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A sample of gas in a balloon has a temperature of (+ 23.1oC), a current volume of 15.93 L and a pressure of 763 mmHg. If the balloon rises in the atmosphere and takes on a new volume of 45 .00 L at a pressure of 720 mmHg, what is the temperature at this altitude?

Respuesta :

Answer:

516°C is the temperature at this altitude.

Explanation:

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 in balloon = 763 mmHg

[tex]P_2[/tex] = final pressure of gas in balloon= 720 mmHg

[tex]V_1[/tex] = initial volume of gas in balloon= 15.93 L

[tex]V_2[/tex] = final volume of gas in balloon= 45.00L

[tex]T_1[/tex] = initial temperature of gas in balloon= [tex]23.1^oC=273+23.1=296.1 K[/tex]

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

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

[tex]\frac{763 mmHg\times 15.93 L}{296.1 K}=\frac{720 mmHg\times 45.00L}{T_2}[/tex]

[tex]T_2=789 K=789-273 ^oC=516^oC[/tex]

516°C is the temperature at this altitude.

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