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b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/Obliczenia.md @@ -0,0 +1,145 @@ +## Materiał: Mosiądz +### 1. Dane pomiarowe i stałe +* **Pomiary długości $l_0$:** [0.4048, 0.4047, 0.4046] m +* **Odczyt czujnika $S$:** 0.00021 m +* **Temp. wrzenia $T_{wrz}$:** 99.71 $^\circ$C +* **Temp. otoczenia $T_0$:** 21.0 $^\circ$C +* **Dokładności przyrządów:** + * Termometr: $\Delta T_0 = 1.0$ K + * Tabela wrzenia: $\Delta T_{tab} = 0.01$ K + * Suwmiarka: $\Delta l = 1e-05$ m + * Czujnik: $\Delta S = 1e-05$ m + +### 2. Obliczenia wielkości fizycznych +**a) Średnia długość początkowa:** +$$\overline{l}_0 = \frac{1.21410}{3} = 0.40470 \, m$$ +**b) Różnica temperatur:** +$$\Delta T = T_{wrz} - T_0 = 99.71 - 21.0 = 78.71 \, K$$ +**c) Wydłużenie bezwzględne:** +$$\Delta l = S_{końc} - S_{pocz} = 0.00021 - 0.0 = 0.00021 \, m$$ +**d) Współczynnik rozszerzalności** +$$\alpha = \frac{0.00021}{0.40470 \cdot 78.71} = \mathbf{6.59 \cdot 10^{-6} \, K^{-1}}$$ +### 3. Szczegółowa analiza niepewności +**a) Niepewności standardowe typu B:** +* Termometr: $u_B(T_0) = \frac{1.0}{\sqrt{3}} = 0.5774$ K +* Tabela wrzenia: $u_B(T_{wrz}) = \frac{0.01}{\sqrt{3}} = 0.0058$ K +* Suwmiarka: $u_B(l_0) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +* Czujnik wydłużenia: $u_B(\Delta l) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +**b) Niepewność różnicy temperatur:** +$$u(\Delta T) = \sqrt{u_B^2(T_{wrz}) + u_B^2(T_0)} = \sqrt{0.0058^2 + 0.5774^2} = 0.5774 \, K$$ +**c) Niepewność typu A:** +$$u_A(l_0) = \sqrt{\frac{\sum (l_i - \overline{l})^2}{n(n-1)}} = 0.0000577 \, m$$ +**d) Udziały niepewności:** +* Od wydłużenia: $(\frac{u(\Delta l)}{\Delta l})^2 = 7.56e-04$ +* Od długości: $\frac{1}{l_0^2}(u_A^2 + u_B^2) = 2.06e-08$ +* Od temperatury: $(\frac{u(\Delta T)}{\Delta T})^2 = 5.38e-05$ +* **Suma pod pierwiastkiem:** $8.10e-04$ +**e) Niepewność całkowita:** +$$u(\alpha) = \alpha \cdot \sqrt{0.0008} = 0.19 \cdot 10^{-6} \, K^{-1}$$ + +> **Zestawienie końcowe:** +> * **Wynik z pomiaru:** $\alpha = (6.59 \pm 0.19) \cdot 10^{-6} \, K^{-1}$ +> * **Wartość tablicowa:** $\alpha_{tab} \approx 19 \cdot 10^{-6} \, K^{-1}$ +> * **Błąd względny:** +> $$\delta = \frac{|6.59 - 19.0|}{19.0} \cdot 100\% = \mathbf{65.3\%}$$ + +--- +## Materiał: Glin +### 1. Dane pomiarowe i stałe +* **Pomiary długości $l_0$:** [0.4037, 0.4036, 0.4036] m +* **Odczyt czujnika $S$:** 0.0001 m +* **Temp. wrzenia $T_{wrz}$:** 99.71 $^\circ$C +* **Temp. otoczenia $T_0$:** 21.0 $^\circ$C +* **Dokładności przyrządów:** + * Termometr: $\Delta T_0 = 1.0$ K + * Tabela wrzenia: $\Delta T_{tab} = 0.01$ K + * Suwmiarka: $\Delta