From 29f4fa2bd1ce0dfdfc5ce2e2a42c6c877d755f18 Mon Sep 17 00:00:00 2001 From: Szymon P Date: Thu, 15 Jan 2026 19:08:14 +0100 Subject: [PATCH] sprawozdanie 105 --- .../Sprawozdania/105/105.md | 17 ++ .../Sprawozdania/105/Obliczenia.md | 192 ++++++++++++++ .../Sprawozdania/105/Obliczenia.pdf | Bin 0 -> 306832 bytes .../Sprawozdania/105/obliczenia.py | 219 ++++++++++++++++ .../Sprawozdania/105/obliczenia_raport.py | 234 ++++++++++++++++++ 5 files changed, 662 insertions(+) create mode 100644 uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/105.md create mode 100644 uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.md create mode 100644 uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.pdf create mode 100644 uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/obliczenia.py create mode 100644 uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/obliczenia_raport.py diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/105.md b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/105.md new file mode 100644 index 0000000..99700a0 --- /dev/null +++ b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/105.md @@ -0,0 +1,17 @@ +![](../../../../media/tabelka.png) +# Cel +Pomiar wilgotności powietrza +# Wstęp teoretyczny +Parowanie cieczy to proces polegający na zmianie stanu skupienia z cieczy w gaz, zachodzący na powierzchni cieczy w każdej temperaturze. Cząsteczki o największej energii odrywają się od powierzchni, co prowadzi do obniżenia średniej energii układu. +Wyróżniamy dwa rodzaje pary: parę nasyconą oraz parę nienasyconą. Para nasycona to stan, w którym liczba cząsteczek opuszczających ciecz jest równa liczbie cząstek do niej powracających, w wyniku skraplania. Ciśnienie pary nasyconej osiąga maksymalną wartość i zależy wyłącznie od temperatury i rodzaju cieczy. Para nienasycona ma niższe ciśnienie od pary nasyconej w tej samej temperaturze. Może przyjąć dodatkowe cząsteczki odparowanej cieczy. +Prężność pary nasyconej jest maksymalnym ciśnieniem, jakie para danej cieczy może wywierać w danej temperaturze. Zależy ono wyłącznie od temperatury i rodzaju cieczy. +
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+Rosa powstaje, gdy temperatura powietrza spadnie poniżej tzw. punktu rosy. Wówczas para wodna zawarta w powietrzu staje się parą nasyconą i zaczyna się skraplać na chłodnych powierzchniach. +Wrzenie polega na gwałtownym parowaniu zachodzącym w całej objętości cieczy. Ciecz paruje, gdy prężność pary nasyconej wewnątrz pęcherzyków staje się równa ciśnieniu wewnętrznemu. Wzrost ciśnienia powoduje podwyższenie temperatury wrzenia, zaś spadek powoduje jej obniżenie. +Wilgotność powietrza opisuje zawartość pary wodnej w atmosferze. Wydzielamy dwa rodzaje wilgotności: wilgotność bezwzględną i względną. Wilgotność bezwzględna to masa pary wodnej zawarta w jednostce objętości powietrza. Wilgotność