Question

A weather balloon is inflated to a volume of 27.6 L at a pressure of 755 mmHg and a temperature of 29.9 ∘C. The balloon rises in the atmosphere to an altitude where the pressure is 385 mmHg and the temperature is -14.1 ∘C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Answer 1

Answer: The volume of the balloon at this altitude is 46.3 L

Step-by-step explanation:

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law

The combined gas equation is,

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

where,

`P_1` = initial pressure of gas = 755 mm Hg

`P_2` = final pressure of gas (at STP) = 385 mm Hg

`V_1` = initial volume of gas = 27.6 L

`V_2` = final volume of gas = ?

`T_1` = initial temperature of gas =
`29.9^0C=(29.9+273)K=302.9K`

`T_2` = final temperature of gas =
`-14.1^0C=((-14.1)+273)K=258.9K`

Putting all the values we get:

`(755* 27.6)/(302.9)=(385* V_2)/(258.9)`

`V_2=46.3L`

Thus the volume of the balloon at this altitude is 46.3 L