Domanda 1 — Colore e temperatura (4 punti)
Il colore della radiazione di corpo nero dipende dalla sua temperatura. In astronomia, la temperatura delle stelle è determinata dal loro indice di colore, il rapporto degli illuminamenti misurati attraverso due diversi filtri colorati.
The colour of the black body radiation depends on its temperature. In astronomy, the temperature of stars is determined from their colour index, the ratio of illuminances measured through two different colour filters.
(a) La tavola 1 contiene gli illuminamenti misurati attraverso il filtro rosso, verde e blu per una sorgente luminosa a incandescenza standard a temperature note. Scegli filtri luce adatti e costruisci una curva di calibrazione che metta in relazione l’indice di colore scelto con la temperatura.
(a) Table 1 contains the illuminances measured through the red, green and blue filter for a standard incandescent light source at known temperatures. Choose suitable light filters and construct a calibration curve that relates the chosen colour index to the temperature.
(b) Misura la relazione tra la potenza elettrica in ingresso e la temperatura del filamento di tungsteno. Traccia il risultato su un intervallo adeguato, pertinente.
(b) Measure the relationship between the electrical input power and the tungsten filament temperature. Plot the result over a relevant range.
Topic: Thermodynamics, Modern-Quantum Physics, Electromagnetism Metodi: Experimental Data Analysis, Graph Linearization, Physical Modeling Competenze: Experimental Data Analysis, Graph Linearization Objects: Star Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Task 1 - Colour and temperature (4 pts)
The colour of the black body radiation depends on its temperature. In astronomy, the temperature of stars is determined from their colour index, the ratio of illuminances measured through two different colour filters.
(a) Table 1 contains the illuminances measured through the red, green and blue filter for a standard incandescent light source at known temperatures. Choose suitable light filters and construct a calibration curve that relates the chosen colour index to the temperature.
(b) Measure the relationship between the electrical input power and the tungsten filament temperature. Plot the result over a relevant range.
Topic: Thermodynamics, Modern-Quantum Physics, Electromagnetism Metodi: Experimental Data Analysis, Graph Linearization, Physical Modeling Competenze: Experimental Data Analysis, Graph Linearization Objects: Star Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Domanda 2 — Efficacia luminosa (8 punti)
Il rendimento delle sorgenti luminose si misura tramite l’efficacia luminosa, una grandezza misurata in lumen al watt [lm/W], data dal rapporto tra il flusso luminoso e la potenza consumata. Come punto di riferimento, il sole ha un’efficacia luminosa di 93 lm/W.
The efficiency of light sources is quantified by their luminous efficacy, measured in lumens per watt, as the ratio between the luminous flux and the consumed power. As a point of reference, the sun has luminous efficacy of 93 lm/W.
Misura l’efficienza luminosa in funzione della potenza elettrica in ingresso per entrambe le sorgenti luminose nell’intervallo di luce rilevabile. Traccia un grafico delle misurazioni per ciascuna sorgente luminosa. Indica tutte le fasi della procedura di calcolo e presenta tutti i dati misurati.
Measure the dependence of luminous efficacy on the electrical input power for both light sources across the range with detectable light output. Plot the results, one plot per light source. State all steps of the calculation procedure and present all the measured data.
Topic: Thermodynamics, Electromagnetism, Modern-Quantum Physics Metodi: Experimental Data Analysis, Graph Linearization, Physical Modeling Competenze: Experimental Data Analysis, Graph Linearization Objects: Star Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Task 2 - Luminous efficacy (8 pts)
The performance of light sources is quantified by their luminous efficacy, measured in lumens per watt, as the ratio between the luminous flux and the consumed power. As a point of reference, the sun has luminous efficacy of 93 lm/W.
Measure the dependence of luminous efficacy on the electrical input power for both light sources across the range with detectable light output. Plot the results, one plot per light source. State all steps of the calculation procedure and present all the measured data.
Topic: Thermodynamics, Electromagnetism, Modern-Quantum Physics Metodi: Experimental Data Analysis, Graph Linearization, Physical Modeling Competenze: Experimental Data Analysis, Graph Linearization Objects: Star Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Domanda 3 — Riscaldamento radiativo (8 punti)
The following task may be time consuming, plan your work accordingly.
L’attività che segue potrebbe richiedere molto tempo, perciò pianifica bene il tuo lavoro.
Quando la luce colpisce un oggetto, parte di essa viene assorbita. Per piccole differenze di temperatura tra l’oggetto e l’ambiente, possiamo modellizzare la dispersione del calore nell’ambiente con il coefficiente di scambio termico , nella forma seguente:
dove è la temperatura della superficie, la temperatura dell’ambiente e indica la potenza dispersa nell’ambiente, per unità di superficie.
When light hits an object, some of it is absorbed. At moderate temperature differences between the object and the environment, we can model heat dissipation into the surroundings with the heat transfer coefficient , in the form , where is the temperature of the surface, the temperature of the surroundings, and denotes the power lost to the environment due to dissipation, per unit area.
(a) Determina il coefficiente di scambio termico e la conducibilità termica per la plastica nera e fai l’analisi degli errori. Supponi che il materiale assorba tutta la luce ricevuta e che la lampadina a incandescenza emetta tutta la potenza sotto forma di radiazione elettromagnetica.
(a) Determine the heat transfer coefficient and the thermal conductivity for the black plastic, and perform error analysis. Assume the material absorbs all received light and the incandescent light bulb emits all power in the form of electromagnetic radiation.
Topic: Thermodynamics, Electromagnetism, Newtonian Mechanics Metodi: Experimental Data Analysis, Error Propagation, Physical Modeling, First Law of Thermodynamics Competenze: Experimental Data Analysis, Error Propagation Objects: — Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Task 3 - Radiative heating (8 pts)
The following task may be time consuming, plan your work accordingly.
When light hits an object, some of it is absorbed. At moderate temperature differences between the object and the environment, we can model heat dissipation into the surroundings with the heat transfer coefficient , in the form
where is the temperature of the surface, the temperature of the surroundings, and denotes the power lost to the environment due to dissipation, per unit area.
(a) Determine the heat transfer coefficient and the thermal conductivity for the black plastic, and perform error analysis. Assume the material absorbs all received light and the incandescent light bulb emits all power in the form of electromagnetic radiation.
(b) Estimate the albedo (the fraction of the irradiance that is reflected instead of absorbed) of the white plastic and perform error analysis.
Useful relations: An area of a segment of a sphere with radius between polar angles and with is .
Topic: Thermodynamics, Electromagnetism, Newtonian Mechanics Metodi: Experimental Data Analysis, Error Propagation, Physical Modeling, First Law of Thermodynamics Competenze: Experimental Data Analysis, Error Propagation Objects: — Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)