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A certain flexible weather balloon contains 7.4 L of helium gas. Initially, the balloon is in WP at 8500ft, where the temperature is 20.6oC and the barometric pressure is 577.0 torr. The balloon then is taken to the top of Pike’s Peak at an altitude of 14,100ft, where the pressure is 400 torr and the temperature is 7.5oC. What is the new volume of the balloon at the top of Pikes Peak?

Respuesta :

The new volume of the balloon at the top of Pikes Peak is 10.2 L

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 = 577.0 torr

[tex]P_2[/tex] = final pressure of gas = 400 torr

[tex]V_1[/tex] = initial volume of gas = 7.4 L

[tex]V_2[/tex] = final volume of gas = ?

[tex]T_1[/tex] = initial temperature of gas = [tex]20.6^oC=273+20.6=293.6K[/tex]

[tex]T_2[/tex] = final temperature of gas = [tex]7.5^oC=273+7.5=280.5K[/tex]

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

[tex]\frac{577.0\times 7.4}{293.6K}=\frac{400.0\times V_2}{280.5K}[/tex]

[tex]V_2=10.2L[/tex]

Thus the new volume of the balloon at the top of Pikes Peak is 10.2 L

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