From a9060f8490c8334d7308963f494ad51b19ab253a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Wed, 25 Jan 2023 23:36:02 +0100
Subject: fizikalni vaji 7 in 8 in nekaj mat in inf

---
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+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\begin_preamble
+\usepackage{siunitx}
+\usepackage{pgfplots}
+\usepackage{listings}
+\usepackage{multicol}
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children false
+\language slovene
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
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+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
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+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification false
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1cm
+\topmargin 2cm
+\rightmargin 1cm
+\bottommargin 2cm
+\headheight 1cm
+\headsep 1cm
+\footskip 1cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style german
+\dynamic_quotes 0
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+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Plinski zakoni
+\end_layout
+
+\begin_layout Author
+
+\noun on
+Anton Luka Šijanec
+\end_layout
+
+\begin_layout Date
+14.
+ december 2022
+\end_layout
+
+\begin_layout Abstract
+Poročilo šeste vaje pri predmetu 
+\noun on
+F41
+\noun default
+ na Gimnaziji Bežigrad v 4.
+ letniku.
+ Vaja je potekala 10.
+ novembra 2022.
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Uvod
+\end_layout
+
+\begin_layout Standard
+Tlak v plinu je odvisen od prostornine plina, njegove temperature in mase
+ plina.
+ Če opazujemo ves čas isto maso plina in poskrbimo, da je ena od preostalih
+ spremenljivk konstantna, lahko ugotovimo medsebojno odvisnost še zadnjih
+ dveh spremenljivk.
+\end_layout
+
+\begin_layout Section
+Nalogi
+\end_layout
+
+\begin_layout Subsection
+Boylov zakon
+\end_layout
+
+\begin_layout Standard
+Če ob konstantni temperaturi plina spreminjamo njegovo prostornino, se ob
+ tem spreminja tudi tlak plina.
+\end_layout
+
+\begin_layout Subsubsection
+Navodilo
+\end_layout
+
+\begin_layout Standard
+Za dano maso plina v injekcijski brizgi ugotovi, kako je tlak odvisen od
+ njegove prostornine.
+\end_layout
+
+\begin_layout Subsubsection
+Potrebščine
+\end_layout
+
+\begin_layout Itemize
+inkejcijska brizga
+\end_layout
+
+\begin_layout Itemize
+merilnik tlaka
+\end_layout
+
+\begin_layout Itemize
+računalniški vmesnik
+\end_layout
+
+\begin_layout Itemize
+program LoggerPro
+\end_layout
+
+\begin_layout Subsubsection
+Potek dela
+\end_layout
+
+\begin_layout Standard
+Prostornino zraka v brizgi nastavi na 
+\begin_inset Formula $\SI{4}{\milli\meter}$
+\end_inset
+
+ in nato privij brizgo na merilnik tlaka.
+ Način merjenja v programu LoggerPro (Data Collection) nastavi na Events
+ with entry.
+ PAZI! Vse spremembe prostornine delaj počasi, da bo temperatura zraka v
+ brizgi ves čas čim bolj enaka.
+ Raztegni prostornino zraka v brizgi na 
+\begin_inset Formula $\SI{20}{\milli\meter}$
+\end_inset
+
+, začni z meritvijo (Start) in zabeleži prvo vrednost tlaka pri tej prostornini.
+ Zmanjšuj prostornino po 
+\begin_inset Formula $\SI{2}{\milli\liter}$
+\end_inset
+
+ do 
+\begin_inset Formula $\SI{4}{\milli\liter}$
+\end_inset
+
+ ter vsakič zabeleži tlak.
+ Po zabeleženi zadnji meritvi ne pozabi končati meritve (Stop).
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="14" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $V\left[\si{\milli\liter}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $p\left[\si{\kilo\pascal}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+4
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+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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+
+\begin_layout Plain Layout
+105
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+131
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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+
+\begin_layout Plain Layout
+2
+\end_layout
+
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+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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+
+\begin_layout Plain Layout
+176
+\end_layout
+
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+</cell>
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+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+83
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+6
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+70
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+7
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+61
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+8
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+53
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+9
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+48
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+10
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+42
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+15
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+29
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+20
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+22
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+12
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+36
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+17
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+26
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Meritve za prvo nalogo
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Nariši graf 
+\begin_inset Formula $p(V)$
+\end_inset
+
+ za celotno spremembo.
+\end_layout
+
+\begin_layout Standard
+Kakšna je odvisnost?