l = 1e-05$ m + * Czujnik: $\Delta S = 1e-05$ m + +### 2. Obliczenia wielkości fizycznych +**a) Średnia długość początkowa:** +$$\overline{l}_0 = \frac{1.21090}{3} = 0.40363 \, m$$ +**b) Różnica temperatur:** +$$\Delta T = T_{wrz} - T_0 = 99.71 - 21.0 = 78.71 \, K$$ +**c) Wydłużenie bezwzględne:** +$$\Delta l = S_{końc} - S_{pocz} = 0.0001 - 0.0 = 0.00010 \, m$$ +**d) Współczynnik rozszerzalności:** +$$\alpha = \frac{0.00010}{0.40363 \cdot 78.71} = \mathbf{3.15 \cdot 10^{-6} \, K^{-1}}$$ +### 3. Szczegółowa analiza niepewności +**a) Niepewności standardowe typu B:** +* Termometr: $u_B(T_0) = \frac{1.0}{\sqrt{3}} = 0.5774$ K +* Tabela wrzenia: $u_B(T_{wrz}) = \frac{0.01}{\sqrt{3}} = 0.0058$ K +* Suwmiarka: $u_B(l_0) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +* Czujnik wydłużenia: $u_B(\Delta l) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +**b) Niepewność różnicy temperatur:** +$$u(\Delta T) = \sqrt{u_B^2(T_{wrz}) + u_B^2(T_0)} = \sqrt{0.0058^2 + 0.5774^2} = 0.5774 \, K$$ +**c) Niepewność typu A:** +$$u_A(l_0) = \sqrt{\frac{\sum (l_i - \overline{l})^2}{n(n-1)}} = 0.0000333 \, m$$ +**d) Udziały niepewności:** +* Od wydłużenia: $(\frac{u(\Delta l)}{\Delta l})^2 = 3.33e-03$ +* Od długości: $\frac{1}{l_0^2}(u_A^2 + u_B^2) = 7.02e-09$ +* Od temperatury: $(\frac{u(\Delta T)}{\Delta T})^2 = 5.38e-05$ +* **Suma pod pierwiastkiem:** $3.39e-03$ +**e) Niepewność całkowita:** +$$u(\alpha) = \alpha \cdot \sqrt{0.0034} = 0.18 \cdot 10^{-6} \, K^{-1}$$ + +> **Zestawienie końcowe:** +> * **Wynik z pomiaru:** $\alpha = (3.15 \pm 0.18) \cdot 10^{-6} \, K^{-1}$ +> * **Wartość tablicowa:** $\alpha_{tab} \approx 25 \cdot 10^{-6} \, K^{-1}$ +> * **Błąd względny:** +> $$\delta = \frac{|3.15 - 25.0|}{25.0} \cdot 100\% = \mathbf{87.4\%}$$ + +--- +## Materiał: Stal +### 1. Dane pomiarowe i stałe +* **Pomiary długości $l_0$:** [0.4052, 0.4052, 0.4052] m +* **Odczyt czujnika $S$:** 0.00031 m +* **Temp. wrzenia $T_{wrz}$:** 99.71 $^\circ$C +* **Temp. otoczenia $T_0$:** 21.0 $^\circ$C +* **Dokładności przyrządów:** + * Termometr: $\Delta T_0 = 1.0$ K + * Tabela wrzenia: $\Delta T_{tab} = 0.01$ K + * Suwmiarka: $\Delta l = 1e-05$ m + * Czujnik: $\Delta S = 1e-05$ m + +### 2. Obliczenia wielkości fizycznych +**a) Średnia długość początkowa:** +$$\overline{l}_0 = \frac{1.21560}{3} = 0.40520 \, m$$ +**b) Różnica temperatur:** +$$\Delta T = T_{wrz} - T_0 = 99.71 - 21.0 = 78.71 \, K$$ +**c) Wydłużenie bezwzględne:** +$$\Delta l = S_{końc} - S_{pocz} = 0.00031 - 0.0 = 0.00031 \, m$$ +**d) Współczynnik rozszerzalności:** +$$\alpha = \frac{0.00031}{0.40520 \cdot 78.71} = \mathbf{9.72 \cdot 10^{-6} \, K^{-1}}$$ +### 3. Szczegółowa