The pressure 45.0 meters under water is 543 kPa. What is this pressure in atm?

1 Answer
Oct 30, 2016

Answer:

#"5.28 atm"#

Explanation:

Your task here is to convert from kilopascals, #"kPa"#, to atmospheres, #"atm"#, by using a conversion factor.

For starters, you should know that the pascal, #"Pa"#, which is the SI unit for pressure, is defined as a force of #"1 N"# pressing down a surface of #"1 m"^2#

#"1 Pa" = "1 N"/"1 m"^2#

At sea level, the molecules of air that make up the atmosphere press down on each square meter with a force of #"101325 N"#, which basically means that at sea level, the atmospheric pressure is equal to

#"101325 N"/"1 m"^2 = "101325 Pa"#

This is also defined as one standard atmosphere, which means that you have

#"1 atm " = " 101325 Pa"#

Since you know that

#"1 kPa" = 10^3"Pa"#

you can say that you have

#color(purple)(bar(ul(|color(white)(a/a)color(black)("1 atm " = " 101.325 kPa")color(white)(a/a)|)))#

This is your conversion factor. You can use it to say that the pressure at #"45.0 m"# below surface level is equal to

#535 color(red)(cancel(color(black)("kPa"))) * "1 atm"/(101.325color(red)(cancel(color(black)("kPa")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("5.28 atm")color(white)(a/a)|)))#

The answer is rounded to three sig figs.