Question

If 1.00 kilograms of coal is burned, approximately 3.00 x 107 joules (J) of energy is released. How many tons of coal, when burned, would produce approximately 9.00 x 1016 J?

Answer 1

3.3 x 106 tons

Step-by-step explanation:

Since you know that E = mc2, and both equations possess the constant speed of light, set the two equations as equivalencies. For instance, E1/m1 = E2/m2. Solve for m2.

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Answer 2

`3.00*10^(6)\,tons`

Step-by-step explanation:

We can resolve this problem using a proportion because the ratio tons burned and energy produced is constant, using x for tons burned of coal to produce
`9.00*10^(16)J`:

`(x)/(9.00*10^(16)J)=(1.00\,kg)/(3.00*10^(7)J)`

solving the proportion:

`x*3.00*10^(7)J=1.00\,kg*9.00*10^(16)J`

`\frac{x*\cancel{3.00*10^(7)J}}{\cancel{3.00*10^(7)J}}=(1.00\,kg*9.00*10^(16)J)/(3.00*10^(7)J)`

`x=\frac{9.00*10^(16)kg*\cancel{J}}{3.00*10^(7)\cancel{J}}=3.00*10^(9)\,kg`

Now we have the answer but in kilograms we should convert this knowing that 1 ton = 1000 kg:

`3.00*10^(9)\,kg=3.00*10^(9)\,\cancel{kg}*\frac{1\,ton}{1000\,\cancel{kg}}`

`3.00*10^(9)\,kg=3.00*10^(6)\,tons`