High School

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The original pressure at 295 K was 100.8 kPa, and the pressure at the higher altitude at 252 K is 45.6 kPa. Assume the balloon does not burst.

Show a correct numerical setup for calculating the volume of the balloon at the higher altitude.

Answer :

Final answer:

The question involves calculating the new volume of gas in a balloon at higher altitude using the combined gas law formula P1V1/T1 = P2V2/T2. The correct numerical setup for the problem requires solving for V2.

Explanation:

The student is asking about the behavior of a gas within a balloon when it is subjected to changes in temperature and pressure at different altitudes according to the gas laws, particularly looking for how to calculate the volume at a higher altitude.

To answer this question, we need to apply the combined gas law, which is derived from Boyle's, Charles's, and Gay-Lussac's laws and is represented by the formula: P1V1/T1 = P2V2/T2. In this case, you need to solve for V2, which represents the new volume at the higher altitude.

To set up the correct numerical calculation you would rearrange the combined gas law to solve for V2: V2 = (P1V1T2)/(P2T1).

For example, if you had an initial pressure (P1) of 100.8 kPa, initial volume (V1) of 1,150 L at a temperature (T1) of 295 K, and you know that the pressure at the higher altitude (P2) is 45.6 kPa at a temperature (T2) of 252 K, you would plug those values into the equation to find the new volume (V2).

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