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To keep a cup warm, heat losses through conduction, convection and radiation should be minimized as much as possible. The easiest way to do this is to hold it in your hands and cover the top.
The month is January and winter is in full swing. It’s snowing outside, but you have to reach the office. Your hands are freezing and you grab a cup of warm coffee to beat the chill. Holding the cup in your freezing palms, your hands slowly warm up and become comfortable again. However, you notice that the cup has become colder and wonder if putting the cup on the table would have kept it warmer.
But would the coffee have stayed warmer if placed on the table? And why did the cup cool down in your hands anyway?
A warm object loses heat until it reaches a state of thermal equilibrium with its surroundings. (Photo Credit : twenty20)
The answer to the above questions is provided by Thermodynamics.
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Heat Energy And Heat Flow
Thermodynamics (thermal + dynamic) is a branch of science that studies the interaction of heat energy with the surrounding matter. The feeling of hot or cold is a measure of kinetic energy (energy due to motion) of the molecules constituting that object. If something is perceived as being hot (a higher temperature), then the molecules of that object possess greater kinetic energy than an object that is perceived to be cold (lower temperature).
Whenever two objects at different temperatures (i.e., constituent molecules having different kinetic energies) are brought in contact with each other, the following happens:
- The object at a higher temperature (higher kinetic energy of molecules) loses heat.
- The object at a lower temperature (lower kinetic energy of molecules) gains heat.
- The flow of heat from the object at a higher temperature to the object at lower temperature occurs as long as a temperature differential exists. The flow stops when both the objects reach the same temperature. This is called ‘thermal equilibrium’.
Mechanisms Of Heat Transfer
Heat transfer occurs in the following ways:
1) Conduction: The flow of energy between two objects at different temperatures in physical contact with each other is called conduction. Kinetic energy is transferred due to the collision of molecules at the interface of both the objects without inter-mixing, e.g., your palms wrapped around a warm coffee cup.
The molecules of coffee, having high kinetic energy, collide with the cup walls and impart energy to its molecules. Some of that kinetic energy is then imparted by the sides of the cup to your hands.
The rate of heat transferred per unit time (Q) is given by:
where
A = Area of surface (cup wall) in contact between the hotter object;
k = Thermal Conductivity of the medium (cup) through which heat flows;
d = Thickness of medium (cup cross section) conducting heat;
= Temperature of hotter object (coffee);
= Temperature of colder object (Palms);
Heat energy travels from the end near the flame to the opposite end due the collision of molecules with each other
2) Convection: The flow of energy from a fluid to a surface due to the movement of fluid in bulk along the surface is called convection. Transfer of heat occurs from the fluid to the surface, e.g., heat felt on the palms beside the hot coffee cup (without your hands touching the cup).
The cup walls gain energy by conduction from coffee. The walls then heat the surrounding air through conduction. The hot air beside the cup rises and moves along the surface of the nearby palms, imparting energy. The rate of heat transferred per unit time (Q) is given by:
where
h = Convective heat transfer coefficient;
A = Area of the surface in contact with fluid;
= Temperature of the fluid in motion;
= Temperature of the surface;
The hot fluid rises up and the cold fluid falls down. The upward motion of hot fluid imparts some energy to the cold fluid above.
3) Radiation: The flow of energy in the form of electromagnetic waves without the presence of a physical medium is called radiation. If a medium is present, no energy is imparted to that medium (unlike in conduction and convection).
