Rates of Radiation Absorbed, Reflected and Emitted

The three fabrics are the same distance from the intense light source, so the amount of incoming radiation for each cloth sample is identical. The varying rates of radiation absorbed by each fabric depend on their reflectivity.  Since the fabrics are black, most of the visible light is absorbed by each sample, so we need to consider what is happening to the light we cannot see – the near-infrared, and Fabric A absorbs the most and Fabric B the least.

Since the lightbulb is emitting roughly 12% visible light compared to greater than 70% near-infrared, the variation in reflectivity of near-infrared creates quite a difference in the amount of radiation absorbed by each fabric.

In these experiments, the amount of visible and near-infrared transmitted through the swatches of black cloth was negligible, which simplifies our calculations.

Rate Incoming Radiation = Rate Reflected + Rate Transmitted + Rate Absorbed

Rate Incoming Radiation = Rate Reflected +  Rate Absorbed

Rate Absorbed = Rate Incoming Radiation – Rate Reflected

See the Interaction of Radiation with Matter for more details about absorption, reflection, and transmission.

Fabric A absorbs the most radiation with time since it absorbs nearly all of visible light and near-infrared (NIR).  Fabric C has a moderate rate of absorbed radiation since it is somewhat reflective of NIR, and Fabric B has the lowest rate of absorption since it is quite reflective in the NIR.

The data are also available in the Blackbody Radiation software.

The absorbed radiation transforms into thermal energy within the fabric, so A warms most quickly, C at a moderate rate, and B at the slowest rate.

This concept map highlights two of the three factors that affect the fabric’s temperature:

1. 1. the rate of absorbed radiation which warms the material, so how much radiation coming from the lightbulb is critical,
   2. the amount of radiation reflected by the cloth which decreases the rate of absorbed radiation, and
   3. the rate of radiation emitted by the heated fabric, which limits the heating when the light is on and cools the material when the lightbulb is off.

The interconnected processes of absorbed radiation heating the fabric and the emitted radiation cooling the material create negative feedback that limits how warm the cloth becomes.

Energy Surplus versus Deficit

In this scenario, the lightbulb is turned on, instantly illuminating the samples of black fabric in a constant intensity of visible and near-infrared light.  Each of the swatches emits less thermal radiation compared to that absorbed. There is an energy surplus: more is coming in than that leaving.  The excess energy is converted to thermal energy, which, in turn, increases the amount of thermal radiation emitted from the black fabric.  When the rates of absorption and emission are equal, the material is in radiative equilibrium, and the temperature remains constant.  Note that this is a first-order approximation since other heat transfer processes are affecting the fabric’s temperature.

Turning off the lightbulb creates an energy deficit: there is more radiation emitted than absorbed, so the fabric quickly cools.  Since the materials cool back to room temperature, there must be additional factors in play that help control the temperature of the cloth, such as conduction of heat with the tabletop below and the air above.  In the simulation, conduction was not directly calculated; however, its effect was estimated by assuming the was at a constant temperature and emitted thermal radiation back to the fabric.

The black fabric experiment is an example of a simple radiation budget in which incoming radiation is instantly on or off. When on, it shines at a constant intensity onto the material.  Since Earth is a rotating sphere, the intensity of sunlight illuminating the ground changes throughout the day, explore how this affects the Earth’s surface radiation budget in Diurnal Heating.