Question

an arctic weather balloon is filled with 47.6 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 -5. °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

$T_1 = 14^\circ\text{C} + 273.15 = 287.15\ \text{K}$, $T_2 = -5^\circ\text{C} + 273.15 = 268.15\ \text{K}$

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

$V_2 = V_1 \times \frac{T_2}{T_1} = 47.6\ \text{L} \times \frac{268.15}{287.15}$

Step3: Calculate and round

$V_2 \approx 47.6 \times 0.9338 \approx 44.4\ \text{L}$

Answer:

44.4