Question #10023

1 Answer
Nathan L.
Jun 10, 2017

#96# #"kPa"#

Explanation:

We're asked to calculate the new pressure of a gas after it is subjected to a change in volume with constant temperature.

We can solve this problem using the pressure-volume relationship of gases, illustrated by Boyle's law:

#P_1V_1 = P_2V_2#

Since we're trying to find the final pressure, let's rearrange this equation to solve for #P_2#:

#P_2 = (P_1V_1)/(V_2)#

Plugging in the known variables, we have

#P_2 = ((41"kPa")(14cancel("L")))/(6cancel("L")) = color(red)(96# #color(red)("kPa"#

rounded to two significant figures, the amount given in the problem.

The pressure thus increases to #96# kilopascals. This makes logical sense since because the #sfcolor(blue)("volume decreased"#, the #sfcolor(green)("pressure"# must have #sfcolor(green)("increased"#. Pressure and volume are inversely proportional.

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