Question

an arctic weather balloon is filled with 33.7 l of helium gas inside a prep shed. the temperature inside the shed is 7. °c. the balloon is then taken outside, where the temperature is -4. °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

Use the formula \(T(K)=T(^{\circ}C)+273.15\).
For initial temperature \(T_1 = 7^{\circ}C\), \(T_1=7 + 273.15=280.15\space K\).
For final temperature \(T_2=- 4^{\circ}C\), \(T_2=-4 + 273.15 = 269.15\space K\).

Step2: Apply Charles's Law

Charles's Law is \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\), where \(V_1 = 33.7\space L\), \(T_1 = 280.15\space K\), \(T_2=269.15\space K\).
Rearrange for \(V_2\): \(V_2=\frac{V_1\times T_2}{T_1}\).
Substitute values: \(V_2=\frac{33.7\times269.15}{280.15}\).
Calculate \(V_2=\frac{9070.355}{280.15}\approx32.4\space L\).

Answer:

\(32.4\space L\)