Question

Question #10023

Answer 1

`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.