The Energy in a Gram

solved MassEnergy

Q. What is the energy equivalent of 1 g $m = 1$ g of substance, in joules?

Inputs

mass

m

1 g

Outputs

energy

E

How it's solved

Solved with MassEnergy

Given

$m = 1$ g

Find $E$ .

Working

$m = 1$ g $= 0.001$ kg
einsteins mass energy(substance) $E = m \cdot c^{2}$
$E = 0.001 \cdot {(2.99792458 \times 10^{8})}^{2}$
$E = 8.988 \times 10^{13}$ J
$E \approx 9.0 \times 10^{13}$ Jto 2 significant figures

Conclusion

Mass is energy, at the exchange rate of the speed of light squared; a gram holds as much as a large city uses in a day or more.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :the_energy_in_a_gram do4  kind :numerical5  describes "%{energy} of %{mass} of substance, in joules?"6  given mass: "1 g"7  asks energy: "What is the energy equivalent"8end

solution.rb

1require_relative "../questions/the_energy_in_a_gram"2require_relative "../science/nuclei/mass_energy"34solve :the_energy_in_a_gram, using: MassEnergy do5  objects :substance6  take mass: substance.mass78  energy = substance.energy9  answer energy:, in: "J", figures: 21011  conclusion "Mass is energy, at the exchange rate of the speed of light squared; a gram holds as much as " \12             "a large city uses in a day or more."13end

playground.rb

1require_relative "../solutions/the_energy_in_a_gram"23play_with :the_energy_in_a_gram do4  title "The Energy in a Gram"5end

The laws it drew on

quantity	written	units	within	from
speed of light	$c$	m/s	—	MassEnergy
hydrogen atom mass	$m_{H}$	kg	—	MassEnergy
neutron mass	$m_{n}$	kg	—	MassEnergy
mass	$m$	kg	0 … ∞	MassEnergy
energy	$E$	J	—	MassEnergy
atomic number	$Z$	—	—	MassEnergy
mass number	$A$	—	0 … ∞	MassEnergy
mass defect	$dm$	kg	—	MassEnergy
binding energy	$E_{b}$	J	—	MassEnergy
q value	$Q$	J	—	MassEnergy
energy of ground	$E_{g}$	J	—
mass of ground	$m_{g}$	kg	0 … ∞
energy of substance	$E$	J	—
mass of substance	$m$	kg	0 … ∞
mass defect of ground	${dm}_{g}$	kg	—
atomic number of ground	$Z_{g}$	—	—
mass number of ground	$A_{g}$	—	0 … ∞
mass defect of substance	$dm$	kg	—
atomic number of substance	$Z$	—	—
mass number of substance	$A$	—	0 … ∞
binding energy of ground	$E_{b,g}$	J	—
binding energy of substance	$E_{b}$	J	—
q value of ground	$Q_{g}$	J	—
q value of substance	$Q$	J	—

E_{b} = m_{b} \cdot c^{2}

einsteins mass energy

{dm}_{n} = Z_{n} \cdot m_{H} + (A_{n} - Z_{n}) \cdot m_{n} - m_{n}

mass lost in binding

E_{b,n} = {dm}_{n} \cdot c^{2}

energy of the lost mass

Q_{r} = {dm}_{r} \cdot c^{2}

energy a reaction gives out

E_{g} = m_{g} \cdot c^{2}

einsteins mass energy(ground)

E = m \cdot c^{2}

einsteins mass energy(substance)

{dm}_{g} = Z_{g} \cdot m_{H} + (A_{g} - Z_{g}) \cdot m_{n} - m_{g}

mass lost in binding(ground)

dm = Z \cdot m_{H} + (A - Z) \cdot m_{n} - m

mass lost in binding(substance)

E_{b,g} = {dm}_{g} \cdot c^{2}

energy of the lost mass(ground)

E_{b} = dm \cdot c^{2}

energy of the lost mass(substance)

Q_{g} = {dm}_{g} \cdot c^{2}

energy a reaction gives out(ground)

Q = dm \cdot c^{2}

energy a reaction gives out(substance)