Hold a steel paper clip. Its mass is about 1 gram. If that single gram were converted entirely to energy, the release would run a city's lights, kettles and trains for a long time. This lesson says how long, and why the answer is always the same.
Mass is itself a form of energy, locked up in every object. This lesson puts a scale on the store: the exchange from mass to energy runs at an enormous rate, and the rate is fixed.
Converting even a tiny amount of mass releases a huge amount of energy.
Converting just 1 gram of mass releases about 9 × 10¹³ J.
That is roughly a large power station's full output for a day, from one gram.
The rate is fixed: every gram converted releases the same 9 × 10¹³ J, whatever the material.
Twice the mass converted releases twice the energy; the rate itself never changes.
The next lesson writes this exchange rate down as an equation.
A process converts 3 grams of mass entirely to energy. About how much energy is released?
Converting 1 gram of mass releases about 9 × 10¹³ J.
The process converts 3 grams, three times as much mass.
Three times the mass converted releases three times the energy, so the release is 27 × 10¹³ J, written 2.7 × 10¹⁴ J.
About 2.7 × 10¹⁴ J is released.
Burning 1000 kg of coal releases about 3 × 10¹⁰ J. Converting just 1 gram of mass releases about 9 × 10¹³ J. How many times as much energy does the gram's conversion release?
The two energies are 9 × 10¹³ J for the gram's conversion and 3 × 10¹⁰ J for the coal.
Divide the conversion's energy by the coal's energy.
9 ÷ 3 = 3, and the powers of ten make 10³, so the gram's conversion releases 3 × 10³ times as much.
The gram's conversion releases 3 × 10³ times as much energy: three thousand times the energy of a thousand kilograms of coal.
Lorcan fully converts two wax beads to energy. The first bead loses 1 gram of mass; the second loses 5 grams. How does the energy from the 5 gram conversion compare?
Caspian says: 'Every gram of mass, from any material, converts to the same enormous amount of energy.' Is Caspian correct?
Converting just 1 gram of mass releases about 9 × 10¹³ J. Which everyday energy total is that closest to?
Which statement about the mass-to-energy exchange rate is true?
A full tank of gasoline releases about 2 × 10⁹ J when it burns. Converting just 1 gram of mass releases about 9 × 10¹³ J. How many times as much energy is the gram's conversion? Give your answer to two significant figures.
A large power station runs at full output for one whole day. Roughly what mass, fully converted, would match the energy it puts out in that day?