Video: GCSE Physics Higher Tier Pack 1 • Paper 2 • Question 7

GCSE Physics Higher Tier Pack 1 • Paper 2 • Question 7

14:33

Video Transcript

The principle of conservation of energy states: the amount of energy before an energy conversion is equal to the amount of energy after the conversion. There have been some examples where a scientist has claimed to have found an energy conversion process in which more energy existed after the conversion than before. A scientist does experiments where they measure a small energy increase after a conversion process. Suggest why the scientist might not want to share their experimental results publicly.

We see here what the principle of energy conservation states. And we also see that in the history of science, there have been some examples where this principle seems to have been violated. Nonetheless, the principle continues to stand and in fact is one of the better supported notions in science.

With that as background, we come to our particular question which is a scientist has done a set of experiments, in which it does seem that this principle is violated — that more energy came out of a process than went into it. We want to make a suggestion as to why the scientists might not be enthusiastic about sharing these results publicly.

The reason for this goes back to what we were saying about this principle of energy conservation being so well established. We can use an analogy to this particular instance to help explain. Imagine that we’re working on a laboratory exercise. And in this exercise, we’re studying circuits.

In particular, by making measurements of the various components of this circuit, we want to verify Ohm’s law, which says that 𝑉, the potential difference, is equal to the current in the circuit multiplied by the total resistance.

Let’s imagine that we’re given the potential difference 𝑉 and we measure 𝑅 one, 𝑅 two, and 𝑅 three, the three resistors in the circuit. And then we’ve our ammeter placed in series, we measure the current running through this loop. With all these values calculated, say we combine them then to see if they confirm Ohm’s law. And say that even allowing for experimental uncertainty, they don’t; that is, they seem to contradict Ohm’s law.

If this happened to us in a laboratory exercise scenario, there are a few different conclusions we could draw. One conclusion is that our result is correct and Ohm’s law, one of the best supported and most thoroughly tested laws in physics, is actually incorrect. We could also conclude that our result as well as Ohm’s law are both incorrect or — and this is perhaps more likely — we might look with suspicion on the numbers that we measure in the calculation we went through.

After all, if it doesn’t agree with such a carefully evaluated law, might there be something incorrect about what we’ve done. This gets to the heart of this question of why the scientists doing an energy conservation experiment might not want to present those results at first.

We could say that the scientists might well think that it was quite possible that results that disagree with a well-known theory would contain errors and so would not want to present them. It’s possible of course that the scientist’s process and conclusions were all correct and that it’s the theory that needs to be adjusted.

But again, when a theory is so well tested as this one is, the more likely explanation is that an error has been made in the experiment. If you were in the scientist’s situation, what would you do? Let’s continue on and see what happens.

The scientist repeats the experiments and continues to find a small energy increase after each conversion. The scientist has no explanation for how the energy increases happen and cannot find any errors in their measurements. The scientist decides to share the results publicly to see if any other scientists know of any theories that can explain the energy increases. Suggest two other reasons why the scientist might publicly share the results.

So the plot has thickened. The experiment has been redone. But instead of resolving the question, it just deepens the question. What’s going on? Many of us have been in the same situation. No matter how carefully we walk through an experiment, our results simply do not agree with what we expect.

So now, the scientist decides it’s time to share news of this experiment with the scientific community to see if anyone else can explain just why the energy is increasing through this process. What we want to do is suggest two other reasons why the scientist might have an incentive to share the results. Let’s think through what would likely happen if news of this experimental result comes out publicly.

One thing that will probably happen is that other scientists will try to reproduce these results. That is, they’ll try to run the same exact experiment and see if they find the same thing. If and when they do that, a couple different outcomes could occur; both of which will be helpful for addressing this overall question.

In the first case, they might run the same experiment and indeed find results that seem to violate the principle of energy conservation; that is, the results would support what the scientist has found. So that’s one reason to share the results publicly in order to see if any other scientists can get experimental results that also do not conserve energy.

And another possible outcome is that when these other scientists redo the original experiment, they themselves might detect an error or errors in the process. In other words, they’re reviewing or double-checking the work of the first scientist. This then is a second reason to share these results publicly to see if anyone else can spot errors in the original process.

At this point, it’s more helpful to discover any errors that might be there than to go on being confused about why the results don’t seem to agree with a well-established principle. We see then that there is a time for double-checking our work before going public with it and that there’s a time of asking for input from others in order to spot any errors we might have made or to confirm our results.

Next, let’s start working with some of the numbers involved in this experiment.

A hypothesis is suggested to the scientist. According to the hypothesis, the input power to the energy conversion is predicted to be 1.00065 gigawatts and the output power from it is predicted to be 1.00068 gigawatts. How many watts is equal to 1.0006 gigawatts? Give your answer in standard form.

One thing we can notice about this question is that it refers to a number, which is different from either the input or output values given to us in this background statement. So we just want to be careful not to confuse these values we want then to convert this value, 1.0006 gigawatts, into units of watts.

To start on our solution, let’s consider this prefix giga and what it means for the number we’ve been given. In general, the prefix giga refers to one billion, 10 to the ninth of whatever quantity is being considered. When we’re talking about watts then like in this case, we can say that one gigawatt is equal to 10 to the ninth or one billion watts.