analiza niepewności +**a) Niepewności standardowe typu B:** +* Termometr: $u_B(T_0) = \frac{1.0}{\sqrt{3}} = 0.5774$ K +* Tabela wrzenia: $u_B(T_{wrz}) = \frac{0.01}{\sqrt{3}} = 0.0058$ K +* Suwmiarka: $u_B(l_0) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +* Czujnik wydłużenia: $u_B(\Delta l) = \frac{1e-05}{\sqrt{3}} = 0.0000058$ m +**b) Niepewność różnicy temperatur:** +$$u(\Delta T) = \sqrt{u_B^2(T_{wrz}) + u_B^2(T_0)} = \sqrt{0.0058^2 + 0.5774^2} = 0.5774 \, K$$ +**c) Niepewność typu A:** +Pomijalna + +**d) Udziały niepewności:** +* Od wydłużenia: $(\frac{u(\Delta l)}{\Delta l})^2 = 3.47e-04$ +* Od długości: $\frac{1}{l_0^2}(u_A^2 + u_B^2) = 2.03e-10$ +* Od temperatury: $(\frac{u(\Delta T)}{\Delta T})^2 = 5.38e-05$ +* **Suma pod pierwiastkiem:** $4.01e-04$ +**e) Niepewność całkowita:** +$$u(\alpha) = \alpha \cdot \sqrt{0.0004} = 0.19 \cdot 10^{-6} \, K^{-1}$$ + +> **Zestawienie końcowe:** +> * **Wynik z pomiaru:** $\alpha = (9.72 \pm 0.19) \cdot 10^{-6} \, K^{-1}$ +> * **Wartość tablicowa:** $\alpha_{tab} \approx 12 \cdot 10^{-6} \, K^{-1}$ +> * **Błąd względny:** +> $$\delta = \frac{|9.72 - 12.0|}{12.0} \cdot 100\% = \mathbf{19.0\%}$$ + +--- + +## 4. Wnioski +1. Na podstawie przeprowadzonych obliczeń wyznaczono współczynniki liniowej rozszerzalności cieplnej dla badanych materiałów. Otrzymane wartości nie są jednak zgodne ilościowo z danymi tablicowymi — w szczególności dla glinu i mosiądzu różnice przekraczają 60–80%. +2. Analiza niepewności wykazała, że niepewności losowe oraz dokładność zastosowanych przyrządów pomiarowych są niewielkie i nie tłumaczą zaobserwowanych rozbieżności względem wartości tablicowych. Wskazuje to na obecność istotnego błędu systematycznego. +3. Najprawdopodobniejszą przyczyną zaniżenia wyników jest nieuwzględnienie charakterystyki układu pomiarowego wydłużenia, w szczególności ewentualnego przełożenia mechanicznego pomiędzy rzeczywistym wydłużeniem próbki a wskazaniem czujnika. Skutkiem tego zmierzona wartość Δl była mniejsza od rzeczywistej. +4. Spośród badanych materiałów wynik uzyskany dla stali wykazuje najmniejszą rozbieżność względem wartości tablicowej, jednak również on nie mieści się w granicach niepewności pomiarowej i obarczony jest błędem. \ No newline at end of file diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/Obliczenia.pdf b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/Obliczenia.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7c6e4ec48f6bdab7f64421a1db8243e8562f3932 GIT binary patch literal 326945 zcma%>Q*b6>vw&k88{4*Rn;YBMe6ejOUu@gP#@N`-CfV3FPyWBo&AB^sHPh48)75X+ zQ$5{Hp)4-Rz{1D{M-lja!NIX|5;GG!n%Kbc^TRPoTHCpp1BjU$3B_HZ8A7rq;{96SzNAAV7;1jMWqs?cCzfhU8{>muNu z0dWE%0W3RXZ{VP=`P!A0B|6@pt4Ng2Z2q=PvKTTqMdGptV1SQpc!TTLy6Jbzf*o1U zkI$nz|F>JgPK;gKcYhdEd}SIYgp3?Zq`KbsyA}U0raJ$R*ES{>!J&2Iw-wosx4d3_ zl}9El@P!GM@atE{uV-Ga&jTex|EKup*M+ao*ORuo-Z!