modified the assignment for black body

1 files changed, 11 insertions, 1 deletions

diff --git a/blackbody_new.tex b/blackbody_new.tex
index c3bf73d..102a027 100644
--- a/blackbody_new.tex
+++ b/blackbody_new.tex
@@ -155,7 +155,17 @@ In the lab report plot the reading from the radiation sensor (convert to $W/m^2$
 \begin{equation}\label{SBlmod}
  S =\epsilon\sigma T^4
 \end{equation}
-where the coefficient $\epsilon$ is called \emph{emissivity} and is defined as the ratio of the energy radiated from a material's surface to that radiated by a perfect blackbody at the same temperature. The values of $\epsilon$ vary from 0 to 1, with one corresponding to an ideal blackbody. All real materials have $\epsilon<1$, although some come quite close to the ideal (for example, carbon black has $\epsilon=0.95$). However, emissivity of a tungsten wire varies from $\epsilon=0.032$ (at $30^{\circ} C$) to $\epsilon=0.35$ (at $3300^{\circ}C$). Using the result of your fit, and assuming we know the Stephan-Boltzman constant $\sigma$ by some other means, what is $\epsilon$ and what is the uncertainty on it?  Is it consistent with tungsten? What else could be affecting this measurement?
+where the coefficient $\epsilon$ is called \emph{emissivity} and is defined as the ratio of the energy radiated from a material's surface to that radiated by a perfect blackbody at the same temperature. The values of $\epsilon$ vary from 0 to 1, with one corresponding to an ideal blackbody. All real materials have $\epsilon<1$, although some come quite close to the ideal (for example, carbon black has $\epsilon=0.95$). However, emissivity of a tungsten wire varies from $\epsilon=0.032$ (at $30^{\circ} C$) to $\epsilon=0.35$ (at $3300^{\circ}C$).
+
+Unfortunately, it is impossible to measure the exact value of emissivity
+from the experimental data, as one needs to know the surface area of the
+filament and the precise distance from it to the detector. However, we
+should be able to qualitatively verify the validity of Eq.~(\ref{SBlmod}). From
+fitting experimental data, find the proportionality coefficient between the
+emitted radiation and the filament temperature $T^4$ and its uncertainty.
+Estimate the quality of the linear fit (a linear fit would assume that the
+emissivity does not depend on temperature).
+
 
 Let us examine the quality of the fit more carefully. For that it is convenient to make a separate plot of the \emph{residual} - the difference between the experimental points and the fit values. For a proper fit function, we expect the residuals to be randomly distributed around zero. Analyze your results. Do the points seem to systematically differ from the fit line in a particular region?  Can you think of a reason why that would be?