From 3598bbeb1f11117acb7de81dbab1052ab546d72a Mon Sep 17 00:00:00 2001
From: "Eugeniy E. Mikhailov" <evgmik@gmail.com>
Date: Thu, 17 Sep 2020 09:48:35 -0400
Subject: changed equation label to make it uniq

---
 blackbody_new.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'blackbody_new.tex')

diff --git a/blackbody_new.tex b/blackbody_new.tex
index 8a72e51..c3bf73d 100644
--- a/blackbody_new.tex
+++ b/blackbody_new.tex
@@ -152,7 +152,7 @@ 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 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}
+\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?
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