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

2 Answers
Aug 6, 2018

Answer:

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

Answer:

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