$}%-w!(X-wPg54U-c2E89I zXIJ2#gJ*4D516wm#1Su$b=#k#XIC^U7KVEAYgCt0H}N$%_@KhXxEJi}b7}(^l3XP% z$z%utp6`NR^Xo-)5W@ZO+h5feJRpFRi!m<7ehO;g7k0ZFSg_bUQ`5VZ?e+UTI`K43 zP>)Fku-RA2qd+m8*X#b25SBNVl1*)zIA0jQ>1Jm_eB;Q3(U|$Vn!kMapg4nx54&KV z@xWRhr7LdBt9;^ELSGL-YYS+3&=E6#>r+KWuzifM&ac%)@mixt98*U^G_kaLaUs8) zOd3xYd5R=jK35qpXpF#wcv5VHBX@*1Ac5!*YlJ`JjO7`8`?0U4{)e%)xy)n_ut+0L zaDvWbv@CQ_t_hDYOn6d#QP3~4<)z zXiy%*x|OHpAIyBE&Aj7?EG6^u9OaVK;nkwge>C}2pZAF^c0}RTA;O2t$~o5>NO_P* z5;EOZqyPv!L52xI`eXQN+JRvB;NH9SEI}Q@tdhhnzmXMMqCxZ(cM!R3l42sHvuOTa zdr+mvVf2Rrebdzjs3ey)E_gcBMb+bO!1-Vk@XXK(P)$tuzr68tne5u@Dr~jIJ zr; zjoe7nSdVR3)TTLB{c5RU0??0?J2XXmTP?r6;MU%KJth7ayh=TJG8LT~_LPy;9j%~k?2(D&wwqGkp+81^N@)-MJH@zI{ur^33V z(n^}Bm;^C$8oSybFep9!iKRnkE>$8tn@-(o0b3L*6>E9J62FC|wfdYdnVG``K^u*v zti=7KZTgYG1vnQ8>f;Dxl8aH!0J}PAS8Ws{4WLOyu4WIO5XLoUMBUn;88d)GKP+M| zq+4b&U zNkiu^^DJb97_zhyg-ZxOS9T$QfbgOn9Ale7ql~ zN7JZAC#)Q}P~JF^1PVFGtWp@U7wyE6@28keV2`AbUrNIW5mLOSh(81+7_jWpjijZK z1^IX65g?PvZu0V6RxwJey0Q2cZ;Y45#lK^SEBXj0 zd5O|<;z8%p6uKX7a)2g?JlJ_7D1u}o$J=`gmIa}^vZeSN2;8E+|hG3?>`8rlYc_p><0~)IGJ0%l3-vZ{7QOm7NZz22QE45gHX0l zHuhag7I?2hq*dn0ukzFFnyRi{QR^G>ARohZs{SoS>PUe#b#6BG6Uxib3(O=SDDfcN z&lD2bRvrxM-zJ1X$-YwUUS5L)T0kE&j1jde;|fvAv?rXC(3(rh;CIJ0ia|^|QLKeQ zQt(}~{Hu{=%K!E0frp&t{3iZMezyId+tzzU_jCee z8hW+UW(nuuq%n-FI!Vv$ zyalU+b?4rX+(HzwTTAUCH2%D*Bi`fZqKG?C71_K31e}ng4K@YnZ#iPfJnT>WLrt+| zqBI{Ed(M#nCstKtbbmkTFyUaS9^fIKtXsw1cp6v-)x)A9BGdsV`!EW@;?zZst3ilg zQXcmo0G<&V6ZsoAW6~g8`HYmzKhq?HykuaCnRlngylf*PGtbjqA0J*X4ES7%*Z92$ zBgVVvEwP_G;NCI&Fc_qJg-vA80gMQ(D*)aT*cHczXK&vj^&<3d-(Bycuf5&As$ zxhPG}x*H(;J2L*Ky08nLEwA{ib3_cJA}u5GmyaDiiPfIpvr?Lmh+UrT*e*W;Fl9UJxQE~*LkF2U@l5Z(p z4f(0AsC=E??gY3!t1OyR8+JqAf{Sq!{FuQdPVo-f6m^$NOm-zBxzcTVUfe))k{$93 zvClZR*Lfsf z4@hs!2+bkcfQ*HwagG*0f&l6fed|qR+P?Eq|E(@*@d&OPmfjQ)EG?g9)(y*)#++p_ z7aSg{ul62pXOO9B2U$@qmMglJ_|S6qUVlS|w`TcUu|uwgUZrv3Vya*2u7t%MyItjRB;Oqlaw8FDyj zUmcdLtIm$5u@{7F*P$fcq1H?5f+}vVQ2D^U#L*d7kZi0r3kFjwR#vNsU|eUdA3#8c!t1Ji0(;> z6>CiEWEDCYfFS00xX=UzUmVZ6Lt%7C!CgMMBo?!nWs#F)oSH1lDr~|8HrVT)`WWib zZjJn(f|;IiadW9@wvb8$GIKyef=yZ_GJjQUr>g%K@23W3jzKF{WwKzLlLNvrIc@nAx3tC@P5uXk)yJ+s~WSw<+4{q7lLfJDK| z9Lf0O20tt?UmDXMK*Up&r2la zU}BEN46;~t9xfPkUl3aAb9Y8Lx9fvKwjkGVAs&*AHM^p{W5N1GXh-w`9sf3ybOQ2Q z>NYRlejmi3O+K438Kd{p#T>z%g~6vM3-w5$8%k>kvBu5?v*a25k8X2>GRqmZoh(lFDQ#GXSbwFEAand<~VGUV*nY|PUeABE#? z@-9UXTK(0!wzCG+hv%5)Vp6}zZ7gw7DlO&47&2)4jp+!)C&DkTsnOau-#@#BJ6kcf znYqOSjUfBC{?PweYhluEVt!?u`lVcWO}V)GC0MtgoPaj!