Intuition The ONE core ideaHeat always slides downhill from hot to cold on its own; a refrigerator is a machine that pushes heat back uphill by paying with work. Everything on this topic is just careful bookkeeping of three amounts of energy — heat pulled from the cold side, work paid, and heat dumped on the hot side — and one ratio (the COP) that scores how much heat you moved per unit of work.
Before you can read a single formula on the parent page, you must be able to read the pictures . This page builds every symbol the topic uses, one at a time, from nothing. Nothing here is assumed — if the main note leaned on it, we construct it here.
Q In words: Q quantity of energy that crosses from one body to another only because one is hotter than the other . It is measured in joules (J), the same unit as work and any other energy.
The picture: think of tiny invisible energy-parcels drifting from the warm thing into the cold thing.
Why the topic needs it: the whole device is about moving heat around , so we need a name and a unit for "how much" moved.
The single most important fact — the one the entire chapter is built to fight against:
Intuition Heat flows downhill by itselfLeft alone, heat only goes from hot to cold, never the reverse. A hot cup cools in a room; a room never spontaneously warms the cup by cooling itself. Making heat go the wrong way (cold → hot) is exactly what a fridge does, and that is why a fridge needs to be plugged in .
Definition Reservoir — "a body so big its temperature doesn't change"In words: a reservoir is a heat source or sink so large that you can pour heat in or take heat out without its temperature budging. The room is a reservoir for a fridge; the ocean is a reservoir for a power plant.
The picture: an enormous tank of water — dip a cup of hot tea in and the tank stays the same temperature.
Why the topic needs it: it lets us pin down two fixed temperatures to work between, instead of a temperature that drifts as we operate.
Temperature needs its own careful build, because the parent topic quietly demands a particular scale .
Definition Kelvin — the absolute temperature scaleIn words: Celsius (°C) puts its zero at the freezing point of water — a human convenience, not a physical zero. Kelvin (K) puts its zero at absolute zero , the coldest anything can ever be, where all thermal motion stops.
Convert: T ( K ) = T ( ° C ) + 273 The picture: a thermometer whose bottom is nailed to "no heat left at all," not to "ice melts."
Why the topic needs it: the Carnot formulas contain ratios like T C / ( T H − T C ) 0 0
W In words: W mechanical or electrical means — the compressor squeezing the gas, driven by electricity. It is not heat; it does not need a temperature difference to happen.
The picture: a hand pushing a piston, or the plug on the wall feeding the compressor motor.
Why the topic needs it: work is the cost . The 2nd law says you cannot move heat uphill for free, so W W denominator .
Here is the whole machine as one energy diagram — memorise the three arrows.
Definition Cycle — "one full loop back to the start"In words: the working substance (the refrigerant gas) goes through a repeating loop of compress → cool → expand → warm, ending in exactly the state it began . One trip round the loop is one cycle .
The picture: a runner going once around a track and stopping on the same start line.
Why the topic needs it: because the substance returns to its start, its own stored energy hasn't changed over the cycle. That is what lets us write a clean energy balance with no leftover terms.
Definition Internal energyU Δ U In words: U held inside the working substance. The symbol Δ "change in" : Δ U = U end − U start The picture: a fuel gauge on the gas itself. After one full lap it reads the same, so the needle moved by zero.
Why the topic needs it: over a cycle Δ U cycle = 0 First Law of Thermodynamics (energy in − energy out = change in internal energy) and you get Q C + W − Q H = 0 Q H = Q C + W Δ U
Definition A ratio — "how many of the bottom fit in the top"In words: a ratio b a "per one unit of b a If you moved 800 200 800/200 = 4 4 joules of heat moved per joule paid .
Why the topic needs it: "how good is my fridge?" is precisely a benefit-per-cost question, and benefit-per-cost is a ratio. That ratio is the COP .
The Carnot (best-possible) formulas need one more idea, borrowed from Entropy and the Second Law of Thermodynamics .
Definition Entropy transferQ / T In words: when heat Q T entropy equal to Q / T The picture: the same heat is "worth more disorder" when delivered to a cold body (small T Q / T hot one (large T Q / T Why the topic needs it: a perfect (reversible, Carnot ) machine generates no extra entropy, so entropy pulled from cold equals entropy dumped hot:
T C Q C = T H Q H ⇒ Q C Q H = T C T H . temperature ratio, giving the Carnot COPs T H − T C T C T H − T C T H
Energy balance QH = QC + W
Kelvin temperatures TH and TC
Entropy transfer Q over T
Read it top-down: heat, work and the cycle give the energy balance ; the balance plus the ratio idea give the COP ; adding kelvin temperatures and entropy gives the Carnot limit .
Test yourself — you are ready for the parent note only if every reveal matches what you'd say.
What is heat Q Energy that crosses between bodies because of a temperature difference; measured in joules (J).
Which way does heat flow on its own? Downhill — from hot to cold only. Reversing it needs work.
What is a reservoir? A body so large its temperature stays fixed while heat is added or removed.
What do T H T C The hot reservoir temperature (dump-to) and the cold reservoir temperature (pull-from), with T H > T C
Why must temperatures be in kelvin, not Celsius? Carnot formulas use temperature ratios , which only make sense when 0 is absolute zero (true "no heat"), not the arbitrary Celsius zero.
Convert 27 °C to kelvin 27 + 273 = 300
What is work W Energy pushed in mechanically/electrically (the compressor); it is the cost you pay, the denominator of COP.
State the energy balance and why it holds Q H = Q C + W Δ U = 0
Why is Δ U = 0 The working substance returns to its exact starting state, so its internal energy is unchanged.
Why is COP usually greater than 1? It is heat moved per work paid (a leverage ratio), not a fraction of energy converted — you can move more heat than the work you spend.
What entropy condition defines the reversible (Carnot) case? Q C / T C = Q H / T H Q H / Q C = T H / T C
