# Energy in a gram

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If I understand special theory of relativity right, than mass is not the amount of matter in an object, but rather the amount of energy in it. This question just came to me out of nowhere, but how much energy does it take to equal a gram?

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Well, mass is the amount of matter in the object. That matter is equivalent to a certain amount of energy. They are not the same.

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Then what is that amount of energy equivalent to?

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Then what is that amount of energy equivalent to?

E=mc2

c2 = 931.5 MeV/amu

There are 6.02 x 1023amu/gram, and 1.6 x 10-19Joule/eV

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E=mc^2

Energy in Joues = mass(kg) times the speed of light squared. speed of light is 3x10^8m/s

0.001x(9x10^16)

E=9x10^13J

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I'm not entirely sure how much energy a joul is, I'm more familiar with watts, but I'm not sure if watts is metrics or english. so how much is a joule?

E=mc2

c2 = 931.5 MeV/amu

There are 6.02 x 1023amu/gram, and 1.6 x 10-19Joule/eV

How do you do the exponents?

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I'm not entirely sure how much energy a joul is' date=' I'm more familiar with watts, but I'm not sure if watts is metrics or english. so how much is a joule?

How do you do the exponents?[/quote']

A Joule is equal to one watt-sec, therefore a gram of matter equals 25 million kilowatt-hours.

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What do you mean by '-hours'?

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What do you mean by '-hours'?

Watts in of themselves are not measures of energy, but measures of power. To get energy use must measure wattage against time.

For example, the amount of energy a light bulb uses depends on its wattage and how long it is on, or wattage x time. Ten 100 watt bulb use 1000 watts, if you had the bulbs on for an hour, the total energy used would equal 1000 x 1 = 1 kilowatt-hour. (kilowatt-hrs are also the measure your electric company uses to tell how much electricity you use in a month.)

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"A Joule is equal to one watt-sec, therefore a gram of matter equals 25 million kilowatt-hours."

Therefore, with that one gram you could power those ten 100 watt bulbs for about 2854 years (for those who have problems using the calculator ).

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"A Joule is equal to one watt-sec' date=' therefore a gram of matter equals 25 million kilowatt-hours."

Therefore, with that one gram you could power those ten 100 watt bulbs for about 2854 years (for those who have problems using the calculator ).[/quote']

Or another way of looking at it, 154 metric tons of matter could supply the Entire U.S. with electricity for one year. As a comparison, the U.S. mined some 973 million metric tons of coal last year. IOW, if we could convert it to directly to energy, we could power the U.S. at its present energy usage for a few million years on just the coal mined in one year.

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If the one gram is accelerated to near light speed so its mass increases , does the energy equivalent also increase to an observer travelling with it ? I assume it must to an stationary observer .

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If mass is in grams & velocity is cm/sec , is not energy equivalent in ergs ?

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If mass is in grams & velocity is cm/sec , is not energy equivalent in ergs ?
Ergs, Joules, Btu, calories, electron-Volts. Doesn't matter, as long as you've done the conversion properly. They're all energy units.

But yes, a g-cm2/s2 is an erg.

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If the one gram is accelerated to near light speed so its mass increases , does the energy equivalent also increase to an observer travelling with it ? I assume it must to an stationary observer .

Yes. I forget the expanded equation for this, but as you approach c your mass increases accordingly.

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