Question

Show the simplification from `(8.31 "LKPa")/("molK"` to `(8.31 "J")/("molK")`?

Answer 1

LkPa and joules can both be simplified to `Nm` as shown below

Explanation:

We are trying to prove that `1 LkPa=1 J`

`J=Nm` so we want to find the same units on the left side of the equation

Liters can be measured in cubic meters
`1 L=.001 m^3=10^-3m^3`

Pascals are measured in Newtons per square meter (`N/m^2`)
`kPa=10^3N/m^2`

So `LkPa=10^-3m^3*10^3N/m^2` giving us `Nm`

`Nm=J` as said before

Answer 2

See below

Explanation:

Through dimensional analysis:

`(8.31 LKPa)/(molK)xx(1000 ml)/(1L)xx(1 cm^3)/(1 ml)xx(1m)^3/(100cm)^3xx(1000Pa)/(1KPa)xx(1Nm^-2)/(1 Pa)=`

The units should cancel out and you should be left with `(8.31Nm)/(molK)`

And since `J=Nm` we are done