Energy Transfers Lab Simulator

What Is the Energy Transfers Simulator?

How to use the energy transfers physics simulator

1. Read the four cards before you touch anything. They sit at the top of the panel and are already answering for a one-litre kettle: Energy supplied 220.0 kJ, Into the store 209.1 kJ, To the surroundings 10.95 kJ, and Pathways in use electrically -> by heating, by radiation.
2. Read the sub-line under each one, because that is where the card shows its working. They read P × t = 2200 W × 100 s, water’s thermal store, by heating 10.45 kJ · by radiation 496.1 J and mechanically carries 0 J here. The last of those is a pathway that carries nothing being named rather than hidden.
3. Now look at the strip of six cells under the diagram, and do not cross two of them. by heating reads 219.5 kJ there, which is the total on that pathway — the branch into the water plus the branch into the room. It is a different quantity from the To the surroundings card’s 10.95 kJ, and the diagram draws them as two separate branches.
4. Drag Run time t from 100 s to 200 s and watch only the store stand still. Energy supplied doubles to 440.0 kJ, To the surroundings goes to 231.0 kJ and the radiated cell to 992.1 J, while Into the store sits exactly where it was at 209.1 kJ.
5. Pull Water temperature rise dT all the way down to 0 K. Into the store reads 0 J, the radiated cell reads 0 J because the body is now at room temperature, and the pathway card shortens to electrically -> by heating. A pathway carrying nothing is dropped from that line instead of being printed as a zero branch.
6. Break the account on purpose: put Mass m at 2.00 kg with everything else back at its opening value. Into the store climbs to 418.1 kJ against a 220.0 kJ supply, the status cell reads cannot balance — short by 198.6 kJ, the balance cell reads no remainder to check, and the store’s sub-line gains · demanded, not supplied.
7. Move Device to the winch and watch the mass slider refuse to carry its old value. 1.00 kg is below the winch’s own minimum, so the slider comes to rest on 5 kg rather than jumping anywhere; Water temperature rise goes disabled and dimmed and Lift height h comes live. Press Winch, 120 kg load and the store becomes 11.77 kJ of gravitational potential store, with by radiation carries 0 J here underneath.
8. Press Reset when you have finished. It puts the device back to the kettle and the sliders back to 2200 W, 100 s, 1.00 kg and 50 K, with the lift height disabled again at 10.0 m, and it replays the settle, so the diagram grows back out of nothing rather than cutting straight to the answer.

Dragging is the right way to find out which readings move together and a poor way to hit an exact figure, because the supply slider steps ten watts at a time and the run time five seconds. When you already have a volume of water and a temperature rise in front of you and want the joules typed rather than dialled, the water heating energy calculator takes them directly. The written guide to energy transfers in physics is where the stores-and-pathways model itself is set out, with the four pathway names defined and worked problems on each.

One thing this panel will not decide for you is which store a given device is supposed to fill. That is a judgement about what the machine is for, and it is upstream of every joule on the screen: call the wrong branch the useful one and the account still balances perfectly while telling you nothing. Settle that first, then come back and read the widths.

Worked example: the same store, two different supplies

Nothing in the two tables below was worked out here. Each row is a setting the lab was put into through its own sliders and then read back from, cell by cell, so every string in them is the panel’s own. The first table is two presets side by side; the second is all five.

One: the same joules into the water, from two different supplies

Press Kettle, one litre and then Low power, long run. The mass and the temperature rise are identical in both, so the water takes identical joules; only the power and the run time differ, and they differ in opposite directions.

Read the third column first, because it is the one that does not move. Both rows put 209.1 kJ into the water, and the panel prints the same four characters in both. The water cannot tell which supply filled it, and nothing in the second and third columns is a rounding coincidence.

Now read the fourth column. The slow run hands the surroundings 30.95 kJ where the fast one hands them 10.95 kJ, for the same job done. The whole of that 20.00 kJ difference is the extra supply: the trunk reads 240.0 kJ against 220.0 kJ, the store does not move, and most of the extra leaves by heating — the sub-line under that card goes from by heating 10.45 kJ to by heating 28.57 kJ.

