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| -rw-r--r-- | blackbody_new.tex | 42 |
1 files changed, 35 insertions, 7 deletions
diff --git a/blackbody_new.tex b/blackbody_new.tex index 203b759..c9e8ace 100644 --- a/blackbody_new.tex +++ b/blackbody_new.tex @@ -100,7 +100,7 @@ Before starting actual experiment take some time to have fun with the thermal ra % Resistance of filament (room temperature)=&$\underline{\hskip .7in}$ %\end{tabular} -\item To indirectly measure the temperature of the filament, we will use the known dependence of its resistance on the temperature, given in table shown in Fig.~\ref{w_res:fig}. To ensure the accurate measurement, we will again use the four-point probe method (review the video on the course web site, if you need a refresher) by measuring the voltage drop across the lamp. VERY IMPORTANT: +\item To indirectly measure the temperature of the filament, we will use the known dependence of its resistance on the temperature, given in table shown in Table.~\ref{w_res:table}. To ensure the accurate measurement, we will again use the four-point probe method (review the video on the course web site, if you need a refresher) by measuring the voltage drop across the lamp. VERY IMPORTANT: make all connections to the lamp when the power is off, and ask the instructor to check your connections before proceeding. \item Place the thermal sensor at the same height as the filament, with the front face of the sensor approximately 5~cm away from the filament and fix their relative position. Make sure no other objects are viewed by the sensor other than the lamp. @@ -108,19 +108,47 @@ Before starting actual experiment take some time to have fun with the thermal ra \item Turn on the lamp power supply. Set the voltage, $V$, in steps of 1-2 volt from 1-6 volts. At each $V$, record the current running through 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}. Don't forget to use Kelvin scale for the temperatures (conversion equation is $T[K]=T[^oC]+273$). + the temperature $T$ of the lamp from the table shown in Table + \ref{w_res:table}. Don't forget to use Kelvin scale for the temperatures (conversion equation is $T[K]=T[^oC]+273$). \item Calculate the values of $T^4$ - these are going to be the $x$-values for the graph. Are they more or less equally distributed? If not (which is probably the case), estimate the big gaps, and measure additional points to fill them in. \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. Here, $R_{300K}$ is the resistance of tungsten at the temperature of 300~K.} -\end{figure} +% \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. Here, $R_{300K}$ is the resistance of tungsten at the temperature of 300~K.} +% \end{figure} +\begin{table}[h] + \centering +\begin{tabular}{|ccc|ccc|ccc|ccc|} + \hline + $\mathrm{R/R_{300K}}$ & \multicolumn{1}{p{0.3in}}{\centering Temp\\ K} & \multicolumn{1}{p{0.7in}|}{\centering Resistivity\\ $\mu\Omega \mathrm{cm}$} +& $\mathrm{R/R_{300K}}$ & \multicolumn{1}{p{0.3in}}{\centering Temp\\ K} & \multicolumn{1}{p{0.7in}|}{\centering Resistivity\\ $\mu\Omega \mathrm{cm}$} +& $\mathrm{R/R_{300K}}$ & \multicolumn{1}{p{0.3in}}{\centering Temp\\ K} & \multicolumn{1}{p{0.7in}|}{\centering Resistivity\\ $\mu\Omega \mathrm{cm}$} \\ + \hline + \hline +1.0 & 300 & 5.65 & 5.48 & 1200 & 30.98 & 16.29 & 3000 & 92.04 \\ +1.43 & 400 & 8.06 & 6.03 & 1300 & 34.08 & 16.95 & 3100 & 95.76 \\ +1.87 & 500 & 10.56 & 6.58 & 1400 & 37.19 & 17.62 & 3200 & 99.54 \\ +2.34 & 600 & 13.23 & 7.14 & 1500 & 40.36 & 18.28 & 3300 & 103.3 \\ +2.85 & 700 & 16.09 & 7.71 & 1600 & 43.55 & 18.97 & 3400 & 107.2 \\ +3.36 & 800 & 19.00 & 8.28 & 1700 & 46.78 & 19.66 & 3500 & 111.1 \\ +3.88 & 900 & 21.94 & 8.86 & 1800 & 50.05 & 26.35 & 3600 & 115.0 \\ +4.41 & 1000 & 24.93 & 9.44 & 1900 & 53.35 & & & \\ +4.95 & 1100 & 27.94 & 10.03 & 2000 & 56.67 & & & \\ + \hline +\end{tabular} +% this table is lifted from Pasco manual +% numbers somewhat disagree with literature for example +% "Analytical expressions for thermophysical properties of solid and liquid +% tungsten relevant for fusion applications" +% https://doi.org/10.1016/j.nme.2017.08.002 +\caption{\label{w_res:table}Table of tungsten's resistance and resisitivity as a function of temperature. Here, $\mathrm{R_{300K}}$ is the resistance of tungsten at the temperature of 300~K.} + +\end{table} 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: |