Specific heat capacity

When heat flows from one material to another, the temperature of the contact layer of the cooler material increases.  From the contact layer thermal energy has to spread throughout the cooler material by conduction or convection.  How fast the temperature in the contact layer increases depends on the specific heat capacity of the material.  The specific heat capacity c is the amount of energy it takes to raise the temperature of one kg of material by 1 degree Kelvin or Celsius.

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The specific heat capacity of water is approximately 4 times higher than that of air.  The exact specific heat capacity of a substance depends on the condition under which it is measured.  For gases, the specific heat capacity measured at constant volume is different from the specific heat capacity measured at constant pressure.

The smaller the specific heat capacity of a material that touches your skin, the less heat it takes to bring the temperature of the boundary layer up to the temperature of your skin.  How fast the heat is carried away from this boundary layer now depends on the thermal conductivity of the material and on whether or not convection currents are present.  To minimize heat loss from your skin, surround it by material of low specific heat capacity and low conductivity, and prevent convection.  In addition you must minimize heat loss via radiation.

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Radiation laws

The primary law governing radiation is the Planck Radiation Law, which gives the intensity of radiation emitted by a blackbody as a function of wavelength for a fixed temperature.  The Planck law gives a distribution, which peaks at some wavelength.  The peak shifts to shorter wavelengths for higher temperatures, and the area under the curve grows rapidly with increasing temperature.  The diagram below shows the intensity distribution predicted by the Plank law in J/(m²s) for blackbodies at various temperature.

A blackbody is a body that absorbs all the radiation that falls onto it.  It does not reflect any radiation.  It reaches thermal equilibrium with its surroundings, and in thermal equilibrium emits exactly as much radiation it absorbs.  It has emissivity = 1.  Emissivity measures the fraction of radiative energy that is absorbed by the body.

The Wien Law gives the wavelength of the peak of the radiation distribution, l_max = 3´10⁶/T.  Here l is measured in units of nanometer = 10^-9 m and T is in Kelvin.

The Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by the body.

Radiated power = emissivity ´ s ´ T⁴ ´ Area

Here s is the Stefan-Boltzmann constant, s = 5.67´10^-8W/(m²K⁴).

The Wien law explains the shift of the peak to shorter wavelengths as the temperature increases, while the Stefan-Boltzmann law explains the growth in the height of the curve as the temperature increases.  This growth is very abrupt, since it varies as the fourth power of the temperature.

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Light-colored or reflective objects have low emissivity.  They do absorb a smaller percentage of the incoming radiation than do dark objects, and also emit radiation less readily.  If you wrap a hot object in reflective aluminum foil, then the foil reflects most of the radiation emitted by the object back onto the object.  Heat loss by radiation is thus slowed down.

The Planck radiation law tells us the intensity of the radiation emitted by a hot object as a function of wavelength.  The Wien Law gives the wavelength of the peak of the distribution.  The surface temperature of the sun is 5800 ^oC = 6073 K.  The wavelength of the peak of the distribution therefore is 494 nanometer.  This wavelength lies in the yellow region of the visible spectrum.

In an incandescent light bulb a filament is heated to approximately 2500 ^oC = 2773K.  This is the maximum temperature that a tungsten filament can stand without evaporating quickly.  Compared to the sun, such a filament emits a greater fraction of its radiation in the infrared region of the electromagnetic spectrum.  The wavelength of the peak of the distribution is 1082 nanometer.  This wavelength lies in the infrared region of the spectrum.

Sunlight and light from an incandescent bulb contain all the colors of the visible spectrum.  But the intensity distribution over the different colors is different.  Sunlight appears brilliant white while a light bulb looks yellowish.

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Phase Transitions

In general, heat flows from an object of higher temperature to an object of lower temperature.  Temperature is the quantity that indicates whether or not heat will flow and in what direction it will flow.  When heat flows from a hotter to a cooler object, the temperature of the hotter object decreases, while the temperature of the cooler object rises.  The average kinetic energy of the molecules in the hotter object decreases, while the average kinetic energy of the molecules in the cooler object increases.  But when an object changes phase, its temperature does not change, even though heat is added or removed.  The melting of ice and the boiling of water are familiar examples.  During a change of phase the temperature T does not change, but the internal energy U does.  The internal energy U is the sum of the kinetic energy of the molecules and the chemical potential energy of the molecules.  During a change of phase, the average kinetic energy of the molecules stays the same, but the average potential energy changes.