The sixth column is the mechanism, not the bulk of it. The radiated branch grows from 496.1 J to 2.381 kJ, because radiation is a rate multiplied by a time and the slow run gives it 4.8 times as long, and that growth is under two kilojoules of the twenty. The three mechanisms behind the two thermal pathway names are set out in the guide to conduction, convection and radiation.

The fifth column is the one to read carefully. It is the total on the by-heating pathway, so it counts the branch into the water as well as the branch into the room, and that is why it reads 219.5 kJ and 237.6 kJ rather than anything resembling the fourth column.

Two: the five presets, and what each one is for

These are the buttons above with the readings they produce. The fourth column is the sub-line under Into the store, which is the only place the panel names the store by name, and the last column is the pathway card itself.

Rows one and two are the same device at two sizes, and the diagram is identical. The mug takes under a third of the joules, and every branch shrinks by the same factor, so the three widths come out exactly where the kettle’s do. One shared scale means the picture shows shares, and shares are what two rows of this kind have in common.

Rows four and five are the other device, and the sixth column is the tell. It reads 0 J on both, because the winch has no modelled radiating surface, and the pathway card in the last column names mechanically in its place. At most three of the four pathway names ever carry joules at once, and on all five presets exactly three do; empty a branch, as the zero temperature rise above does, and the card simply gets shorter. The store those two rows fill is the subject of the guide to gravitational potential energy, which also covers the masses and heights this lab’s sliders cannot reach.

Formula and symbol reference: the names on the diagram

The identity at the head of this page is the whole model: the joules that came in equal the joules into the named store plus the joules to the surroundings. What fills in each term depends on the device, and the lab uses four short expressions and nothing else.

The trunk is E_in = P × t on both devices. The kept branch is m × c × dT on the kettle and m × g × h on the winch. The radiated branch is sigma × A × emissivity × (T_surf^4 - T_room^4) × t, with sigma the Stefan–Boltzmann constant and T_surf taken as the water temperature. The last term, the joules the surroundings take by heating, is then whatever is left of the supply.

The names the diagram prints, and what each one means

Four of these are pathways, two are stores, and the seventh is where the remainder goes. The lab never mixes the two kinds: a pathway is how joules travelled, a store is where they ended up, and no line in the panel describes a pathway as a place.

There is no row here for an electrical store, and that is the point rather than an omission. Electrically is a pathway in this model and only a pathway: joules travel by it and then stop somewhere else. The guide to what energy is in physics is where the question of what the quantity itself is gets answered.

Twelve quantities, and what each is allowed to do here

Five of the twelve rows below are sliders you can drag; the sixth slider is the device switch, which is in the control table higher up this page. The rest are cards, strip cells or fixed assumptions. For the sliders the last column gives the end stops, the step and a reading the panel printed at one of them; for everything else it gives the strings the lab printed and the setting they came from.

If you read one row twice, make it T^4. It is the only non-linearity in the whole model, and it is why the radiated branch cannot be scaled in your head from the temperature rise the way the store can. The water’s own figure is the ordinary one: the specific heat calculator will do the same arithmetic for a material that is not water.

The physics: why the last branch is a deduction

The surroundings branch is the one figure on this panel that no slider produces. The trunk comes from the power and the run time; the store comes from the mass and either the temperature rise or the lift height; the radiated branch comes from the stated area, the emissivity and the two temperatures. Whatever is left of the supply after those three is handed to the surroundings by heating, because conservation leaves it nowhere else to be, and the balance cell therefore reads zero by construction — the method, not a coincidence.

Be blunt about that, because a panel printing 0 J unaccounted looks like a panel that has checked something. It has not. The cell is still worth watching, but for a different reason: a branch computed wrongly would land in the remainder, and the widths beside it would look absurd long before any figure complained. What the panel will not do is break that remainder into parts it has not modelled, which is why the third card has two components under it and no more.

