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| -rw-r--r-- | blackbody.tex | 38 |
1 files changed, 25 insertions, 13 deletions
diff --git a/blackbody.tex b/blackbody.tex index c04b048..4ead1fc 100644 --- a/blackbody.tex +++ b/blackbody.tex @@ -62,10 +62,10 @@ he who originated what is now known as {\it modern physics}. At the turn of the century, at the December 14, 1900 meeting of the German Physical Society, Planck presented his ideas on the subject, which were so unusual and so grotesque that he himself could hardly believe them, even though they caused -intense excitement in the audience and the entire world of physics}'' +intense excitement in the audience and the entire world of physics}.'' From George Gamow, {\it ``Thirty Years that Shook Physics, The Story of Quantum Physics''}, Dover Publications, -New York, 1966.) +New York, 1966. \end{boxedminipage} @@ -93,19 +93,19 @@ Imagine a metal wire connected to a cold reservoir at one end and a hot reservoi \begin{figure}[h] \includegraphics[height=2.5in]{./pdf_figs/bbx} -\caption{\label{bbx}Thermal Radiation Setup} +\caption{\label{bbx}Thermal radiation setup} \end{figure} \begin{enumerate} \item Connect the two multimeters and position the sensor as shown in Fig.~\ref{bbx}. The multimeter attached to the cube should be set to read resistance while the one attached to the infrared radiation sensor will monitor the potential (in the millivolt range). Make sure the shutter on the sensor is pushed all the way open! \item Before turning on the cube, measure the resistance of the thermistor at room temperature, and obtain the room temperature from the instructor. You will need this information for the data analysis. % -\item Turn on the Thermal Radiation Cube and set the power to ``high.'' When the ohmmeter reading decreases to 40 k$\Omega$ (5-20 minutes) set power switch to ``$8$''. (If the cube has been preheated, immediately set the switch to ``$8$''.) +\item Turn on the thermal radiation cube and set the power to ``high''. When the ohmmeter reading decreases to 40 k$\Omega$ (5-20 minutes) set power switch to ``$8$''. (If the cube has been preheated, immediately set the switch to ``$8$''.) \\ \begin{boxedminipage}{\linewidth} \textbf{Important}: when using the thermal radiation sensor, make each reading quickly to keep the sensor from heating up. Use both sheets of white isolating foam (with the silvered surface facing the lamp) to block the sensor between measurements. \\ -\textbf{Sensor calibration}: To obtain the radiation sensor readings for radiated power per unit area $S$ in the correct units ($W/m^2$), you need to use the voltage-to-power conversion factor: $22~mV/mW$, and the area of the sensor $2mm\times2mm$: +\textbf{Sensor calibration}: To obtain the radiation sensor readings for radiated power per unit area $S$ in the correct units ($W/m^2$), you need to use the voltage-to-power conversion factor $22~mV/mW$, and the area of the sensor $2mm\times2mm$: \begin{displaymath} S[W/m^2]=\frac{S[mV]}{22 [mV/mW]}\cdot 10^{-3}\cdot \frac{1}{4\cdot 10^{-6}[m^2]} @@ -175,12 +175,12 @@ Use your data to address the following questions in your lab report: \begin{figure} \includegraphics[height=4in]{./pdf_figs/tcube} -\caption{\label{tcube}Resistance vs temperature for the Thermal Radiation Cube} +\caption{\label{tcube}Resistance vs. temperature for the thermal radiation cube} \end{figure} \begin{figure} \includegraphics[height=3.5in]{./pdf_figs/bbht} -\caption{\label{bbht}Lamp Connection for High-Temperature Stefan-Boltzmann -Setup} +\caption{\label{bbht}Lamp connection for high-temperature Stefan-Boltzmann +setup} \end{figure} \subsection*{Tests of the Stefan-Boltzmann Law} @@ -216,23 +216,35 @@ Lamp, Power supply. \item Place the thermal sensor at the same height as the filament, with the front face of the sensor approximately 6 cm away from the filament (this distance will be fixed throughout the measurement). Make sure no other objects are viewed by the sensor other than the lamp. % -\item Turn on the lamp power supply. Set the voltage, $V$, in steps of one volt from 1-12 volts. At each $V$, record the ammeter (current) reading from the lamp and the voltage from the radiation sensor. Calculate the resistance of the lamp using Ohm's Law and determine the temperature $T$ of the lamp from the table shown in Fig. \ref{w_res:fig}. +\item Turn on the lamp power supply. Set the voltage, $V$, in steps of one + volt from 1-12 volts. At each $V$, record the ammeter (current) + reading from the lamp and the voltage from the radiation sensor. + Calculate the resistance of the lamp using Ohm's Law and determine + the temperature $T$ of the lamp from the table shown in Fig. + \ref{w_res:fig}. You can use a table to record your data similar to + the sample table~\ref{tbl:sampla_data_table}. \end{enumerate} \begin{figure}[h] \includegraphics[width=\columnwidth]{./pdf_figs/w_res} -\caption{\label{w_res:fig}Table of Tungsten's Resistance as a function of temperature.} +\caption{\label{w_res:fig}Table of tungsten's resistance as a function of temperature.} \end{figure} -Sample table for experimental data recording: - +\begin{table}[ht] +\begin{center} \begin{tabular}{|p{20mm}|p{20mm}|p{20mm}|p{20mm}|p{20mm}|p{20mm}|}\hline \multicolumn{3}{|c|}{Data($\pm$ error)}& \multicolumn{3}{|c|}{Calculations}\\ \hline $V$((volts)&$I$(amps)&$Rad(mV)$&$R$(ohms)&$T(K)$&$T^4(K^4)$\\\hline 1.00&&&&&\\\hline \dots &&&&&\\\hline&&&&&\\\hline \end{tabular} +\caption{ + Sample table for experimental data recording + \label{tbl:sampla_data_table} % spaces are big no-no withing labels +} +\end{center} +\end{table} In the lab report plot the reading from the radiation sensor (convert to $W/m^2$) versus $T^4$. According to the Stefan-Boltzmann Law, the data should fall along a straight line. Do a fit and report the value of the slope that you obtain. How does it compare to the accepted value of Stefan's constant? @@ -244,7 +256,7 @@ Don't be alarmed if the value of slope is way off from Stefan's constant. The St power supply, meter stick. \begin{figure} \includegraphics[height=2.5in]{./pdf_figs/bb31} -\caption{\label{bb31}Inverse Square Law Setup} +\caption{\label{bb31}Inverse square law setup} \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 |