4.1.1: Illustrations

Specific heat (which is sometimes also called the specific heat capacity) describes how much heat is required to increase the temperature of a given quantity of material. In this Illustration a blue mass sits in an insulated oven (time is given in minutes and temperature is given in degrees Celsius). Restart. Assume that the block absorbs all the heat from the heater. Not surprisingly, a higher-powered heater (the amount of heat delivered/second) will result in a higher temperature of the blue mass during the same time interval. Notice that as you change the mass of the object, the temperature change is different (for a given power of the oven). The quantitative description of this is given by the equation

\[Q=mc(T_{f}-T_{i})\nonumber\]

where \(Q\) is the heat, \(m\) is the mass, \(c\) is the specific heat, and \(T\) is the temperature (with subscripts indicating final and initial temperatures). Note that if you double the mass, for the same total heat delivered, the temperature change will be cut in half. Different materials have different values of specific heat (or specific heat capacity). Water has a much higher specific heat than copper, for example. This is why it doess not take long for a copper kettle on the stove to increase in temperature in comparison with the water inside. Furthermore, with a full kettle of water, the water is more massive, so it also takes longer to reach an acceptable final temperature (usually around \(100^{\circ}\text{C}\) to boil).

Note

Note that the specific heat usually has units of \(\text{joules/(kg}\cdot\text{C}^{\circ})\), where \(\text{C}^{\circ}\) represents a change in temperature (your text book may or may not follow this notation).

Illustration authored by Anne J. Cox.

Exploration 2: Heat Transfer, Conduction

Heat transfers via three mechanisms: convection, radiation, and conduction. This Illustration briefly describes these mechanisms, but the animation focuses on conduction (temperature is given in degrees Celsius). Restart.

Convection is the transfer of heat energy through the motion of a gas (or liquid): Heated air expands and rises, displacing cooler air, which moves downward and is then heated and rises again, setting up "convection currents."

Radiative heat transfer occurs when an object absorbs/emits electromagnetic radiation and gains/loses energy (see Illustration 19.3).

Conduction, as shown in the animation, is the transfer of heat within a material due to a temperature difference across the object (think of a spoon in hot coffee). We describe materials that transfer heat easily (more heat/time) as having a high conductivity (e.g., metal spoon) and those that do not (e.g., cloth) as having low conductivity. The reason for having insulation in a house, for example, is to reduce the conductivity of the walls so that it requires less power to keep the inside of a house at a given temperature, even though the outside is much colder or warmer. Use the animation to change the conductivity, the temperature on the outside of the "wall," and/or the thickness of the "wall" to see the power loss. The power loss is the power required to heat or cool the inside of the house.

Illustration authored by Anne J. Cox.

Exploration 3: Heat Transfer, Radiation

Heat from the Sun is transferred via radiation to planets. A planet, in turn, radiates energy back out into space. A planet reaches its equilibrium temperature when the power delivered to it from the Sun is equal to the power a planet radiates. The power it radiates is given by the following equation:

\[P=\sigma\varepsilon AT^{4}\nonumber\]

where \(\sigma\) is the Stefan-Boltzmann constant (\(5.67\times 10^{-8}\text{ W/m}^{2}\cdot\text{ K}^{4})\), \(\varepsilon\) is the emissivity (\(1\) for a "blackbody" absorber/emitter; \(0\) for a perfect reflector), \(A\) is the surface area \((4\pi R^{2})\), and \(T\) is the temperature. The power/area delivered to a planet varies as the inverse square of the distance from the Sun. Note that the effective area of a planet that the Sun's radiation hits is \(\pi R^{2}\), where \(R\) is the radius of the planet. However, the total area over which the planet radiates is equal to its surface area, which is the surface area of a sphere \((4\pi R^{2})\) of radius \(R\). Restart.

If we neglect the planet's atmosphere (which reflects some of the light from the Sun and traps some of the radiation from the planet's surface), we can predict the temperature of the planet. Drag the red planet in the animation to different distances from the sun and see the various surface temperatures that result. Notice that when the red planet is at Earth's position, its temperature is below Earth's true average temperature of \(287\text{ K}\). Once the effect of the atmosphere is taken into account, the power delivered to Earth's surface is reduced further (since the atmosphere reflects some light). What keeps Earth from being a frozen planet? The greenhouse effect, in which gases in the atmosphere do not allow some of the radiation (in the infrared) that Earth radiates to escape from the atmosphere, does that. This radiation is trapped in Earth's atmosphere, thus warming Earth up to its current average temperature. As "greenhouse" gases increase in the atmosphere, Earth's average temperature will increase.

Illustration authored by Anne J. Cox.

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