The state that is not settled in advance is the one where the account cannot be closed. Ask for more joules than were supplied and there is nowhere for the deficit to go: the lab clamps the remainder at zero rather than printing a negative branch, says in the status cell by how much the account is short, and clips the drawn widths to the trunk with a band saying they are no longer to scale. That is the single place this panel teaches something the arithmetic could have hidden.

The picture itself is a Sankey diagram, which is a flow diagram in which the width of the arrows is proportional to the flow rate of the depicted extensive property; the form is named after the Irish engineer Captain Matthew Henry Phineas Riall Sankey, who used one in 1898 in a figure about a steam engine. Here the extensive property is energy and the width is joules, on one scale shared by the trunk and every branch. That is why the mug and the kettle draw the same shape at different totals.

What the diagram cannot do is show a branch that is too thin to see, so below about two pixels it stops being honest about width and says so in a caption instead. The number beside the branch is always exact to four figures, the width is not always exact, and on the settings where nothing has been floored the caption is left out rather than printed as a standing disclaimer.

Where the energy transfers simulator breaks down

Every slider position this lab can reach is answered, and the arithmetic is not where it can let you down. What it cannot do is model a real appliance, and what it chooses not to do is split the remainder into named parts. Nine limits sit under the readings on this page.

Four of the numbers behind the diagram are assumptions, not measurements

The panel prints them in its own fixed line and calls them assumptions there: water at 4181 J/(kg·K), surroundings at 20.00 °C, a kettle body of 0.045 m² and an emissivity of 0.30. The first is an ordinary textbook value for liquid water near room temperature. The last two are the lab’s own stand-in for a brushed stainless shell and describe no product you can buy, so the radiated branch should be read as what follows from those stated values rather than as a fact about kettles.

The kettle body has no thermal store of its own

A real kettle warms up as well as the water in it, and those joules are genuinely stored rather than passed on. Here the body has a temperature and an area for the purpose of radiating, and no heat capacity at all. Anything that would have gone into warming the shell therefore turns up inside the remainder instead, which is one reason the surroundings branch is bigger than a careful experiment would find.

Steam carrying energy out of the spout is inside the remainder, not beside it

Evaporation is a real and sometimes large branch of a kettle’s account, and it is not drawn here. The lab names four pathways and splits the surroundings into the two it can compute, so everything else that left the device — steam, conduction through the base, convection off the sides — is lumped into the by-heating branch to the surroundings. The account still closes; it simply closes with one coarse branch where a real audit would have several.

The surface is assumed to sit at the water temperature

The radiated branch is computed from a surface temperature equal to the room temperature plus the water’s own rise, which is the most generous assumption available. A real shell is cooler than the water inside it, usually by a good deal, so the radiated figure here is an upper bound rather than an estimate. It is also the branch the T^4 term makes most sensitive to that choice.

The balance row cannot fail, so it proves nothing on its own

It reads 0 J unaccounted on every setting that balances because the remainder was defined to make it so. Treat it as a bookkeeping line rather than a check. The reading that can genuinely change is the one beside it: the account status, which goes from balances to a deficit as soon as the named branches ask for more than the trunk holds.

No negative figure is reachable, and that is enforced rather than hoped for

When the account cannot close, the remainder is clamped to zero instead of going below it, the balance cell prints no remainder to check rather than a number, and the branch widths are clipped to the trunk under a band saying they are not to scale. A 1.000 kJ supply asked to heat three kilogrammes of water by 80 K is reported as cannot balance — short by 1003 kJ, and even there no branch is drawn with a negative height.

A branch carrying nothing is not drawn at all

A zero-width branch cannot be painted, so on the winch there is no radiation branch in the picture and on a kettle with no temperature rise there is no store branch. The strip of six cells under the diagram reports the 0 J in each case, and the pathway card drops the name rather than printing an empty branch. If you are looking for a branch that is not there, read the strip before concluding the lab has lost it.

No pixel in the drawing is a measurement

The scene is drawn to whatever width the canvas has, so the same account occupies a different number of pixels on a phone and on a desktop, and the drawing promises no fixed width per kilojoule. What it does guarantee is one shared scale across the trunk and every branch on a given setting. Below about two pixels even that is suspended for the branch concerned, and the caption underneath says so whenever it has happened.

