Question

Mr. Fredrickson fills 1 million balloons to a volume of 2.5 liters each at sea level (1.00 atm), at 19 degrees Celsius. If the balloons carry his house to a height of 20,000 feet (0.77 atm), what is the temperature (Celsius) if they each shrink to a volume of 2.0 liters?

Answer 1

Answer : The temperature (Celsius) if they each shrink to a volume of 2.0 liters is,
`93.1^oC`

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 = 1.00 atm

`P_2` = final pressure of gas = 0.77 atm

`V_1` = initial volume of gas = 2.5 L

`V_2` = final volume of gas = 2.0 L

`T_1` = initial temperature of gas =
`19^oC=273+19=292K`

`T_2` = final temperature of gas = ?

Now put all the given values in the above equation, we get:

`(1.00atm* 2.5L)/(292K)=(0.77atm* 2.0L)/(T_2)`

`T_2=179.9K=273-179.9=93.1^oC`

Therefore, the temperature (Celsius) if they each shrink to a volume of 2.0 liters is,
`93.1^oC`