Physics Relativity/Power Question?

[justinh8]

Physics Relativity/Power Question??

Homework Statement

When a fusion power reactor is possibly created, it is expected to produce about 3 x 10^3 MW of termal power. If a fusion reaction produces 2.808 x 10^-12 Joules, how many fusion reactions must occur per second to generate this power?

The Attempt at a Solution

What i did was 3 x 10^9 J/s / 2.808 x 10^-12 J. But my problem is that if i do that i will only get seconds and not reaction per seconds. Please help.

 

[PeterO]

Homework Statement

When a fusion power reactor is possibly created, it is expected to produce about 3 x 10^3 MW of termal power. If a fusion reaction produces 2.808 x 10^-12 Joules, how many fusion reactions must occur per second to generate this power?

The Attempt at a Solution

What i did was 3 x 10^9 J/s / 2.808 x 10^-12 J. But my problem is that if i do that i will only get seconds and not reaction per seconds. Please help.

The key to the question is in red above. So presumably the answer will have units s^-1.

When you do your calculations, looking an the units, it is (Js^-1) divide (J) which gives s^-1, which seems like a good start.

By the way, the "reactions" in "reactions per second" is a count, so has no dimensions.

 

[justinh8]

Ok, can you tell me if this is correct: N = the number of reactions and Eo = 2.808x10^-12J
P = 3.0 × 10 ⁹ W = 3.0 × 10 ⁹ J / s
P = E / t --> E = P t
E = N E₀ --> N = E / E₀
N = P t / E₀ … --> … N / t = P / E₀ = [ 3.0 × 10 ⁹ J / s ] / [ 2.808 × 10 ^⁻ 12 J ]
N / t = 1.0683 × 10 ^21 / s
Is this correct?

 

[PeterO]

Ok, can you tell me if this is correct: N = the number of reactions and Eo = 2.808x10^-12J
P = 3.0 × 10 ⁹ W = 3.0 × 10 ⁹ J / s
P = E / t --> E = P t
E = N E₀ --> N = E / E₀
N = P t / E₀ … --> … N / t = P / E₀ = [ 3.0 × 10 ⁹ J / s ] / [ 2.808 × 10 ^⁻ 12 J ]
N / t = 1.0683 × 10 ^21 / s
Is this correct?

it looks to be about the right size.

EDIT: Though you were not asked for the value of N/t, you were asked "how many fusion reactions per second, so a better answer would be

There would be 1.0683 × 10 ^21 fusion reactions per second.

If a question is asked in words, it should be answered in words.
If the question was "what is the number of fusion reactions per second, then you would give just the number.

 

[justinh8]

Did i do it correctly in terms of the units? So basically isn't it just 3.0 × 10 ⁹ J / s / 2.808 × 10 ^⁻ 12 J?

 

[PeterO]

Did i do it correctly in terms of the units? So basically isn't it just 3.0 × 10 ⁹ J / s / 2.808 × 10 ^⁻ 12 J?

Yes.