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.

Step-by-step 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.

`(V_(1))/(T_(1)) = (V_(2))/(T_(2))`

Substitute the values into above formula as follows.

`(V_(1))/(T_(1)) = (V_(2))/(T_(2))\\(38.5 L)/(8^(o)C) = (V_(2))/(41^(o)C)\\V_(2) = (38.5 L * 41^(o)C)/(8^(o)C)\\= 197.31 L`

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