Temperature Balances

Temperature Balance Concept

An object reaches an equilibrium temperature when the energy it absorbs equals the energy it emits. At this point, its temperature stays constant because the energy gained from the surroundings is balanced by the energy lost.

The temperature of the surroundings affects this balance. If the surroundings are hotter than the object, the object absorbs more energy than it emits and warms up. If the surroundings are cooler, the object emits more energy than it absorbs and cools down.

This balance explains why objects do not keep heating up or cooling down indefinitely but settle at a stable temperature.

Black Body Radiation Basics

A black body is an idealised object that absorbs all the radiation that hits it—none is reflected or transmitted. Because it absorbs all radiation, it is also the best possible emitter of radiation.

The radiation emitted by a black body depends only on its temperature. It emits a continuous spectrum of wavelengths, with the intensity and distribution of wavelengths changing as the temperature changes.

Real objects approximate black bodies to varying degrees. For example, the Sun and planets behave roughly like black bodies when considering their radiation.

Temperature and Radiation

Hotter objects emit more radiation overall than cooler objects. As temperature increases, the total energy radiated per second rises sharply.

The wavelength of the peak radiation shifts to shorter wavelengths as temperature increases. This means hotter objects emit more radiation in the visible or ultraviolet range, while cooler objects emit mainly infrared.

This behaviour is described qualitatively by the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body increases rapidly with temperature. The law can be expressed as $P = \sigma T^4$, where $P$ is the power emitted per unit area, $T$ is the absolute temperature in kelvins, and $\sigma$ is the Stefan-Boltzmann constant.

For instance, doubling the temperature of an object causes it to emit about 16 times more radiation per unit area.

For example, the Sun’s surface at about 6000 K emits mostly visible light, while Earth at around 300 K emits mostly infrared radiation.

Applications of Temperature Balance

Temperature balance helps explain planetary temperatures. Planets absorb energy from the Sun and emit radiation back into space. Their equilibrium temperature depends on the balance between absorbed solar radiation and emitted infrared radiation.

Thermal insulation works by reducing energy loss, helping objects maintain their temperature balance for longer.

This concept is closely related to energy conservation, as it involves balancing energy flows without net gain or loss over time.

Example: Calculating Equilibrium Temperature Conceptually

Imagine a black body in a room at 20°C. It absorbs radiation from the surroundings and emits radiation itself. When the energy absorbed equals the energy emitted, the black body’s temperature stabilises at 20°C.

If the room temperature rises to 30°C, the black body absorbs more energy, so its temperature rises until it again balances absorption and emission at 30°C.

For example, if the black body absorbs 400 W and emits 400 W at 20°C, and the surroundings warm to 30°C causing absorption to rise to 450 W, the black body will warm until it emits 450 W, reaching a new equilibrium temperature.

Example: Effect of Temperature on Radiation Emission

A black body at 300 K emits radiation mainly in the infrared range. If its temperature increases to 600 K, the peak wavelength shifts to shorter wavelengths and the total radiation emitted per unit area increases significantly.

This explains why hotter objects glow visibly (like a red-hot iron) while cooler objects do not.

Example: Understanding Black Body Radiation Spectrum

The Sun’s surface temperature is about 6000 K, so it emits a spectrum peaking in visible light. Earth’s temperature is about 300 K, so it emits mainly infrared radiation.

This difference in emission explains why Earth absorbs visible light from the Sun but emits infrared radiation back into space.