# Question 10023

Jun 10, 2017

$96$ $\text{kPa}$

#### 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:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Since we're trying to find the final pressure, let's rearrange this equation to solve for ${P}_{2}$:

${P}_{2} = \frac{{P}_{1} {V}_{1}}{{V}_{2}}$

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.