względna to stosunek aktualnego ciśnienia cząstkowego pary wodnej do ciśnienia pary nasyconej, w tej samej temperaturze, wyrażony w procentach. +Wilgotność powietrza możemy wyznaczyć na wiele sposobów. Jedną z takich metod jest metoda psychrometryczna. Polega ona na wykorzystaniu dwóch termometrów: suchego i mokrego. Parowanie wody z mokrego obniży jego temperaturę. Różnica wskazań pozwoli odczytać wilgotność z tablic psychrometrycznych. Inną metodą jest metoda higrometryczna. Wykorzystuje ona właściwości materiałów organicznych, które zmieniają swoją długość pod wpływem wilgoci. Ostatnią omawianą metodą jest metoda punktu rosy. Wykorzystując ją, należy schłodzić lustrzaną powierzchnię do momentu pojawienia się na niej rosy i dokonaniu pomiaru temperatury, w której to nastąpiło. diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.md b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.md new file mode 100644 index 0000000..4205ba8 --- /dev/null +++ b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.md @@ -0,0 +1,192 @@ +# Obliczenia +## 1. Dane wstępne i niepewności przyrządów +- Ciśnienie atmosferyczne: $b = 1015 \text{ hPa} = 761.25 \text{ mmHg}$ +- Niepewność standardowa termometrów: $$u(t) = \frac{0.1}{\sqrt{3}} = 0.0577 \, ^\circ\text{C}$$ +- Niepewność standardowa barometru (w mmHg): $$u(b) = \frac{0.75}{\sqrt{3}} = 0.4330 \text{ mmHg}$$ + +## 2. Obliczenia krok po kroku dla każdego pomiaru +### Pomiar nr 1 +Dane: $t_m = 17^\circ\text{C}$, $t_s = 22.5^\circ\text{C}$ + +**A. Wyznaczenie prężności pary nasyconej:** +- Dla termometru mokrego ($t_m=17$): Wartość z tabeli dla $t=17$. + $$p_m = 14.53 \text{ mmHg}$$ + Niepewność odczytu: $\Delta p_m = 0.475$. + $$u(p_m) = \frac{0.475}{\sqrt{3}} = 0.2742 \text{ mmHg}$$ +- Dla termometru suchego ($t_s=22.5$): Interpolacja między 22°C (19.83) a 23°C (21.07). + $$p_0 = 20.45 \text{ mmHg}$$ + $$u(p_0) = \frac{0.620}{\sqrt{3}} = 0.3580 \text{ mmHg}$$ + +**B. Obliczenie prężności pary nienasyconej $p$:** +Wzór: $$p = p_m - 0.5 \cdot (t_s - t_m) \cdot \frac{b}{755}$$ +Podstawienie: +$$p = 14.53 - 0.5 \cdot (22.5 - 17) \cdot \frac{761.2}{755}$$ +$$p = 14.53 - 2.7728 = \mathbf{11.76 \text{ mmHg}}$$ + +**C. Obliczenie niepewności $u(p)$:** +$$u(p) = \sqrt{u^2(p_m) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_s) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_m) + \left(0.5 \frac{t_s-t_m}{755}\right)^2 u^2(b)}$$ +$$u(p) = \sqrt{0.075208 + 0.000847 + 0.000847 + 0.000002}$$ +$$u(p) = \sqrt{0.076905} = 0.2773 \text{ mmHg}$$ + +**D. Obliczenie wilgotności względnej $w_1$:** +$$w_1 = \frac{p}{p_0} \cdot 100\% = \frac{11.76}{20.45} \cdot 100\% = \mathbf{57.49 \%}$$ + +**E. Niepewność pomiaru $u(w_1)$:** +$$u(w_1) = w_1 \cdot \sqrt{\left(\frac{u(p)}{p}\right)^2 + \left(\frac{u(p_0)}{p_0}\right)^2}$$ +$$u(w_1) = 57.49 \cdot \sqrt{\left(\frac{0.2773}{11.76}\right)^2 + \left(\frac{0.3580}{20.45}\right)^2} = 1.69 \%$$ +--- +### Pomiar nr 2 +Dane: $t_m = 18.2^\circ\text{C}$, $t_s = 21.8^\circ\text{C}$ + +**A. Wyznaczenie prężności pary nasyconej:** +- Dla termometru mokrego ($t_m=18.2$): Interpolacja między 18°C (15.48) a 19°C (16.48). + $$p_m = 15.68 \text{ mmHg}$$ + Niepewność odczytu: $\Delta p_m = 0.500$. + $$u(p_m) = \frac{0.500}{\sqrt{3}} = 0.2887 \text{ mmHg}$$ +- Dla termometru suchego ($t_s=21.8$): Interpolacja między 21°C (18.65) a 22°C (19.83). + $$p_0 = 19.59 \text{ mmHg}$$ + $$u(p_0) = \frac{0.590}{\sqrt{3}} = 0.3406 \text{ mmHg}$$ + +**B. Obliczenie prężności pary nienasyconej $p$:** +Wzór: $$p = p_m - 0.5 \cdot (t_s - t_m) \cdot \frac{b}{755}$$ +Podstawienie: +$$p = 15.68 - 0.5 \cdot (21.8 - 18.2) \cdot \frac{761.2}{755}$$ +$$p = 15.68 - 1.8149 = \mathbf{13.87 \text{ mmHg}}$$ + +**C. Obliczenie niepewności $u(p)$:** +Wzór (złożona niepewność standardowa): +$$u(p) = \sqrt{u^2(p_m) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_s) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_m) + \left(0.5 \frac{t_s-t_m}{755}\right)^2 u^2(b)}$$ +Podstawienie wartości kwadratów składników: +$$u(p) = \sqrt{0.083333 + 0.000847 + 0.000847 + 0.000001}$$ +$$u(p) = \sqrt{0.085029} = 0.2916 \text{ mmHg}$$ + +**D. Obliczenie wilgotności względnej $w_1$:** +$$w_1 = \frac{p}{p_0} \cdot 100\% = \frac{13.87}{19.59} \cdot 100\% = \mathbf{70.76 \%}$$ + +**E. Niepewność pomiaru $u(w_1)$:** +$$u(w_1) = w_1 \cdot \sqrt{\left(\frac{u(p)}{p}\right)^2 + \left(\frac{u(p_0)}{p_0}\right)^2}$$ +$$u(w_1) = 70.76 \cdot \sqrt{\left(\frac{0.2916}{13.87}\right)^2 + \left(\frac{0.3406}{19.59}\right)^2} = 1.93 \%$$ +--- +### Pomiar nr 3 +Dane: $t_m = 17.8^\circ\text{C}$, $t_s = 21.4^\circ\text{C}$ + +**A. Wyznaczenie prężności pary nasyconej:** +- Dla termometru mokrego ($t_m=17.8$): Interpolacja między 17°C (14.53) a 18°C (15.48). + $$p_m = 15.29 \text{ mmHg}$$ + Niepewność odczytu: $\Delta p_m = 0.475$. + $$u(p_m) = \frac{0.475}{\sqrt{3}} = 0.2742 \text{ mmHg}$$ +- Dla termometru suchego ($t_s=21.4$): Interpolacja między 21°C (18.65) a 22°C (19.83). + $$p_0 = 19.12 \text{ mmHg}$$ + $$u(p_0) = \frac{0.590}{\sqrt{3}} = 0.3406 \text{ mmHg}$$ + +**B. Obliczenie prężności pary nienasyconej $p$:** +Wzór: $$p = p_m - 0.5 \cdot (t_s - t_m) \cdot \frac{b}{755}$$ +Podstawienie: +$$p = 15.29 - 0.5 \cdot (21.4 - 17.8) \cdot \frac{761.2}{755}$$ +$$p = 15.29 - 1.8149 = \mathbf{13.48 \text{ mmHg}}$$ + +**C. Obliczenie niepewności $u(p)$:** +Wzór (złożona niepewność standardowa): +$$u(p) = \sqrt{u^2(p_m) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_s) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_m) + \left(0.5 \frac{t_s-t_m}{755}\right)^2 u^2(b)}$$ +Podstawienie wartości kwadratów składników: +$$u(p) = \sqrt{0.075208 + 0.000847 + 0.000847 + 0.000001}$$ +$$u(p) = \sqrt{0.076904} = 0.2773 \text{ mmHg}$$ + +**D. Obliczenie