Cost of Rest Energy of 1.0 Kg at $0.60/kWh

[jackster18]

Homework Statement

How much would the rest energy of a 1.0 Kg mass cost at the typical utility rate of $0.60/ kWh?

Homework Equations

E=mc^2

The Attempt at a Solution

Heres what somone told me from another website:

"The rest energy of a mass is the energy calculated by E=mc^2 when the mass is at rest.

E = (3E8 m/s)^2 * 1kg = 9E16 J

1 kWh = (1000 J/s)(3600 s) = 3.6E6 J

Energy * Cost/Energy = Cost
(9E16 J) * (1 kWh / 3.6E6 J) * ($0.60 kWh) = 15 billion dollars"

but i don't understand the last part, where they multiply (9E16 J) * (1 kWh / 3.6E6 J) * ($0.60 kWh). The eprson said Energy * Cost/Energy = Cost, so wouldn't that just be (9E16 J)(($0.60 kWh)/(9E16 J))?

 

[jackster18]

anyone there?

 

[alphysicist]

Hi jackster18,

The first two terms

$$(9\times 10^{16} \mbox{ J}) \times \left(\frac{1 \mbox{ kWh} }{ 3.6\times 10^6 \mbox{ J}}\right)$$

converts the energy in units of Joules to units of kWh.

Once you have the amount of energy in kWh, you know that each kWh costs 60 cents. So you multiply:

$$(\mbox{energy in kWh}) \times \left(\frac{\$ 0.60 }{ \mbox{kWh}}\right)$$

to find the total cost in dollars.