The Energy in a Gram

Q. What is the energy equivalent of 1 g of substance, in joules? expects 9.0 × 10¹³ J

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

The playground

Inputs

mass

m

1 g

Outputs

energy

E

The solution

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 Ruby

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

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

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

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)