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| -rw-r--r-- | blackbody_new.tex | 18 |
1 files changed, 13 insertions, 5 deletions
diff --git a/blackbody_new.tex b/blackbody_new.tex index 4230be0..56b3a35 100644 --- a/blackbody_new.tex +++ b/blackbody_new.tex @@ -40,8 +40,8 @@ Most hot, opaque objects can be approximated as blackbody emitters, but the most \begin{equation} u(\lambda,T) = \frac{8\pi kT}{\lambda^4} \end{equation} -where $u(\lambda)(J/m^4)$ is the spectral radiance -- energy radiated per unit area at a single wavelength $\lambda$. This law agrees with the experiment for radiation at long wavelengths (infrared), but predicts that $u(\lambda)$ should increase infinitely at short wavelengths. This is not observed experimentally (Thank heaven, or we would all be constantly bathed in ultraviolet light - a true ultraviolet catastrophe!). In reality, the peak of radiation distribution as a function of its wavelength depends on the black body temperature as described by {\bf Wien's law:} -\begin{equation} +where $u(\lambda)(J/m^4)$ is the spectral radiance -- energy radiated per unit area at a single wavelength $\lambda$. This law agrees with the experiment for radiation at long wavelengths (infrared), but predicts that $u(\lambda)$ should increase infinitely at short wavelengths. This is not observed experimentally (Thank heaven, or we would all be constantly bathed in ultraviolet light - a true ultraviolet catastrophe!). In reality, the peak of radiation distribution as a function of its wavelength depends on the blackbody temperature as described by {\bf Wien's law:} +\begin{equation} \label{weins} \lambda_{max}T = 2.898\times 10^{-3} m\cdot K \end{equation} and approaches zero for short wavelengths. @@ -136,7 +136,7 @@ Before starting actual experiment take some time to have fun with the thermal ra -In the lab report plot the reading from the radiation sensor (convert to $W/m^2$) (on the y axis) versus the temperature $T^4$ on the x axis. According to the Stefan-Boltzmann Law, the data should show a linear dependence, since according to Eq.(\ref{SBl}) $S\propto T^4$. Fit the experimental data using a linear fit and its uncertainty. For an ideal black body we expect the slope to be equal to the Stephen constant $\sigma=5.6703 \times 10^{-8} W/m^2K^4$. However, there exists no ideal black bodies. For real objects the Eq.(\ref{SBl}) is modified, and written as: +In the lab report plot the reading from the radiation sensor (convert to $W/m^2$) (on the y axis) versus the temperature $T^4$ on the x axis. According to the Stefan-Boltzmann Law, the data should show a linear dependence, since according to Eq.(\ref{SBl}) $S\propto T^4$. Fit the experimental data using a linear fit and its uncertainty. For an ideal blackbody we expect the slope to be equal to the Stephen constant $\sigma=5.6703 \times 10^{-8} W/m^2K^4$. However, there exists no ideal black bodies. For real objects the Eq.(\ref{SBl}) is modified, and written as: \begin{equation}\label{SBl} S =\epsilon\sigma T^4 \end{equation} @@ -158,7 +158,7 @@ power supply, meter stick. \end{figure} A point source of radiation emits that radiation according to an inverse square law: that is, the intensity of the radiation in $(W/m^2)$ is proportional to -the inverse square of the distance from that source, so that the intensity at the certain distance from the black body integrated over surface of the sphere of such radius is always constant. Mathematically, we expect the following relationship between the total power of the radiation source $P$ and the distance to the point source $r$ to be: +the inverse square of the distance from that source, so that the intensity at the certain distance from the blackbody integrated over surface of the sphere of such radius is always constant. Mathematically, we expect the following relationship between the total power of the radiation source $P$ and the distance to the point source $r$ to be: \begin{equation} \label{invlaw_theory} S(r)=\frac{P}{2\pi r^2} \end{equation} @@ -187,6 +187,14 @@ S(r)=\frac{P}{2\pi r^2} \end{enumerate} +\newpage + +\section*{Universal thermometer} +Blackbody radiation gives us an ability to measure the temperature of remote objects. Have you ever asked yourself how do astronomer know the temperature of stars or other objects many light years away? The answer - by measuring the light they emit and analyzing it using the expressions for the blackbody radiation spectrum. Wein's law Eq.(\ref{weins}) links the wavelength at which the most radiation is emitted to the inverse of the object's temperature, thus the colder stars emit predominantly in red (hence the name ``red giants''), while emission pick for hot young stars is shifted to the blue, making them emit in all visible spectrum. +\includegraphics[height=2.5in]{./pdf_figs/blackbody_radn_curves} + +The human bodies, of course, are much cooler than stars, and emit in infrared range. This radiation is invisible for human eye, but using proper detection method it is possible to create thermal maps of the surroundings with the accuracy better than $1/10$th of a degree. Forward-looking infrared (FLIR) cameras have wide range of applications, from surveillance and military operations to building inspection and repairs, night-time navigation and hunting. As I write this in Fall 2020, in the middle of COVID19 pandemic, more and more locations use such sensors to measure visitors' temperature at the entrance of a building or a check points in the airports. + \end{document} \hrule @@ -315,7 +323,7 @@ First, tabulate your data and include it (with label and caption). Then use you %\end{figure} %\begin{figure} %\includegraphics[height=2.5in]{cobespc.eps} -%\caption{\label{Cobe}Cobe: Cosmic Black Body Spectrum} +%\caption{\label{Cobe}Cobe: Cosmic blackbody Spectrum} %\end{figure} %\begin{figure} % |