Question

an arctic weather balloon is filled with 34.4 l of helium gas inside a prep shed. the temperature inside the shed is 6. °c. the balloon is then taken outside, where the temperature is -22. °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 initial temperature \( T_1 = 6^\circ\text{C} + 273.15 = 279.15\,\text{K} \)
The final temperature \( T_2 = -22^\circ\text{C} + 273.15 = 251.15\,\text{K} \)

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

We know \( V_1 = 34.4\,\text{L} \), \( T_1 = 279.15\,\text{K} \), \( T_2 = 251.15\,\text{K} \)
Solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \)
Substitute values: \( V_2 = 34.4\,\text{L} \times \frac{251.15\,\text{K}}{279.15\,\text{K}} \)
Calculate: \( V_2 \approx 34.4 \times 0.8997 \approx 31.0\,\text{L} \)

Answer:

\( 31.0 \)