This lab answers a different question from the ratio one

How much of the supply reached the store, as a proportion, is a real and useful question, and it is deliberately not asked here: this panel computes no ratio and prints no percentage at all. The branches in joules and the share they represent are two different readings, and conflating them is the easiest way to misread a Sankey diagram. The efficiency formula calculator is where the proportion is worked out properly, and it takes the kind of figures this panel prints.

Where energy accounting is actually used

Deciding whether a slower setting is really kinder

This is the clearest thing the panel does and it takes two clicks. The same litre at the same 50 K rise draws 220.0 kJ on the fast preset and 240.0 kJ on the slow one, with 209.1 kJ reaching the water either way. The difference went to the room, and the radiated branch alone grew from 496.1 J to 2.381 kJ because it had 4.8 times as long to run.

Working out how much water a given supply can actually heat

Put the supply where your appliance sits and raise the mass until the account breaks. At 2200 W for 100 s with a 50 K rise the panel stops balancing between 1.00 kg and 2.00 kg: at two kilogrammes it reads cannot balance — short by 198.6 kJ. That boundary is the honest answer to how much you can heat in the time, and it arrives as a refusal rather than as a quietly wrong number.

Sizing a hoist against the job rather than against its plate

Switch to the winch and the same question becomes a lifting one. 750 W for 20 s supplies 15.00 kJ, and a 120 kg load raised 10.0 m takes 11.77 kJ of that; double the height with nothing else changed and the demand becomes 23.54 kJ, which the panel reports as cannot balance — short by 8.536 kJ. Either the run gets longer or the supply gets bigger. The guide to power in physics is where the trade between the two is set out.

Seeing which branch is worth attacking before spending anything on it

On the opening kettle the branch into the room by heating is 10.45 kJ and the radiated branch is 496.1 J, so radiation is under a twentieth of what the room took in all, and the widths say it before the figures do. The panel cannot price a fix, though: the emissivity and the area are fixed stated values, and since the remainder is whatever is left, a lower emissivity would move joules out of the radiated branch into the remainder and leave the 10.95 kJ total unmoved. Read the pair as which branch is large, not as what attacking it would save. On the slow run the balance shifts and the radiated branch becomes worth a second look.

Showing a class that a named pathway can carry exactly nothing

Press the winch preset and the strip reads 0 J beside by radiation, with by radiation carries 0 J here under the pathway card. Press the kettle preset and the same thing happens to mechanically. Naming a pathway and then giving it zero is a much stronger demonstration than leaving it out, and it is the fastest way to stop a class assuming all four are always running.

Reading somebody else’s Sankey diagram without being fooled by it

Published energy diagrams routinely redraw a thin branch so that it can be seen, and they do not always say so. This panel does the same thing at a two-pixel floor and prints a caption whenever it has, so it is a safe place to learn the habit of checking the number against the width. On the opening kettle the smallest branch is drawn more than three times wider than its share deserves, and the figure beside it is still exact.

Where to go next

A panel can show you an account and let you break it, and that is the end of what a panel is for. Energy transfers in physics is where the subject itself is written out: what a store is, what a pathway is, how a transfer differs from a transformation, and worked problems on both devices with every step shown.

Two guides sit either side of this one. The guide to energy conversion examples keeps the other account of the same joules — what became what, rather than which route it took — and the guide to conservation of energy is where the rule that makes the remainder deducible in the first place is set out.

Three more are about the thermal half of the diagram. The guide to heat and temperature separates the two quantities the kettle slider pair keeps together, the three mechanisms guide names what is actually happening inside the two thermal pathways, and the guide to the first law of thermodynamics is the same bookkeeping written as a law.

On the tool side there are the water heating energy calculator, the specific heat calculator, the gravitational potential energy calculator and the work and power calculator, with the specific heat lab and the efficiency lab for the drawn versions. Beyond them there is the simulation library, an index of calculators, and the blog for everything written out at length.