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

2 Answers
Aug 6, 2018

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

Aug 6, 2018

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