OII 2022 Sperimentale

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)

Question 1 Color and temperature (4 points)

The color of black body radiation depends on its temperature. In astronomy, the temperature of stars is determined by their color index, the ratio of illumination measured through two different color filters.

The color of the black body radiation depends on its temperature. In astronomy, the temperature of stars is determined from their color index, the ratio of illuminations measured through two different color filters.*

(a) Table 1 contains the illuminations 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 color index to the temperature.

• (a) Table 1 contains the illuminations 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 color index to the temperature.*

(b) Measures the relationship between the incoming electrical power and the temperature of the tungsten filament. Track the result over an appropriate, relevant time frame.

(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)

Question 2 Light efficiency (8 points)

The efficiency of light sources is measured by light efficiency, a measure in lumen per watt [lm/W], given the ratio of the light flux to the power consumed. As a reference point, the sun has a luminous efficiency of 93 lm/W.

The efficiency of light sources is quantified by their luminous efficiency, measured in lumens per watt, as the ratio between the luminous flux and the power consumed. As a point of reference, the sun has luminous efficacy of 93 lm/W.

Measures the light efficiency in relation to the input power for both light sources in the detectable light range. Draw a graph of measurements for each light source. It shall indicate all the steps of the calculation procedure and shall present all measured data.

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 to 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 $h$, nella forma seguente:

$\frac{P}{A}=h(T-T_0)$

dove $T$ è la temperatura della superficie, $T_0$ la temperatura dell’ambiente e $P/A$ 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 $h$, in the form $P/A=h(T-T_0)$, where $T$ is the temperature of the surface, $T_0$ the temperature of the surroundings, and $P/A$ denotes the power lost to the environment due to dissipation, per unit area.

(a) Determina il coefficiente di scambio termico $h$ e la conducibilità termica $\lambda$ 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 $h$ and the thermal conductivity $\lambda$ 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)

Question 3 Radiative heating (8 points)

The following task may be time consuming, plan your work accordingly.

The next activity may take a long time, so plan your work well.

When light hits an object, some of it is absorbed. For small temperature differences between the object and the environment, we can model the heat dissipation in the environment with the heat exchange coefficient $h$, as follows:

$\frac{P}{A}=h(T-T_0)$

where $T$ is the surface temperature, $T_0$ the ambient temperature and $P/A$ indicates the power dispersed in the environment, per unit area.

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 $h$, in the form $P/A=h(T-T_0)$, where $T$ is the temperature of the surface, $T_0$ the temperature of the surroundings, and $P/A$ denotes the power lost to the environment due to dissipation, per unit area.*

(a) Determine the heat exchange coefficient $h$ and the thermal conductivity $\lambda$ for black plastic and analyse the errors. Suppose the material absorbs all the light received and the incandescent light bulb emits all the power in the form of electromagnetic radiation.

(a) Determine the heat transfer coefficient $h$ and the thermal conductivity $\lambda$ for the black plastic, and perform error analysis. Assumes 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)