You Can’t Win
We used to think that energy and mass were conserved independently, and for many practical purposes we still consider them so conserved. But Einstein united the two with the famous equation
E = mc²
where
E = energy (in joules)
m = mass (in kilograms)
c = speed of light
(300,000,000 meters per second)
Notice the resemblance to the kinetic energy equation shown earlier. Energy cannot appear without the disappearance of mass. When energy is locked up in a fuel, it is stored as mass. In the gasoline combustion problem, 1 gram of gasoline was burned with air to give 48,000 joules of energy. Einstein’s equation says that in this case mass disappeared in the amount
m = E/c² = (4.8 × 10⁴)/(9 × 10¹⁶) = 5.3 × 10⁻¹³ kilogram
(half a billionth of a gram)
But, when an H-bomb is exploded, grams and even kilograms of mass are converted to energy.
In direct conversion processes we do not need to worry about these mass changes, but at each point we must make sure that all energy is accounted for. For example, in outer space all energy released from fuels (even food) must ultimately be radiated away to empty Space. Otherwise the vehicle temperature will keep rising until the Spaceship melts.