#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" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \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 \paperfontsize default \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 \papercolumns 1 \papersides 1 \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 \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $V\left[\si{\milli\liter}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $p\left[\si{\kilo\pascal}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 105 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 131 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 176 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 83 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 6 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 70 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 7 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 61 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 8 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 53 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 9 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 48 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 10 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 42 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 15 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 29 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 20 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 22 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 12 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 36 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 17 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 26 \end_layout \end_inset \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