And let’s now apply this relationship to our actual given number, 1.0006 gigawatts. This number of gigawatts must equal that same number times 10 to the ninth watts. This is the number of watts written in standard form equal to 1.0006 gigawatts.

Let’s continue on with another calculation related to this experiment.

The energy conversion is measured by the scientist to last for 1.25 nanoseconds, using timing apparatus that has a resolution of 0.01 nanoseconds. How many more joules of energy output than energy input does the hypothesis predict would be produced in 1.25 nanoseconds?

To go about answering this question, let’s recall what the hypothesis predicted. What the hypothesis let us to expect is 1.00065 gigawatts of power input to the process and 1.00068 gigawatts output.

We notice that according to these numbers there is more power output than input. And that’s the source of our confusion about this result. For the purposes of this question though, we’ll leave that aside and we’ll simply consider how many more joules of energy output than energy input does this hypothesis predict.

We can start off by comparing the output power to the input power. And like we said, the output is actually greater than the input. We can call the change in power that occurs over the 1.25 nanoseconds in the energy conversion to be Δ𝑃.

Δ𝑃 is equal to the output power 1.00068 gigawatts minus the input power 1.00065 gigawatts. When we perform this subtraction, we get the very small seeming number of 0.00003 gigawatts. But remember giga is a prefix indicating billion. And when we recall this conversion and apply it to this particular number, we see we’re actually working with the number of three times 10 to the fourth or 30000 watts.

By calculating Δ𝑃, we’ve now calculated how many more watts of power output than power input occurred in this process according to the hypothesis. But our question doesn’t ask for watts of power, but rather joules of energy. So we want to convert between these two units.

To do that, here’s what we can recall: a watt which is the unit of power is defined as a number of joules of energy divided by a time in seconds. We can apply this definition of watt to our result Δ𝑃. This amount of power is equal to the total number of joules of energy converted in the process divided by the time the process took. And in fact, we’re told what this time is in the question statement. It’s 1.25 nanoseconds.

The prefix nano is like the opposite of the prefix giga. Whereas giga means billion, nano means one billionth, which means that 1.25 nanoseconds is equal to 1.25 times 10 to the negative ninth seconds. And looking at this resulting equation, we see it involves what we want to solve for: the joules of energy converted as well as known values.

Rearranging this equation, we see that the number of joules output greater than the number of joules of energy input is equal to three times 10 to the fourth watts multiplied by 1.25 times 10 to the negative ninth seconds. This results in a value of 3.75 times 10 to the negative fifth joules. This — so it seems from our experimental results — is the amount of energy that’s created, seemingly out of nowhere, through this experimental process.

For our next step, let’s consider the precision of one of the numbers involved in these calculations.

The power input and output values used in the hypothesis have a precision of six significant figures. To how many significant figures a precision is the measurement of the time during which the energy conversion occurs?

Let’s recall what that time was. The time for this conversion process was given as 1.25 nanoseconds using a process that had a resolution of 0.01 nanoseconds. That resolution tells us that all three of these figures are significant. When we write out this time value in standard form, we see that the coefficient — also called the significant — confirms this.

All three of the digits — one and two and five — are significant in this time. Our answer to this question then is three significant figures. That’s the precision to which the time is measured during this energy conversion process.

Lastly, as we consider this experimental process, let’s take a step back and think of any assumptions we might have made.

The input power and output power cannot be properly tested with the experimental instruments that the scientist uses. What assumption does the hypothesis make to conclude that the energy is not conserved?

Recalling that hypothesis from earlier, we recall that it told us that the output power minus the input power is equal to a positive value 30000 watts. This number would have to be zero for energy to be conserved in this process according to the hypothesis. Since it’s not and since it’s a positive value, it tells us that this process is hypothesized to create energy out of nothing.

That’s where this agreement with the energy conservation principle comes in and that’s what this whole discussion is about. But like any hypothesis we might make about experimental results, there are certain assumptions involving this one. Here is one way to picture our understanding of this experimental process.

Our understanding is that some amount of energy goes in to our experimental process or setup or method and then some amount of energy comes out. When we compare the energy out to the energy in, we expect those to be equal to one another. After all, that would agree with the principle of energy conservation.

But notice something we’re assuming. We’re assuming there’s only one energy input source and only one energy output; that is, that there’s a single overall process going on by which energy is taken in and energy is output and that it’s those inputs and outputs we’re comparing. That’s an assumption we’re making because as a matter of fact there could be more than one energy input source and more than one energy output.

If this was the case, then simply comparing one energy input source with one energy output source wouldn’t be a good test of the principle of energy conservation. Instead, we would need to consider all the energy inputs and all the energy output across however many processes we’re going on in this experiment.

When we claim through our hypothesis that there is only one energy input source and one energy output source, that’s an assumption we’re making which might not be correct. Moreover, not only could there be multiple processes going on, but remember that we’re looking at energy conservation, whereas our hypothesis speaks to power.

Power unlike energy involves the element of time. And we’ve made an assumption when we talked about the process taking 1.25 nanoseconds that the energy input and the energy output processes were taking the same amount of time.

Let’s put all this into words about what assumptions this hypothesis makes. We can write that the hypothesis assumes that the input power to the process continues for the same amount of time that the output power from the process continues.

In other words, the input and output are all part of the same process, which takes the same amount of time. That’s an assumption we’re making and it might not be accurate. Indeed, it may point to the source of our disagreement with the principle of energy conservation.

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