wilgotności względnej $w_1$:** +$$w_1 = \frac{p}{p_0} \cdot 100\% = \frac{13.48}{19.12} \cdot 100\% = \mathbf{70.47 \%}$$ + +**E. Niepewność pomiaru $u(w_1)$:** +$$u(w_1) = w_1 \cdot \sqrt{\left(\frac{u(p)}{p}\right)^2 + \left(\frac{u(p_0)}{p_0}\right)^2}$$ +$$u(w_1) = 70.47 \cdot \sqrt{\left(\frac{0.2773}{13.48}\right)^2 + \left(\frac{0.3406}{19.12}\right)^2} = 1.92 \%$$ +--- +### Pomiar nr 4 +Dane: $t_m = 17.8^\circ\text{C}$, $t_s = 21.8^\circ\text{C}$ + +**A. Wyznaczenie prężności pary nasyconej:** +- Dla termometru mokrego ($t_m=17.8$): Interpolacja między 17°C (14.53) a 18°C (15.48). + $$p_m = 15.29 \text{ mmHg}$$ + Niepewność odczytu: $\Delta p_m = 0.475$. + $$u(p_m) = \frac{0.475}{\sqrt{3}} = 0.2742 \text{ mmHg}$$ +- Dla termometru suchego ($t_s=21.8$): Interpolacja między 21°C (18.65) a 22°C (19.83). + $$p_0 = 19.59 \text{ mmHg}$$ + $$u(p_0) = \frac{0.590}{\sqrt{3}} = 0.3406 \text{ mmHg}$$ + +**B. Obliczenie prężności pary nienasyconej $p$:** +Wzór: $$p = p_m - 0.5 \cdot (t_s - t_m) \cdot \frac{b}{755}$$ +Podstawienie: +$$p = 15.29 - 0.5 \cdot (21.8 - 17.8) \cdot \frac{761.2}{755}$$ +$$p = 15.29 - 2.0166 = \mathbf{13.27 \text{ mmHg}}$$ + +**C. Obliczenie niepewności $u(p)$:** +Wzór (złożona niepewność standardowa): +$$u(p) = \sqrt{u^2(p_m) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_s) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_m) + \left(0.5 \frac{t_s-t_m}{755}\right)^2 u^2(b)}$$ +Podstawienie wartości kwadratów składników: +$$u(p) = \sqrt{0.075208 + 0.000847 + 0.000847 + 0.000001}$$ +$$u(p) = \sqrt{0.076904} = 0.2773 \text{ mmHg}$$ + +**D. Obliczenie wilgotności względnej $w_1$:** +$$w_1 = \frac{p}{p_0} \cdot 100\% = \frac{13.27}{19.59} \cdot 100\% = \mathbf{67.74 \%}$$ + +**E. Niepewność pomiaru $u(w_1)$:** +$$u(w_1) = w_1 \cdot \sqrt{\left(\frac{u(p)}{p}\right)^2 + \left(\frac{u(p_0)}{p_0}\right)^2}$$ +$$u(w_1) = 67.74 \cdot \sqrt{\left(\frac{0.2773}{13.27}\right)^2 + \left(\frac{0.3406}{19.59}\right)^2} = 1.84 \%$$ +--- +### Pomiar nr 5 +Dane: $t_m = 18.2^\circ\text{C}$, $t_s = 21.6^\circ\text{C}$ + +**A. Wyznaczenie prężności pary nasyconej:** +- Dla termometru mokrego ($t_m=18.2$): Interpolacja między 18°C (15.48) a 19°C (16.48). + $$p_m = 15.68 \text{ mmHg}$$ + Niepewność odczytu: $\Delta p_m = 0.500$. + $$u(p_m) = \frac{0.500}{\sqrt{3}} = 0.2887 \text{ mmHg}$$ +- Dla termometru suchego ($t_s=21.6$): Interpolacja między 21°C (18.65) a 22°C (19.83). + $$p_0 = 19.36 \text{ mmHg}$$ + $$u(p_0) = \frac{0.590}{\sqrt{3}} = 0.3406 \text{ mmHg}$$ + +**B. Obliczenie prężności pary nienasyconej $p$:** +Wzór: $$p = p_m - 0.5 \cdot (t_s - t_m) \cdot \frac{b}{755}$$ +Podstawienie: +$$p = 15.68 - 0.5 \cdot (21.6 - 18.2) \cdot \frac{761.2}{755}$$ +$$p = 15.68 - 1.7141 = \mathbf{13.97 \text{ mmHg}}$$ + +**C. Obliczenie niepewności $u(p)$:** +Wzór (złożona niepewność