Question

What is 8200 `N``/m^2` expressed in kilopascals?

Answer 1

`"8.2 kPa"`

Explanation:

The idea here is that a pascal, `"Pa"`, is a unit of pressure defined as a force of one newton, `"1 N"`, pushing on a surface area equal to one square meter, `"1 m"^2`.

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 Pa " = "1 N"/"1 m"^2 = 1"N"/"m"^2)color(white)(a/a)|)))`

This means that the problem is actually providing you with the pressure in pascals, since

`8200 color(red)(cancel(color(black)("N"/"m"^2))) * "1 Pa"/(1color(red)(cancel(color(black)("N"/"m"^2)))) = "8200 Pa"`

All you have to do now is use the fact that

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kPa" = 10^3"Pa")color(white)(a/a)|)))`

to find the value of the pressure in kilopascals

`8200 color(red)(cancel(color(black)("Pa"))) * "1 kPa"/(10^3color(red)(cancel(color(black)("Pa")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("8.2 kPa")color(white)(a/a)|)))`