joule per kilogram

SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol

Name	Symbol	Quantity	Base units
joule per kilogram	J/kg	specific energy	m² s⁻²
The joule per kilogram, symbol J/kg, is the SI coherent derived unit of specific energy. One joule per kilogram is equal to the specific energy of a substance that has one joule of energy associated with one kilogram of the substance.
Definition			c²
$1 \mspace{4mu} \text{J} / \text{kg} \mspace{6mu} = \dfrac{1}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2} \mspace{6mu} c^2\\ \\ \\ 1 \mspace{4mu} \text{J} / \text{kg} \mspace{6mu} \approx 1.112 \mspace{4mu} 650 \mspace{4mu} 056 \mspace{4mu} 053 \mspace{4mu} 618 \mspace{4mu} 432 \times10^{-17} \mspace{6mu} c^2$

The fixed numerical value of the speed of light in vacuum, c, is defined as 299 792 458 when expressed in the unit m s⁻¹.

$c \mspace{6mu} = 299 \mspace{4mu} 792 \mspace{4mu} 458 \mspace{6mu} \text{m} \mspace{6mu} \text{s}^{-1}$

Inverting this relation gives an exact expression for the metre per second in terms of the SI defining constant c :

$1 \mspace{6mu} \text{m} \mspace{6mu} \text{s}^{-1} \mspace{6mu} = \dfrac{c}{299 \mspace{4mu} 792 \mspace{4mu} 458}$

The effect of this definition is that one metre per second is exactly ¹⁄_{299 792 458} of the speed of light in vacuum.

Given that the joule per kilogram is equal to (m s^-1)², when expressed in terms of SI base units, it follows that one joule per kilogram is exactly ¹⁄_{(299 792 458)²} of the square of the speed of light in vacuum.

$1 \mspace{6mu} \text{J/kg} \mspace{6mu} = 1 \mspace{6mu} {(\text{m} \mspace{6mu} \text{s}^{-1})}^2 \mspace{6mu} = \dfrac{c ^2}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}$