Melting

Melting is a phase transition.  Ice and water are different phases of the same substance.  At atmospheric pressure ice exists at temperatures below 0 ^oC.  If we want to raise the temperature of 1 kg of ice by 1 degree Celsius, say from –5 ^oC to – 4 ^oC, we need 0.49 kcal of heat.  But if we want to melt 1 kg of ice at 0 ^oC, we need 80 kcal of heat.  This heat is used to break chemical bonds and is converted into potential energy.  It is called the latent heat of melting or latent heat of fusion. Latent heat is heat that changes the phase of a substance without changing its temperature.  As we add heat to a mixture of water and ice, heat will flow from the water into the ice at 0 ^oC until all the ice has melted.  If we could thermally isolate the mixture, it would reach thermal equilibrium at 0 ^oC, and no more ice would melt.  If heat is removed from water at 0 ^oC it freezes into ice rather tan becoming colder.  The latent heat of fusion is released.

Boiling

Boiling is a phase transition.  Water and steam are different phases of the same substance.  At atmospheric pressure water exists at temperatures between 0 ^oC and 100 ^oC.  If we want to raise the temperature of 1 kg of water by 1 degree Celsius, say from 50 ^oC to 51 ^oC, we need 1 kcal of heat.  But if we want to boil 1 kg of water at 100 ^oC and turn it into steam we need 540 kcal of heat.  This is called the latent heat of vaporization.  It is used to break the bonds that hold the water molecules together in the liquid.  The boiling temperature of water depends on the pressure.  The lower the pressure, the lower is the boiling temperature.  At lower pressure the molecules need less kinetic energy to escape from the liquid.

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Evaporation and Sublimation

The temperature of a substance is a measure of the average kinetic energy of the atoms or molecules that make up the substance.  But not all particles have the same kinetic energy, they have a distribution of energies.  Some particles in a liquid or solid may have enough kinetic energy to break the chemical bonds and leave the substance.  The liquid is evaporating and the solid is subliming.  When the particles with the highest kinetic energy leave the substance, the average kinetic energy of the remaining particles decreases.  The temperature of the substance therefore decreases.  Evaporation cools the substance.

A toy that demonstrates the cooling process of evaporation is the dippy bird.  The dippy bird is made by blowing a glass tube that flows into a bulb like the neck of a funnel.  This upper bulb becomes the head of the bird.  A second bulb becomes the body.  The tube extends almost to the bottom of this lower bulb, like a straw into a softdrink.

The bird is filled with a liquid which has a high vapor pressure.  The bird's head is covered with fuzz, which gives a large area for evaporation.  When the head is wet, evaporation causes cooling and condensation of the fluid inside the head bulb.  This causes the fluid to creep up the neck to the area of lower pressure.  The center of gravity shifts to the head end of the bird.  The bird tips into the beaker of water where the fuzz becomes wet again.  But as the bird reaches its maximum lean, the bottom end of the tube sticks out of the fluid, and the fluid can flow out of the tube back into the bottom bulb.  This shifts the center of gravity back.  The process continues as long as there is water in the beaker.

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Relative Humidity

Molecules can leave liquid water through evaporation, but molecules also can re-enter the liquid water if there is water vapor in the surrounding air.  We call this phenomenon condensation.  The relative humidity is the ratio of the rate of condensation to the rate of evaporation.  If twice as many molecules leave the liquid than are returning to the liquid, then the relative humidity is 0.5 or 50%.  The relative humidity depends on the temperature and on the density of the water vapor in the air.  The higher the temperature, the higher is the average kinetic energy of the molecules and therefore the rate at which they are leaving.  The higher the density of water vapor in the air, the higher is the rate the molecules are returning.  If you seal water inside a container, it will evaporate, until the rate of evaporation equals the rate of condensation.  The relative humidity is then 100% and the air is saturated.

Question:

Would the "Dippy Bird" still work, if the humidity were 100%?

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