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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 :

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

Explanation :

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

The combined gas equation is,

[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]

where,

[tex]P_1[/tex] = initial pressure of gas = 1.00 atm

[tex]P_2[/tex] = final pressure of gas = 0.77 atm

[tex]V_1[/tex] = initial volume of gas = 2.5 L

[tex]V_2[/tex] = final volume of gas = 2.0 L

[tex]T_1[/tex] = initial temperature of gas = [tex]19^oC=273+19=292K[/tex]

[tex]T_2[/tex] = final temperature of gas = ?

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

[tex]\frac{1.00atm\times 2.5L}{292K}=\frac{0.77atm\times 2.0L}{T_2}[/tex]

[tex]T_2=179.9K=273-179.9=93.1^oC[/tex]

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

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