Every object in the universe radiates energy in the form of electromagnetic waves at the infrared end of the EM spectrum. A cup also radiates EM waves. The open top imparts direct radiation from the coffee. The closed bottom and sides gain heat energy by conduction from the coffee, and then radiate some of that energy to the surroundings. The amount of heat energy radiated per unit (Q) time is given by:
where
= Emissivity of the object (gives an idea about how good an emitter the object is);
A = Area of radiating surface (Open top + Lateral Area of Cup walls);
= Stefan’s Constant
= Temperature of radiator
= Temperature of surroundings
Infrared image of a radiator. Red-Yellow indicates high temperature and Blue-Violet indicates low temperature (Photo Credit : Ivan Smuk/Shutterstock)
The Answer
The cup of coffee in our case loses heat through the three mechanisms discussed above. The question presents the following scenarios:
| CASE 1: Cup Kept On The Table | CASE 2: Cup Held In Palms |
| The open top (coffee) radiates heat to the surroundings, given by mechanism 3 | The open top (coffee) radiates heat to the surroundings, given by mechanism 3 |
| The bottom surface loses heat through conduction to the table, given by mechanism 1 | The bottom surface radiates heat to the surroundings, given by mechanism 3 |
| The sides of the cup radiate heat to the surroundings, given by mechanism 3 | The sides of the cup conduct heat to the palms, governed by mechanism 1 |
(NOTE: Since convection is the transfer of heat due to the bulk motion of fluid along a surface, it doesn’t contribute to the cases discussed above. If the palms were kept beside the cup, but not touching it, then convection would have contributed.)
When all variables remain unchanged, radiation is the fastest mode of heat transfer (faster than convection and conduction), as it occurs at the speed of light (3 m/s).
From the above discussion, it is evident that in CASE 1, there is maximum radiative loss directly from coffee/cup walls. This results in a significantly faster loss of heat than in CASE 2.
Therefore, to keep the cup warm, hold it between your hands!
It can be kept warm for longer if the top lid is closed and the bottom surface is covered to minimize conductive loss. Creating a vacuum layer around the cup would take care of convection losses.
Also, since EM waves obey the laws of reflection, keep a highly reflecting surface (mirror) all around the cup beyond the vacuum layer. The radiation emanating from the cup will be reflected back into the cup, keeping the coffee warm for hours. Or you can save yourself a lot of time and just buy yourself a high-end thermos!
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Volcanoes are a vivid example of incandescent molten rock
In the English language, we understand "white hot" to be hotter than "red hot," while "blue" is usually associated with degrees of coldness, as in "cool blue" or "icy blue." In terms of real temperature, "blue hot" is hotter than "red hot."
What is incandescence?
Incandescence is the emission of light by a solid that has been heated until it glows, or radiates light. When an iron bar is heated to a very high temperature, it initially glows red, and then as its temperature rises it glows white. Incandescence is heat made visible – the process of turning heat energy into light energy.
Our colloquial usage of "red hot," "white hot," and so on, is part of the color sequence black, red, orange, yellow, white, and bluish white, seen as an object is heated to successively higher temperatures. The light produced consists of photons emitted when atoms and molecules release part of their thermal vibration energy.
Incandescent light is produced when hot matter releases parts of its thermal vibration energy as photons. The Kelvin scale measures absolute temperature (a change of 1 K is equivalent to 1 °C), with 273 K being equivalent to water’s freezing point. At medium temperatures, say 1073 K (800 °C), the energy radiated by an object reaches a peak in the infrared, with a low intensity at the red end of the visible spectrum. As the temperature is raised, the peak moves toward and finally into the visible region. The temperature range experienced on earth, usually between 100 K and 2000 K, produces electromagnetic energy mostly in the infrared and visible light range, which gives us a convenient color temperature scale.
What is color temperature?
Light may be said to have a color temperature. Color temperature is a scale relating the color of light radiated by an object to its temperature. As color temperature rises, so the light emitted shifts towards bluer hues. In practice, the actual temperature is not the same as the color temperature, which is the reason correction factors are used.
The scale uses the colors of an abstract object called a black body radiator, which absorbs and then radiates all the energy that reaches it. This scale can be applied to a photographic lamp or even the sun, but it can also be applied to any source of light, using correction factors to allow for real surfaces not being perfect black body radiators.
For sources of light that do not rely on incandescence, such as fluorescent light, we use the correlated color temperature (CCT). These light sources will not produce light in the pattern of a black body emission spectrum. Instead, they are assigned a correlated color temperature, based on the match between human color perception of the light they produce and the closest black body radiator color temperature.