=?aUV(E+-HxYv-YQPTEc zcLCWEYy_ElAQCqfBL^~gY{>DeBU!b8PtVT9wJDb#x4x6ol%|uZBZ$)NHZ_fabk+=R zR&y@YQCUxug+*wC3#fPJAc?Eoc~?Y+}YYUR(e4%HE*%b0ugP zRjw`KVVE^T61_+8(wO!4SxbVka^2I3QW5G376P`21{U+t)!m(S?3#>R7DvpGpHQ?+ zO-3KzRLF%vY2h0F%zr5jCrcjv5}3;lJq6K6D}hk`Ce-(_xC+)QK|S;T=yK z^bwH;x$l!sKk@*5MQW`%f>@vJE#LNKMYM_539`|Snkr!nS+L7*Q?tf)h|LThYaom$HF@t*3+>-}z;T_pd+Jxe|PU#(=O@u>= z+oQMG@+kh?zT|hX;Td(m(!Vw5Ii0XU}7|CmQR zEvr;D*M`|poV&qH;w*_%^`sz8YMa(~I=yXgH>Jf)7j_1=_*>q&9Jn~P;JK02Jgh-*h2Po{1^sAa{yELtJXH_$& zt!QfKbe1`TQ>RoaRyh1Muk1Qig#56T1wQxX1N-HLN%onS0y!ip;bbJ;;0&N?=q7P| zcS5(ytCk8&nyalMZw;n`Qs>3Z22pxt7sduBTMgvXFHs0BM{WI6gs-P4=^?Ssgl@qFkFt{RM_@ z@Lx~wqN|Jn!ycSOhnZ*jiwE-yvF8Rf4EHiL3n z%QKdZs|wVy$`?T2dl;*v@;mh}i!h44(DjOm7qxkH>(*h#2b#*&yyRXtjJf;-&s zR2v~4?SU#4v6?l7?$69(x*Kc20fo%Jx|b?`u}Kyp-m$5(u)SX$yfw6?{aQ9OWp-;y zHP7Klcas$*4TXu)iVSa(k^mkKXdhsMo;jvgtR&ut^h-X+&8J31uRp=p=6lJ71rU7= zR7RlQye5TOW7!3+1~^7U8GZUuqwVDi#5ABQEDTQ9?a(maq%Ov^(5ONB{cqMX<#ds= zr<#YlfCZl|q@lh)hGl5FkzL*eAq?$0B4;}P?w z^!=!Bf!*Ij^oLGkUWfb6FS%P6>TIs)#^_9?eL6kKinv_7&aAv`go=%Uy~mxTt##qjv)|hyLSv3^wEp5=985&MTY~`j2*}wL7HK7 zvq|9qt=XiIX*iuV!vM`k%h~Z3VhYPMA95g=;*zBT7X@q%WJ~c_zGkXw#>vN_VOer^ zj=Z}~cvhS{E9b{ucHjNJMd`>Tg&(jTS;9y4X|r1qECU zT#G(-TXO_kYjwYLnqr@@8g^Tm80~%QPRQ1M&wrS$^VKOVxH3gM=Cq86p`0D%oh82O zgXGz%rs3(FrIYe%`1E+m9L{VbHLA?f!X@UZa%r}PjHbpFP;v0T1~j$yxs2&X$?V1g z_qxRvxkOn5!3?fY9>P2JYdS#u!nr>H*d6p!XOy-Vx(l&9Ab%|U5$jdF#vD;y97OjA zc?BJXR}D2a9`(_d>h3^BpX~h6X(`&4Yax*p&WYA8VfKTrV%AU>5rN|B2^->

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b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/obliczenia.py new file mode 100644 index 0000000..60a4119 --- /dev/null +++ b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/obliczenia.py @@ -0,0 +1,182 @@ +import math + +def formatuj_raport(nazwa, l_pomiary, S_koncowe, a_tab_tex, a_tab_val, S_poczatkowe=0.0, T_wrzenia=99.74, T0=21.0): + """ + Funkcja wykonuje obliczenia i zwraca sformatowany raport w Markdown/LaTeX. + Wersja ROZSZERZONA - wypisuje wszystkie dane pośrednie. + """ + output = [] + + # --- 1. STAŁE I DOKŁADNOŚCI PRZYRZĄDÓW --- + dokladnosc_termometru = 1.0 + dokladnosc_tabeli = 0.01 + dokladnosc_suwmiarki = 0.00001 + dokladnosc_czujnika = 0.00001 + + # --- 2. OBLICZENIA WARTOŚCI ŚREDNICH --- + l0 = sum(l_pomiary) / len(l_pomiary) + deltaT = T_wrzenia - T0 + deltaL = S_koncowe - S_poczatkowe + + # Zabezpieczenie przed dzieleniem przez zero + if l0 == 0 or deltaT == 0: return "Błąd: Dzielenie przez zero." + + # --- 3. GŁÓWNY WZÓR NA ALPHA --- + a = deltaL / (l0 * deltaT) + + # --- 4. RACHUNEK NIEPEWNOŚCI (OBLICZENIA) --- + + # Typ B (z przyrządów) - obliczamy wartości + uB_T0 = dokladnosc_termometru / math.sqrt(3) + uB_T_wrz = dokladnosc_tabeli / math.sqrt(3) + u_deltaT = math.sqrt(uB_T_wrz**2 + uB_T0**2) + + uB_l0 = dokladnosc_suwmiarki / math.sqrt(3) + uB_deltaL = dokladnosc_czujnika / math.sqrt(3) + + # Typ A (statystyczna dla długości) + n = len(l_pomiary) + suma_kwadratow = sum([(l - l0)**2 for l in l_pomiary]) + if n > 1: + ua_l0 = math.sqrt(suma_kwadratow / (n * (n - 1))) + else: + ua_l0 = 0.0 + + # Niepewność złożona (składniki) + try: + # Kwadrat niepewności względnej wydłużenia + wzgl_dL_sq = (uB_deltaL / deltaL)**2 + except ZeroDivisionError: + wzgl_dL_sq = 0 + + # Kwadrat niepewności względnej długości (A + B) + wzgl_l0_sq = (1 / l0**2) * (ua_l0**2 + uB_l0**2) + + # Kwadrat niepewności względnej temperatury + wzgl_dT_sq = (u_deltaT / deltaT)**2 + + # Suma i pierwiastek + suma_wzgl = wzgl_dL_sq + wzgl_l0_sq + wzgl_dT_sq + ua_a = a * math.sqrt(suma_wzgl) + + # --- 5. BŁĄD WZGLĘDNY --- + blad_wzgledny = abs(a - a_tab_val) / a_tab_val * 100 + + + # ========================================== + # --- 6. GENEROWANIE RAPORTU (WYPISYWANIE) --- + # ========================================== + + output.append(f"## Materiał: {nazwa}") + + # Sekcja 1: Dane wejściowe + output.append("### 1. Dane pomiarowe i stałe") + output.append(f"* **Pomiary długości $l_0$:** {l_pomiary} m") + output.append(f"* **Odczyt czujnika $S$:** {S_koncowe} m") + output.append(f"* **Temp. wrzenia $T_{{wrz}}$:** {T_wrzenia} $^\\circ$C") + output.append(f"* **Temp. otoczenia $T_0$:** {T0} $^\\circ$C") + output.append(f"* **Dokładności przyrządów:**") + output.append(f" * Termometr: $\\Delta T_0 = {dokladnosc_termometru}$ K") + output.append(f" * Tabela wrzenia: $\\Delta T_{{tab}} = {dokladnosc_tabeli}$ K") + output.append(f" * Suwmiarka: $\\Delta l = {dokladnosc_suwmiarki}$ m") + output.append(f" * Czujnik: $\\Delta S = {dokladnosc_czujnika}$ m") + output.append("") + + # Sekcja 2: Wyniki pośrednie + output.append(f"### 2. Obliczenia wielkości fizycznych") + output.append(f"**a) Średnia długość początkowa:**") + output.append(f"$$\\overline{{l}}_0 = \\frac{{{sum(l_pomiary):.5f}}}{{{n}}} = {l0:.5f} \\, m$$") + + output.append(f"**b) Różnica temperatur:**") + output.append(f"$$\\Delta T = T_{{wrz}} - T_0 = {T_wrzenia} - {T0} = {deltaT:.2f} \\, K$$") + + output.append(f"**c) Wydłużenie bezwzględne:**") + output.append(f"$$\\Delta l = S_{{końc}} - S_{{pocz}} = {S_koncowe} - {S_poczatkowe} = {deltaL:.5f} \\, m$$") + + output.append(f"**d) Współczynnik rozszerzalności:**") + output.append(f"$$\\alpha = \\frac{{{deltaL:.5f}}}{{{l0:.5f} \\cdot {deltaT:.2f}}} = \\mathbf{{{a*1e6:.2f} \\cdot 10^{{-6}} \\, K^{{-1}}}}$$") + + # Sekcja 3: Szczegółowa niepewność (TO JEST NOWE) + output.append(f"### 