standardowa): +$$u(p) = \sqrt{u^2(p_m) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_s) + \left(0.5 \frac{b}{755}\right)^2 u^2(t_m) + \left(0.5 \frac{t_s-t_m}{755}\right)^2 u^2(b)}$$ +Podstawienie wartości kwadratów składników: +$$u(p) = \sqrt{0.083333 + 0.000847 + 0.000847 + 0.000001}$$ +$$u(p) = \sqrt{0.085029} = 0.2916 \text{ mmHg}$$ + +**D. Obliczenie wilgotności względnej $w_1$:** +$$w_1 = \frac{p}{p_0} \cdot 100\% = \frac{13.97}{19.36} \cdot 100\% = \mathbf{72.15 \%}$$ + +**E. Niepewność pomiaru $u(w_1)$:** +$$u(w_1) = w_1 \cdot \sqrt{\left(\frac{u(p)}{p}\right)^2 + \left(\frac{u(p_0)}{p_0}\right)^2}$$ +$$u(w_1) = 72.15 \cdot \sqrt{\left(\frac{0.2916}{13.97}\right)^2 + \left(\frac{0.3406}{19.36}\right)^2} = 1.97 \%$$ +--- +## 3. Opracowanie statystyczne wyników ($w_1$) +**Średnia arytmetyczna:** +$$\bar{w}_1 = \frac{\sum w_i}{n} = \frac{338.61}{5} = \mathbf{67.72 \%}$$ + +**Niepewność typu A (statystyczna):** +$$u_A = \sqrt{\frac{\sum (w_i - \bar{w})^2}{n(n-1) }} = \sqrt{\frac{141.00}{5 \cdot 4}} = \mathbf{2.66 \%}$$ + +**Niepewność typu B (z przyrządów - średnia):** +$$ +u_B = \frac{1}{n} \sum_{i=1}^{n} u(w_i) + = \frac{1.69 + 1.93 + 1.92 + 1.84 + 1.97}{5} + = 1.87\% +$$ + +**Całkowita niepewność standardowa:** +$$u(\bar{w}_1) = \sqrt{u_A^2 + u_B^2} = \sqrt{2.66^2 + 1.87^2} = \mathbf{3.25 \%}$$ +## 4. Zestawienie końcowe i porównanie metod +### Wyniki końcowe: +- **Psychrometr Assmanna ($w_1$):** $$67.72 \% \pm 3.25 \%$$ +- **Metoda tabelaryczna ($w_2$):** $$67.60 \%$$ +- **Higrometr włosowy ($w_3$):** $$35 \% \pm 2.89 \%$$ +- **Higrometr pojemnościowy ($w_4$):** $$30.5 \% \pm 1.44 \%$$ +# Wnioski +- Wyniki dla higrometrów oraz psychrometru i tablic psychrometrycznych drastycznie się od siebie różnią. Higrometr włosowy wskazywał 35%, pojemnościowy 30.5% podczas, gdy psychrometr Assmana wskazał 67.72%, a tablica psychrometryczna pokazała 67.60%. +- Takie rozbieżności mogą wynikać z niedoskonałości przyrządów. Mówimy wtedy o błędzie systematycznym. +- Należy mieć na uwadze, że ekran higrometru pojemnościowego był uszkodzony i mogło to wpłynąć na poprawny odczyt wilgotności powietrza. +- Higrometr włosowy mógł być rozkalibrowany co wpłynęło negatywnie na wynik. \ No newline at end of file diff --git a/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.pdf b/uczelnia/1_semestr/fizyka_dla_informatyków/Sprawozdania/105/Obliczenia.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7e76234577e7e659eba0060bead2f71251320acd GIT binary patch literal 306832 zcma%?V~{4nv+l>XZTlVU*tTukwr$(C%^lnJjy*f}%-#RF_tUxO!|90b%IvC$%&3a$ zi26O*7YqzD3lS5My^$3R4-X8Zn5B)2sS^>Sn2n)}sfekuy@@Fd zql~GYxr+r68#6N}3?Cnivx}3dp)HI@&b97V9bLPl@18zj4p?X<)&!XeWPOp-&&?sg zC%}jkssPCCn-D5WR;_tsX(*3=1Q_j7)R{xsq_Ik(POIliKmC8QBt6a>p2HG~5D550xfwcY!ejnJ*-5&+_RC?gkwi0af^)0D#sz~Q zsko$WDxnd*95Kj|$PS1;`wTgi`81w3pasD)p(c`2Gyzo5h{op%aWo-P>NoRKeo%wh 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