# Why is the joule, the SI unit of energy, also the appropriate unit for measuring heat?

May 6, 2017

1 Joule = 1 $K g {m}^{2} / {s}^{2}$ a complex unit derived from the definition of work.

#### Explanation:

The definition of work is a force acting over a distance.
=> Work = Force x Distance = F x d

From Newton's 2nd Law of Motion, Force = Mass x Acceleration
=> F = m x a

Substituting m x a for F in the Work formula => Work = m x a x d

The SI Unit for mass = $\text{Kilograms} \left(K g\right)$, acceleration $\left(\frac{m e t e r s}{\sec o n d} ^ 2\right)$ =$\left(\frac{m}{s} ^ 2\right)$ and distance = $m e t e r s \left(m\right)$.

Substituting into Work = mass x acceleration x distance

= $\left(K g\right) \left(\frac{m}{s} ^ 2\right) \left(m\right)$ = $K g {m}^{2} / {s}^{2}$ = $\text{Joule}$.

The other unit for heat quantities is the 'scientific calorie', or calorie (c) ; not to be confused with the neutritional calorie (C) (= 1000 scientific calories, or 1 Kilocalorie). The relationship between the two energy terms is as follows ...

1 calorie = 4.184 joules