Here are the color temperatures of some common light sources:
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When we talk about blue light being cool and red light being warm, we are referring to something very different from color temperature. We are using these colors to describe our perceptions or to convey moods. Counterintuitively, blue-hot is actually hotter than red-hot.
Black body radiation
Why use a black body radiator as a standard, when no such thing exists?
It turns out that black body radiation provides us with a set of very precise working equations that relate the temperature of an object to the light it emits. Working from the ideal and using Planck"s law, we can predict the energy distribution across the spectrum for a given temperature. The total emitted power is calculated using the Stefan-Boltzmann law. The wavelength of the peak emission, and hence the color that dominates for this temperature, is provided by Wien’s displacement law. Knowing the ideal case allows us to predict or calculate actual values by correcting for the imperfections of actual hot objects.
For increasing temperatures, the sequence of radiated colors is: black, red, orange, yellow-white, bluish-white.
Planck’s black body radiation curves for increasing temperatures. Planck’s work on deriving this equation led him to a breakthrough in understanding the quantum nature of matter. These curves also show the trend of shifting peak wavelengths for increasing temperature, as predicted by Wien.
Our definition of "white" is derived from emission from the 5800 K temperature near the surface of the sun. Its peak at near 550 nm (2.25 eV) is paralleled in the maximum sensitivity of our eyes in the same region. This is usually attributed to our evolution in the vicinity of our sun. No matter how high a temperature rises, blue-white is the hottest color we are able to perceive.
Incandescence from the sun
We can use the color of hot objects to estimate their temperatures from about 1000 K, as the peak wavelength moves into the visible spectrum. The tungsten filament light bulb, the most common manmade source of light on earth, glows at about 2854 K. The sun is a natural incandescent source whose surface, the photosphere, is about 5800 K.
The emission from the surface of the sun, with its average temperature around 5800 K, gives us our definition of white; its peak wavelength near 550 nm (2.25 eV) is mirrored in the maximum sensitivity of our eyes in the same region, reflecting our evolutionary progress while exposed to the light of the sun.
The sun’s energy is understood to come from nuclear fusion reactions at its core, with the center of the sun having an estimated temperature of around 15,000,000 K. As this energy travels outwards to the sun’s surface, the energy is transferred first by radiation (through a layer called the radiative layer), being absorbed and re-emitted at decreasing temperatures. Closer to the surface, through the convective layer, convection becomes the dominant mechanism for energy transfer as the sun’s plasma is less hot and dense here, and is unable to sustain heat transfer by radiation.
By the time it reaches the surface of the sun, the photosphere, it has reached the temperature of 5800 K that we perceive as visible white light.
In addition to heat and light, the sun also emits a low-density stream of charged particles (mostly electrons and protons) known as the solar wind, which travels throughout the solar system at about 450 km/sec. The solar wind and the much higher energy particles ejected by solar flares can have dramatic effects on the earth, ranging from power line surges and radio interference to the beautiful Aurora Borealis.
The bright white colors of fireworks are examples of incandescence. Metals, such as magnesium, are heated to white-hot temperatures during combustion. The other colors produced in pyrotechnical displays employ luminescence, rather than incandescence.
Other examples of incandescence and its uses
The color of incandescence is used to measure temperature in radiation pyrometers. Illumination sources, from the primitive candle through limelight, arc lamps, and the modern incandescent-filament lamps and flash bulbs, all use incandescence; usually the goal is to avoid color and create light as uniformly white as possible.
Metalworking relies heavily on incandescence to identify distinctive changes of temperature by color. Blacksmiths temper iron at red-hot temperatures, while jewelers need to know the color temperature of a particular metal to anneal it correctly, rendering it ready for working without under- or overheating it.
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A blacksmith removing a red-hot iron ingot from a forge. |
The ideal annealing temperatures for silver (left) and gold produce the color temperatures shown: a dull pink for silver, and a red for gold. |