From b31a054cfb6d4c8fafaf717b7df660bb90cb44ca Mon Sep 17 00:00:00 2001 From: LORDMAK09 <107167478+LORDMAK09@users.noreply.github.com> Date: Thu, 23 Jun 2022 00:28:07 +0530 Subject: [PATCH 1/2] AE21B107 Stefan-Boltzmann Constant --- jan-may-2022-latex/AE21B107/AE21B107.tex | 52 ++++++++++++++++++++- jan-may-2022-latex/AE21B107/EvsT.png | Bin 0 -> 15056 bytes jan-may-2022-latex/AE21B107/variable_e.png | Bin 0 -> 33191 bytes 3 files changed, 51 insertions(+), 1 deletion(-) create mode 100644 jan-may-2022-latex/AE21B107/EvsT.png create mode 100644 jan-may-2022-latex/AE21B107/variable_e.png diff --git a/jan-may-2022-latex/AE21B107/AE21B107.tex b/jan-may-2022-latex/AE21B107/AE21B107.tex index 056fbca..ca4248c 100644 --- a/jan-may-2022-latex/AE21B107/AE21B107.tex +++ b/jan-may-2022-latex/AE21B107/AE21B107.tex @@ -1,2 +1,52 @@ \section{AE21B107} -Student shall edit this file and include stuff for the assignment + +\subsection*{\centering{Stefan-Boltzmann law}} + +This law was formulated by Austrian physicist Josef Stefan in 1879 as a result of experimental studies. The same law, in 1884, was derived by Austrian physicist Ludwig Boltzmann from thermodynamic considerations. + +Stefan-Boltzmann law states that the total radiant heat energy emitted per unit time from a surface is proportional to the fourth power of its temperature (in Kelvins i.e. Absolute temperature). + +The emissivity of blackbody, a theoretical body considered to absorb all radiations incident on it, is 1 and that for ordinary body is between 0 and 1. + +\begin{equation} + \text{E} = {\sigma}{eT^4} +\end{equation} + +where $\sigma$ is known as Stefan-Boltzmann constant. + +\begin{equation*} + {\sigma} = 5.67 \times 10^{-8} +\end{equation*} + +Other forms of this equation can be represented as, + +\begin{equation} + \frac{dq}{dt} = {\sigma}{eT^4} +\end{equation} + +\begin{equation} + \frac{dQ}{dt} = {\sigma}{eAT^4} +\end{equation} + +The symbols used are as follows, + +\begin{table}[h] + \centering + \begin{tabular}{|c|l|} + \hline + E & Radiant heat energy emitted per unit area per second \\ + q & Radiant heat energy per unit area \\ + Q & Radiant heat energy\\ + A & Area of the radiant surface\\ + T & Absolute Temperature of the body\\ + e & Emissivity of the body\\ + $\sigma$ & Stefan-Boltzmann constant \\ + \hline + \end{tabular} + \caption{Symbols used in above representations of Stefan-Boltzmann law} +\end{table} + +The following plots show the variation of E vs T for a given body with e = 1 in Graph 1 and variation of E vs T for various values of e in graph 2. + +\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/EvsT.png} +\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/variable_e.png} diff --git a/jan-may-2022-latex/AE21B107/EvsT.png b/jan-may-2022-latex/AE21B107/EvsT.png new file mode 100644 index 0000000000000000000000000000000000000000..04d26897cb2d72831d361b18e1736e7f75c4e619 GIT binary patch literal 15056 zcmb7rcT|(#)+Ql9RN60sfK&}drS~FDC4iwy6Ql-|ARR<{jRhhIC`buKEC>dqOOqC* 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33191 -> 0 bytes 5 files changed, 5593 insertions(+), 2 deletions(-) create mode 100644 jan-may-2022-latex/AE21B107/EvsT.eps delete mode 100644 jan-may-2022-latex/AE21B107/EvsT.png create mode 100644 jan-may-2022-latex/AE21B107/variable_e.eps delete mode 100644 jan-may-2022-latex/AE21B107/variable_e.png diff --git a/jan-may-2022-latex/AE21B107/AE21B107.tex b/jan-may-2022-latex/AE21B107/AE21B107.tex index ca4248c..6787a9a 100644 --- a/jan-may-2022-latex/AE21B107/AE21B107.tex +++ b/jan-may-2022-latex/AE21B107/AE21B107.tex @@ -48,5 +48,5 @@ \subsection*{\centering{Stefan-Boltzmann law}} The following plots show the variation of E vs T for a given body with e = 1 in Graph 1 and variation of E vs T for various values of e in graph 2. -\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/EvsT.png} -\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/variable_e.png} +\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/EvsT.eps} 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