3. Szczegółowa analiza niepewności") + + output.append(f"**a) Niepewności standardowe typu B:**") + output.append(f"* Termometr: $u_B(T_0) = \\frac{{{dokladnosc_termometru}}}{{\\sqrt{{3}}}} = {uB_T0:.4f}$ K") + output.append(f"* Tabela wrzenia: $u_B(T_{{wrz}}) = \\frac{{{dokladnosc_tabeli}}}{{\\sqrt{{3}}}} = {uB_T_wrz:.4f}$ K") + output.append(f"* Suwmiarka: $u_B(l_0) = \\frac{{{dokladnosc_suwmiarki}}}{{\\sqrt{{3}}}} = {uB_l0:.7f}$ m") + output.append(f"* Czujnik wydłużenia: $u_B(\\Delta l) = \\frac{{{dokladnosc_czujnika}}}{{\\sqrt{{3}}}} = {uB_deltaL:.7f}$ m") + + output.append(f"**b) Niepewność różnicy temperatur:**") + output.append(f"$$u(\\Delta T) = \\sqrt{{u_B^2(T_{{wrz}}) + u_B^2(T_0)}} = \\sqrt{{{uB_T_wrz:.4f}^2 + {uB_T0:.4f}^2}} = {u_deltaT:.4f} \\, K$$") + + output.append(f"**c) Niepewność typu A:**") + output.append(f"$$u_A(l_0) = \\sqrt{{\\frac{{\\sum (l_i - \\overline{{l}})^2}}{{n(n-1)}}}} = {ua_l0:.7f} \\, m$$") + + output.append(f"**d) Udziały niepewności:**") + output.append(f"* Od wydłużenia: $(\\frac{{u(\\Delta l)}}{{\\Delta l}})^2 = {wzgl_dL_sq:.2e}$") + output.append(f"* Od długości: $\\frac{{1}}{{l_0^2}}(u_A^2 + u_B^2) = {wzgl_l0_sq:.2e}$") + output.append(f"* Od temperatury: $(\\frac{{u(\\Delta T)}}{{\\Delta T}})^2 = {wzgl_dT_sq:.2e}$") + output.append(f"* **Suma pod pierwiastkiem:** ${suma_wzgl:.2e}$") + + output.append(f"**e) Niepewność całkowita:**") + output.append(f"$$u(\\alpha) = \\alpha \\cdot \\sqrt{{{suma_wzgl:.4f}}} = {ua_a*1e6:.2f} \\cdot 10^{{-6}} \\, K^{{-1}}$$") + + # Sekcja 4: Podsumowanie + output.append(f"\n> **Zestawienie końcowe:**") + output.append(f"> * **Wynik z pomiaru:** $\\alpha = ({a*1e6:.2f} \\pm {ua_a*1e6:.2f}) \\cdot 10^{{-6}} \\, K^{{-1}}$") + output.append(f"> * **Wartość tablicowa:** $\\alpha_{{tab}} \\approx {a_tab_tex} \\, K^{{-1}}$") + + output.append(f"> * **Błąd względny:**") + output.append(f"> $$\\delta = \\frac{{|{a*1e6:.2f} - {a_tab_val*1e6:.1f}|}}{{{a_tab_val*1e6:.1f}}} \\cdot 100\\% = \\mathbf{{{blad_wzgledny:.1f}\\%}}$$") + + output.append("\n---\n") + return "\n".join(output) + +# --- KONFIGURACJA I URUCHOMIENIE --- + +# Dane wspólne +T_w = 99.71 # Temp. wrzenia [C] +T_p = 21.0 # Temp. pokojowa [C] + +# --- WYWOŁANIA DLA MATERIAŁÓW --- +tresc = "" + +# 1. Mosiądz +tresc += formatuj_raport( + nazwa="Mosiądz", + l_pomiary=[0.40480, 0.40470, 0.40460], + S_koncowe=0.00021, + a_tab_tex="19 \\cdot 10^{-6}", + a_tab_val=19e-6, + T_wrzenia=T_w, T0=T_p +) + +# 2. Glin +tresc += formatuj_raport( + nazwa="Glin", + l_pomiary=[0.40370, 0.40360, 0.40360], + S_koncowe=0.00010, + a_tab_tex="25 \\cdot 10^{-6}", + a_tab_val=25e-6, + T_wrzenia=T_w, T0=T_p +) + +# 