frac{V_2}{T_2} \Rightarrow V_2 = V_1 \times \frac{T_2}{T_1}$

Step3: Calculate new volume

$V_2 = 10.7\ \text{L} \times \frac{256.15}{278.15} \approx 9.78\ \text{L}$

Answer:

9.78 L