Question

Airplane cabins are typically pressurized at 0.67 atm, and assuming the temperature inside an airplane is about the same as inside a potato chip processing plant, by what percentage has the bag "puffed up" in comparison to when it was packaged?

Answer 1

Answer:

$\Delta V\%=49.25\%$

Explanation:

Assuming the pressure inside the packet at the time of packaging, $P_a=1\ atm$

Given that there is no temperature difference between the air inside the pack and the cabin.

Using mathematical expression of Boyle's law:

$P_1.V_1=P_2.V_2$

where subscripts 1 & 2 denote the initial and final conditions respectively.

$1\times V_1=0.67\times V_2$

$V_2=\frac{V_1}{0.67}$

Now change in volume:

$\Delta V=V_2-V_1$

$\Delta V=\frac{V_1}{0.67}-V_1$

$\Delta V=0.4925\ V_1$

Now the % increase in volume:

$\Delta V\%=\frac{\Delta V}{V_1} \times 100$

$\Delta V\%=49.25\%$