diff --git a/docs/sph4u7.md b/docs/sph4u7.md index 9374f89..706e894 100644 --- a/docs/sph4u7.md +++ b/docs/sph4u7.md @@ -437,6 +437,46 @@ Instead of converting between multiple forms of energy, solar heating directly c (Source: Kognity) +## Thermal energy transfer + +!!! definition + - **Radiation** is the transfer of energy via electromagnetic waves emitted away from an object. No medium is needed. + - **Convection** is the transfer of thermal energy via another medium away from an object. + - **Conduction** is the transfer of thermal energy via physical contact. + +### Black bodies + +!!! definition + **Emissivity** ($e$) is a dimensionless value from 0 to 1 indicating the relative ability of an object to emit radiation. Darker and duller surfaces have an emissivity closer to 1 while shinier and whiter ones are closer to 0. + +All bodies with an absolute temperature will emit radiant energy in the form of electromagnetic waves. The temperature of the body determines the wavelengths and power of the radiation emitted. A **perfect emitter** has an emissivity of 1 and is known as a **black body**, absorbing all electromagnetic radiation. + +Generally, as the temperature of a body goes down, its peak power density is reduced and its peak wavelength increases. + +**Wien's displacement law** relates the temperature of a black body to the waves it emits. Where $\lambda_\text{max}$ is the peak wavelength in metres and $T$ is the temperature of the body in kelvin: +$$\lambda_\text{max}\times T=\pu{2.9\times10^{-3} m\cdot K}$$ + +The **Stefan-Boltzmann** law relates the specifications of a body to the power it emits. Where $P$ is the power emitted by the body, $A$ is its surface area, $T$ is its temperature, $e$ is its emissivity, and $\sigma$ is the Stefan-Boltzmann constant (equal to $\pu{5.67\times10^{-8} Wm^{-2}K^{-4}}$): +$$P=e\sigma AT^4$$ + +In problems where the environment temperature is **different** from the temperature of an object, there will be power loss. The net power emitted by a body will be: +$$P_\text{net}=e\sigma A(T_1^4-T_2^4)$$ + +The solar radiation reaching earth is equal to $\pu{S=3.9\times10^{26} W}$ with the assumption that it is a black body. + +### Albedo + +Derived from $I=\frac{P}{A}$, where $d$ is the distance from the Earth to the sun: +$$I=\frac{P}{4\pi d^2}$$ + +**Albedo** ($\alpha$) is the ratio of power from incident rays reflected or scattered to the power absorbed by a body, ranging from 0 to 1. A black body has albedo 0. On average, Earth's albedo is equal to $0.3$ due primarily to the atmosphere but also clouds and ice. +$$\alpha=\frac{\text{energy scattered/reflected}}{\text{energy absorbed}}$$ + +As Earth is not a flat disk pointed at the sun, in reality the sun's intensity is reduced arbitrarily to a quarter. Therefore, the power absorbed/incident to the Earth is equal to, where $S$ is the solar constant: +$$P_\text{in}=(1-\alpha)\frac{1}{4}SA$$ + +Greenhouse gases are responsible for remaining increases in temperature. + ## Resources - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)