Question

An arctic weather balloon is filled with 38.5 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 -41. °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.

Answer 1

Answer: The new volume of the balloon is 197.31 L.

Explanation:

Given: $V_{1}$ = 38.5 L,        $T_{1} = 8^{o}C$

$V_{2}$ = ?,                     $T_{2} = 41^{o}C$

According to Charles law, at constant pressure the volume of a gas is directly proportional to temperature.

Formula used to calculate the new volume is as follows.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

Substitute the values into above formula as follows.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}\\\frac{38.5 L}{8^{o}C} = \frac{V_{2}}{41^{o}C}\\V_{2} = \frac{38.5 L \times 41^{o}C}{8^{o}C}\\= 197.31 L$

Thus, we can conclude that the new volume of the balloon is 197.31 L.