Warming 1 kg of a material by 1 K takes its specific heat in joules: 4,184 for water, 840 for brick and 129 for lead. Water takes about five times as much as brick, so it is slow to warm and slow to cool.
While ice melts or water boils, energy goes in and the temperature does not move. Boiling away a kilogram of water takes 5.4 times the energy of warming it from 0 to 100 °C.
Conduction passes it through a solid, convection carries it off in moving air or water, and radiation sends it out as infrared with no medium at all. A vacuum flask is built to stop each in turn.
A layer of thickness d and conductivity k resists the flow by d/k. Put layers in a row and the resistances add; the U-value of the wall is one over the total. A hundred millimetres of mineral wool is 2.5.
One kilocalorie, the food Calorie, is the energy to warm a kilogram of water by one degree: 4.184 kJ. A litre from 20 to 100 °C takes 335 kJ, a kettle’s worth, and the same energy would warm a kilogram of lead by 2597 °C.
1.7 litres from 20 to 100 °C takes 569 kJ, which is 0.158 kWh. At 3 kW that is 3 minutes 10 seconds if none escapes; a real kettle takes a little longer, because the element and the body of the kettle take some of the energy and some escapes as steam.
Water holds about 5 times as much heat per kilogram as rock or sand, and the sea mixes it down through many metres while the land only warms at the surface. The same sunshine therefore lifts the land by several degrees in a day and the sea by a fraction of one, which is what drives the sea breeze and keeps coastal climates mild.
Take 0.25 kg of tea at 20 °C and drop in 50 g of ice at 0 °C. Melting the ice takes 16.7 kJ, nearly all of the 17.4 kJ the tea gives up in cooling, and the whole settles at 3.4 °C. Ice is far better than the same mass of cold water, because the melting does most of the work.
Single glazing is about 5.7 W/(m²K) and ordinary double glazing about 2.8, because the sealed gap adds a resistance of 0.18. A cavity wall with nothing in the cavity is about 1.5, and filling the cavity with 100 mm of mineral wool takes it to 0.34. The more insulation, the less each extra centimetre does: going from 100 to 200 mm cuts the heat loss by less than the first 100 mm did.
The heat a surface sends out by radiation behaves like a convection coefficient of 4εσT³, which is 5.7 W/(m²K) at 20 °C for a black surface: as much as the convection from still air. Bare skin at 34 °C in a 20 °C room loses about 150 W by radiation and 151 W by convection, 301 W in all from 1.8 m², three times what the body makes at rest.
A steam pipe at 150 °C in a 20 °C room loses 780 W per square metre by convection and 1119 W by radiation, so most of its heat goes as infrared. Wrap it in shiny foil, with an emissivity of 0.05, and the radiation falls to 70 W, which is why a thermos and a space blanket are shiny.
The air of a 4 by 4 by 2.4 metre room, 46 kg, takes 740 kJ to warm by 16 °C, 6 minutes of a 2 kW heater. But the 2 tonnes of brick in its walls take 17 MJ to warm by 10 °C, about 23 times more, which is why a cold house takes hours to feel warm after the air is hot.
The specific heats and conductivities are typical values near room temperature; real wood, concrete, brick and insulation vary by 10 to 30 percent, and the specific heat of most materials rises with temperature, so a long range for a metal is an underestimate. The same specific heat is used in every state for the materials with a melting point, apart from water. The wall is one-dimensional and steady, with no thermal bridges, moisture or draughts, and the cooling is of one lump at one temperature with no evaporation. Not for sizing a heating system or a building U-value certificate.
The energy needed to raise the temperature of one kilogram of a material by one kelvin, in joules per kilogram per kelvin. It is a property of the material: 4,184 for water, 897 for aluminium, 385 for copper, 129 for lead.
Heat capacity belongs to a particular object: its mass times the specific heat, in joules per degree. A bath of water has a heat capacity of hundreds of thousands of joules per degree; a teaspoon of it a few tens. Specific heat is the same for both, per kilogram.
Because heating only speeds the molecules up, but boiling has to pull them apart from each other against the attraction that holds the liquid together, with no rise in temperature. For water that is 2,256 kJ per kilogram, against 418 kJ to heat the same kilogram from 0 to 100 °C.
Melting ice takes 334 kJ per kilogram, which is as much as warming the same mass of water by 80 °C. The ice draws that from the drink and stays at 0 °C while it does, so it cools the drink more than the same mass of cold water would.
The heat flow through a square metre of a wall, window or roof for each degree of difference between the two sides, in watts per square metre per kelvin. It is one over the sum of the thermal resistances, which include the two thin films of still air on the surfaces. A lower U-value is a better insulator.
Because trapped air is a very poor conductor, about 0.026 W/(m K), and an insulating material holds it still in small pockets so that it cannot circulate and carry heat by convection. Mineral wool, expanded polystyrene and foam are mostly air.
It is not colder, it conducts heat away from your hand faster, so your skin cools more quickly and signals cold. Copper conducts about 3,000 times as well as wood. What you feel is the rate of heat flow, not the temperature.
No. Radiation is electromagnetic waves, infrared for things at everyday temperatures, and passes through a vacuum: it is how the Sun heats the Earth. Every surface above absolute zero emits it, in proportion to the fourth power of its absolute temperature and its emissivity.
The space between its two walls is a vacuum, which stops conduction and convection, and the walls are silvered, which stops most radiation by giving them a low emissivity. What is left is conduction through the neck and the lid.
Because much of its heat goes as evaporation from the surface, which the lump model here leaves out. Each gram of water that evaporates carries away about 2.4 kJ. A lid stops most of it.
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