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A weather balloon is infated to a volume of 26.5 L at a pressure of 745 mmHg and a temperature of 23.3 °C. The balloon rises in the atmosphere to an altitude where the pressure is 360. mmHg and the temperature is -13.7°C Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Respuesta :

Answer: 48 Liters.

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 = 745 mmHg

[tex]P_2[/tex] = final pressure of gas =360 mmHg

[tex]V_1[/tex] = initial volume of gas = 26.5 L

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

[tex]T_1[/tex] = initial temperature of gas = [tex]23.3^oC=(273+23.3)K=296.3K[/tex]

[tex]T_2[/tex] = final temperature of gas = [tex]-13.7^oC=273+(-13.7)K=259.3K[/tex]

Now put all the given values in the above equation, we get the final pressure of gas.

[tex]\frac{745mmHg\times 26.5L}{296.3K}=\frac{360mmhg\times V_2}{259.3K}[/tex]

[tex]V_2=48L[/tex]

Therefore, the volume of the gas will be 48 Liters.

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