Temperature, Heat and the Kelvin Scale

Heat and temperature are two different quantities, and the tests know perfectly well that most people use the two words interchangeably. By the end of this lesson you should be able to say what each one actually is, name the unit heat is measured in, convert a temperature between degrees Celsius and kelvin in either direction without hesitating over the sign, explain why the Kelvin scale begins at −273 °C rather than at any other number, and know why a temperature difference comes out as the same figure on both scales.

Heat is energy on the move

Heat is energy transferred from one place to another because of a temperature difference, and the phrase "on the move" carries the whole idea: heat is not a substance that an object contains, it is a transfer that happens between objects. Put a hot spoon into cold water and energy passes out of the spoon and into the water until the two are equally warm, at which point the transfer stops — even though both spoon and water are still full of energy. That is why it is wrong, strictly, to say that an object has a certain amount of heat in it. What it has is internal energy, meaning the total energy of all the particles it is made of; heat is the name for energy crossing the boundary between that object and something else. The direction of the crossing is never in doubt, either: left to itself, energy always passes from the hotter body to the colder one and never the other way round.

Because heat is energy, it is measured in the ordinary unit of energy — the joule, written J. One joule is the energy transferred when a force of one newton acts through a distance of one metre, which is roughly what it takes to lift a small apple from the floor to a table top. A joule is therefore a very small amount for anything involving heat, so quantities in this module run into thousands and millions: a kilojoule is a thousand joules, written kJ, and a megajoule is a million, written MJ. Older books and food labels use the calorie, defined as the heat needed to raise one gram of water by one degree Celsius, and one calorie is about 4.2 joules. It is worth recognising the word, but every item you will meet works in joules.

Temperature is something else entirely

Temperature is how hot something is on an agreed scale, and its practical job is to tell you which way heat will flow when two things are brought into contact: from the higher temperature to the lower one, regardless of how big either object is. What temperature does not tell you is how much energy is available. Temperature tracks the average energy of the individual particles in an object, whereas the total internal energy depends on that average and on how many particles there are — so a large cool object routinely holds far more energy than a small hot one. A lit match burns at something like 800 °C and a bath of water sits at 40 °C, twenty times less on that scale; drop the match into the bath and the bath wins without noticeably warming, because the bath contains a hundred thousand times more particles than the match head does.

That distinction is worth labouring, because it is the first thing the distractors attack. A tonne of water at 20 °C and a teaspoon of water at 90 °C: the teaspoon is at the far higher temperature, and the tonne holds vastly more energy. Neither statement contradicts the other, because they are statements about different quantities. If the item asks which is hotter, it wants the temperature; if it asks which holds more energy, or which could melt more ice, it wants the total, and the total needs the mass as well.

Celsius, and where its two fixed points come from

A temperature scale needs two fixed points to pin it down and a rule for dividing up the range in between. Celsius takes the freezing point of pure water as 0 and the boiling point of pure water as 100, both measured at standard atmospheric pressure, and divides the interval into a hundred equal parts, each one degree Celsius and written °C. The pressure qualification is not fussiness: water boils at a lower temperature when the pressure over it is lower, so the boiling point is only fixed once the pressure is fixed too. Nothing about the two chosen points is deep physics — they were picked because water is convenient and universally available, which is exactly the problem the next section deals with.

The Kelvin scale, and why it starts where it does

Celsius is perfectly good for reporting weather and useless the moment you have to multiply or divide by a temperature, because its zero is an arbitrary choice rather than a real starting point. Consider what happens if you take a sealed quantity of gas, hold its pressure steady, and cool it while measuring its volume. The volume shrinks, and it shrinks in a straight line: every degree of cooling takes away the same slice of volume. Extend that straight line downwards on paper and it reaches zero volume at −273 °C. Do the experiment the other way, holding the volume fixed and measuring the pressure as you cool, and the pressure line heads for zero at the same −273 °C. Different gases, different starting volumes, the same crossing point every time.

That number is therefore telling you something about temperature itself rather than about any particular gas. It is absolute zero: the temperature at which the particles of a substance have the least energy they can possibly have, and hence the coldest temperature there is. Nothing can be cooled below it, because there is no less energy to have. Laboratories have crept to within a tiny fraction of a degree of it and never reached it. Given a genuine bottom to the scale, the sensible thing is to start counting from there, and that is the Kelvin scale: same size of degree as Celsius, but with its zero at absolute zero instead of at the freezing point of water.

So a warm room at 20 °C is at 293 K, and a cold morning at −5 °C is at 268 K. Going the other way is the same relationship rearranged: subtract 273 from both sides, and the 273 on the right cancels to leave the Celsius value alone.

Two points of notation, because both are marked. The unit is the kelvin, written K with no degree symbol and never spoken as "degrees kelvin" — a temperature is 300 K, not 300 °K. And the exact offset is 273.15 rather than 273; the modern definition of the kelvin does not mention water at all, and fixes the unit through a constant of nature instead. Every item in this area is written around 273, so use 273 and you will never lose a mark for it.

A difference is the same number on both scales

Because a kelvin and a degree Celsius are the same size of step, and the scales differ only in where they start counting, any temperature difference comes out identical on the two scales. Warm something from 30 °C to 50 °C and the rise is 20 °C; in kelvin the same change runs from 303 K to 323 K, and the rise is 20 K. The 273s were added to both ends and cancelled out of the subtraction. That is genuinely useful, because it means a temperature change can be quoted in either unit without conversion — while an absolute temperature, the kind that goes into a gas law, must be in kelvin.

Keep the two ideas separate in your head, because they are the difference between a right and a wrong answer: differences may be quoted in either unit, absolute temperatures may not.

Why it matters in aviation

Outside air temperature is one of the numbers a flight crew reads, reports and calculates with most often, because a great deal depends on it. Take-off and climb performance depend on it, the speed of sound in the air around the aircraft depends on it, and so does the gap between the altitude an altimeter indicates and the height the aircraft is actually at — air colder than standard leaves the aircraft lower than the instrument reads, and warmer air leaves it higher.

What is used operationally is rarely the raw reading. The temperature is compared against what a standard atmosphere would give at that level, a model the later lesson in this module sets out, and it is the deviation from standard that gets carried into the calculation. That is this lesson's point about scales doing real work: a temperature figure only means something once you have said what it is being measured against. And wherever the relationship involves a ratio of temperatures rather than a difference — the gas behaviour behind engine and pressurisation systems, for instance — the figure that goes in is the absolute one in kelvin, because only a scale that starts at absolute zero makes such a ratio mean anything.

What the test asks

Two distractors carry most of the traffic here. The first is arithmetical: an item gives a Celsius temperature and offers the answer you get by subtracting 273 instead of adding it, so 27 °C is offered as −246 K. A negative kelvin figure is impossible by construction, since the scale starts at the coldest temperature that exists, so any option below zero kelvin can be crossed out on sight. The second is conceptual, and it is the heat-against-temperature confusion dressed up as a comparison: two objects are described, one plainly larger, and the option invites you to say the larger must be at the higher temperature because it holds more energy. Size has nothing to do with temperature. Expect also an item that asks for a temperature rise and offers the answer in kelvin and in Celsius as two different numbers — they are the same number, and if the options disagree on that point one of them is there purely to be wrong.