Question

The air inside an inflatable standup paddleboard is 68°F and a gauge measures the pressure of this air to be 10 psi. If the volume of the air inside the board is reduced by 12% and the temperature increases to 102.2°F what is the final gauge pressure of this air in psi.?

Answer 1

DATA:

Convert initial temperature to Kelvin, as follows:

Replacing data given value into equation (1) we have:

Solving we obtain:

Similarly, convert the final temperature to Kelvin:

Solving we obtain:

Now, convert the initial pressure to   as follows:

Then, convert this value of gauge pressure to absolute pressure using:

Replacing (4) and 1 atm for atmospheric pressure into equation (5) we have:

Solving we obtain:

We need to find now, the final volume, which is reduced by 12.0% of the initial volume:

or

The gas ideal law is defined as:

For, the initial state we have:

Isolating the number of moles we have:

Similarly, for the final state we have:

isoalting the number of moles from equation (11) we have:

Equaling equations (10) and (12) we have:

or

Isolating from equation (13) we have:

Replacing (7) into equation (14) we obtain:

Inserting (2) , (3) and (6) into equation (15) we have:

Solving we obtain:

Now, the final gauge pressure is:

Solving we obtain:

Converting to psi we obtain:

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