3. Stal +tresc += formatuj_raport( + nazwa="Stal", + l_pomiary=[0.40520, 0.40520, 0.40520], + S_koncowe=0.00031, + a_tab_tex="12 \\cdot 10^{-6}", + a_tab_val=12e-6, + T_wrzenia=T_w, T0=T_p +) + +# --- ZAPIS DO PLIKU --- +nazwa_pliku = "wyniki_szczegolowe.md" +with open(nazwa_pliku, "w", encoding="utf-8") as f: + f.write(tresc) + +print("="*40) +print(f"SUKCES! Wygenerowano plik: {nazwa_pliku}") +print("Raport zawiera teraz WSZYSTKIE dane pośrednie (uA, uB, składniki błędu).") +print("Otwórz plik w Obsidianie.") +print("="*40) diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/podsumowanie.md b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/podsumowanie.md new file mode 100644 index 0000000..e69de29 diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/wstep.md b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/wstep.md new file mode 100644 index 0000000..b1ab84b --- /dev/null +++ b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/112/wstep.md @@ -0,0 +1,16 @@ +![tabelka](../../../../../media/tabelka.png) +# Cel +Wyznaczanie współczynnika rozszerzalności liniowej metalu +# Wstęp teoretyczny +Rozszerzalność cieplna to zjawisko, które polega na zwiększaniu się rozmiarów ciała pod wpływem ciepła. Wyróżniamy rozszerzalność cieplną ciał stałych, cieczy i gazów. Zjawisko to wynika z tego, że wraz ze wzrostem temperatury rośnie energia drgań cząstek składowych ciał, przez co rośnie średnia odległość między nimi. Wyjątkiem od tej zasady jest woda. +Zjawisko to opisujemy za pomocą współczynnika rozszerzalności liniowej $\alpha$, lub objętościowej $\gamma$. + +W celu zrozumienia powodu rozszerzania się ciał, musimy spojrzeć na potencjał oddziaływania międzyatomowego. Gdyby drgania w sieci krystalicznej były harmoniczne, czyli wykres energii potencjalnej byłby idealnie symetryczną parabolą, średnia odległość między atomami nie zmieniłaby się ze wzrostem energii. W rzeczywistości jednak drgania są anharmoniczne. Przy zbliżaniu się atomów siły odpychania rosną gwałtowanie, zaś przy oddalaniu maleją wolniej. + +Wrzenie to proces parowania w całej objętości cieczy. Rozpoczyna się ono w takiej temperaturze, w której ciśnienie pary nasyconej równe jest ciśnieniu zewnętrznemu. Temperatura wrzenia zależy więc od ciśnienia zewnętrznego i wzrasta wraz z jego wzrostem. Nie jest to zależność wprost proporcjonalna, a jej charakter zależy od rodzaju cieczy. Podczas wrzenia temperatura jest stała pomimo dostarczania do cieczy ciepła. Całe pobrane przez ciecz ciepło zużywane jest na zmianę stanu skupienia z ciekłego na gazowy. + + + + +# Tabela pomiarowa +![](../../../../../media/Pasted%20image%2020260108171659.png)