+\begin_inset Formula 
+\[
+pV=nRT=\text{{konstanta}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Svoj odgovor na prejšnje vprašanje dokaži z linearizacijo grafa 
+\begin_inset Formula $p(V)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{tikzpicture}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, ylabel=$p$, domain=0:180, ytick pos=left, samples=25
+6, xlabel=$V$, xtick pos=bottom, xmin=0, ymax=200, ymin=0]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[only marks] table [x=V, y=p] {boylov.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, ylabel=$
+\backslash
+color{red}p
+\backslash
+color{black}$, domain=0:.55, ylabel near ticks, ytick pos=right, samples=256,
+ xlabel=$
+\backslash
+color{red}V^{-1}
+\backslash
+color{black}$, xtick pos=top, xlabel near ticks, xmin=0, ymax=200, ymin=0]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red, only marks] table [x=iV, y=p] {boylov.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(386.934+0.498)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(386.934-0.498)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red] (x, {x*(386.934)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{tikzpicture}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:graf-1"
+
+\end_inset
+
+Odvisnost tlaka od prostornine.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{lstlisting}
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*p) 
+\begin_inset Quotes gld
+\end_inset
+
+boylov.tsv" using 4:3 via p
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{lstlisting}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+p=386,934\pm0,498
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Absolutna ničla
+\end_layout
+
+\begin_layout Subsubsection
+Navodilo
+\end_layout
+
+\begin_layout Standard
+Ugotovi zvezo med tlakom in temperaturo (pri konstantni prostornini) za
+ zrak v stekleni bučki ter iz meritev določi absolutno ničlo.
+\end_layout
+
+\begin_layout Subsubsection
+Potrebščine
+\end_layout
+
+\begin_layout Itemize
+steklena bučka
+\end_layout
+
+\begin_layout Itemize
+stojalo s prižemami
+\end_layout
+
+\begin_layout Itemize
+električna grelna posoda
+\end_layout
+
+\begin_layout Itemize
+računalniški vmesnik z računalnikom
+\end_layout
+
+\begin_layout Itemize
+merilnik tlaka
+\end_layout
+
+\begin_layout Itemize
+merilnik temperature
+\end_layout
+
+\begin_layout Itemize
+čaša za vodo
+\end_layout
+
+\begin_layout Subsubsection
+Potek dela
+\end_layout
+
+\begin_layout Standard
+Preveri, če je v posodi voda do vrha bučke z zrakom (vrat bučke ne sme biti
+ v vodi!).
+ Če ni, dolij ustrezno količino vode.
+ Priključi merilnika za tlak in temperaturo na računalniški vmesnik.
+ Poženi program LoggerPro.
+ Ker bomo gledali odvisnost tlaka od temperature, bomo potrebovali samo
+ en graf, torej raztegni zgornji graf čez spodnjega.
+ Izberi način zajemanja podatkov (gumb Data Collection) 
+\begin_inset Quotes gld
+\end_inset
+
+selected events
+\begin_inset Quotes grd
+\end_inset
+
+ ter izberi količino na navpični osi tlak in količino na vodoravni osi temperatu
+ro.
+ Začneš meritev (gumb Collect) ter shraniš prvo meritev (gumb Keep).
+ Vklopiš grelec in počakaš, da se temperatura dvigne za približno 
+\begin_inset Formula $\SI{10}{\degreeCelsius}$
+\end_inset
+
+.
+ Nato grelec ugasneš ter počakaš (
+\begin_inset Formula $\SI{5}{\second}$
+\end_inset
+
+ do 
+\begin_inset Formula $\SI{10}{\second}$
+\end_inset
+
+), da se temperatura ustali.
+ Zapišeš novo meritev (gumb Keep).
+ Postopek iz zadnjega stavka ponavljaš, dokler ni temperatura približno
+ 
+\begin_inset Formula $\SI{90}{\degreeCelsius}$
+\end_inset
+
+.
+ Takrat meritev zaključiš (gumb Stop).
+ S programom preveri, kakšna je zveza med tlakom in temperaturo, ter iz
+ grafa določi absolutno ničlo.
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{tikzpicture}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, ylabel=$p$, domain=-300:100, ytick pos=left,
+ samples=256, xlabel=$T$, xtick pos=bottom, xmin=-300, xmax=100]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[only marks] table [x=T, y=p] {absolutna.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+addplot[green] (x, {x*(0.316881+0.007238)});
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+addplot[green] (x, {x*(0.620649-0.007238)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red] (x, {x*(0.316881)+91.852});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{tikzpicture}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:graf-1-1"
+
+\end_inset
+
+Odvisnost tlaka od temperature.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{lstlisting}
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (k*(x+n)) 
+\begin_inset Quotes gld
+\end_inset
+
+absolutna.tsv" using 2:3 via k, n
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{lstlisting}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+n=T_{0}=\SI{289,863}{\degreeCelsius}\pm\SI{0,5144}{\degreeCelsius}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Komentar
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\sigma$
+\end_inset
+
+ je precej majhna, torej so podatki zelo točni, niso pa natančni, od dejanske
+ absolutne ničle občutno odstopajo.
+ To pa zato, ker je bilo za dosego večje točnosti izvedenih 655 meritev,
+ med vsako meritvo pa je pretekla le ena sekunda.
+ Graf je zato zamaknjen, saj se plin ni v celoti ogrel na temperaturo vode,
+ termometer pa je bil v vodi, ki se je segrela prej kot plin.
+ S čakanjem na ustaljenost temperature bi težavo natančnosti za ceno manjše
+ točnosti odpravili.
+\end_layout
+
+\begin_layout Section
+Uporabljen program
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+lstinputlisting[language=Python]{boy.py}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
-- 
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