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

Aug 6, 2018

LkPa and joules can both be simplified to $N m$ as shown below

#### Explanation:

We are trying to prove that $1 L k P a = 1 J$

$J = N m$ so we want to find the same units on the left side of the equation

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

Pascals are measured in Newtons per square meter ($\frac{N}{m} ^ 2$)
$k P a = {10}^{3} \frac{N}{m} ^ 2$

So $L k P a = {10}^{-} 3 {m}^{3} \cdot {10}^{3} \frac{N}{m} ^ 2$ giving us $N m$

$N m = J$ as said before

Aug 6, 2018

See below

#### Explanation:

Through dimensional analysis:

$\frac{8.31 L K P a}{m o l K} \times \frac{1000 m l}{1 L} \times \frac{1 c {m}^{3}}{1 m l} \times {\left(1 m\right)}^{3} / {\left(100 c m\right)}^{3} \times \frac{1000 P a}{1 K P a} \times \frac{1 N {m}^{-} 2}{1 P a} =$

The units should cancel out and you should be left with $\frac{8.31 N m}{m o l K}$

And since $J = N m$ we are done