Experiment_Problem - 39th International Physics Olympiad -...

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39th International Physics Olympiad - Hanoi - Vietnam - 2008 Experimental Problem DIFFERENTIAL THERMOMETRIC METHOD In this problem, we use the differential thermometric method to fulfill the two following tasks: 1. Finding the temperature of solidification of a crystalline solid substance. 2. Determining the efficiency of a solar cell. A. Differential thermometric method In this experiment forward biased silicon diodes are used as temperature sensors to measure temperature. If the electric current through the diode is constant, then the voltage drop across the diode depends on the temperature according to the relation ( ) ( ) ( ) 0 VT VT T T α =− 0 (1) where ( ) VT and ( ) 0 are respectively the voltage drops across the diode at temperature and at room temperature (measured in T 0 T o C), and the factor ( ) o 200 003 mV/ C .. ( 2 ) The value of ( ) 0 may vary slightly from diode to diode. If two such diodes are placed at different temperatures, the difference between the temperatures can be measured from the difference of the voltage drops across the two diodes. The difference of the voltage drops, called the differential voltage , can be measured with high precision; hence the temperature difference can also be measured with high precision. This method is called the differential thermometric method . The electric circuit used with the diodes in this experiment is shown in Figure 1. Diodes D 1 and D 2 are forward biased by a 9V battery, through 10 k Ω resistors, 1 R and 2 R . This circuit keeps the current in the two diodes approximately constant. V 1 V 2 Δ V D 1 D 2 R 1 R 2 E Figure 1. Electric circuit of the diode If the temperature of diode D 1 is 1 T and that of D 2 is , then according to (1), we have: 2 T 1
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39th International Physics Olympiad - Hanoi - Vietnam - 2008 Experimental Problem ( ) ( ) ( ) 11 10 1 0 VT VT T T α =− and ( ) ( ) ( ) 22 20 2 0 The differential voltage is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 0 V V TV T T T V T T T αα Δ= = − = Δ ( ) 0 VV T Δ −Δ T 1 (3) in which . By measuring the differential voltage 2 TTT Δ= − V Δ , we can determine the temperature difference. To bias the diodes, we use a circuit box, the diagram of which is shown in Figure 2. Blue The circuit box contains two biasing resistors of 10 k for the diodes, electrical leads to the 9 V battery, sockets for connecting to the diodes D 1 and D 2 , and sockets for connecting to digital multimeters to measure the voltage drop on diode D 2 V 2 and the differential voltage of the diodes D V Δ 1 and D 2 . Common- Black Black Figure 2. Diagram of the circuit box (top view) 9 V To D 2 - Red 1 - Blue 10 k Ω 10 k Ω Red V 2 Δ V Red 2
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39th International Physics Olympiad - Hanoi - Vietnam - 2008 Experimental Problem B. Task 1: Finding the temperature of solidification of a crystalline substance 1. Aim of the experiment If a crystalline solid substance is heated to the melting state and then cooled down, it solidifies at a fixed temperature , called temperature of solidification , also called the melting point of the substance. The traditional method to determine is to follow the change in temperature with time during the cooling process. Due to the fact that the
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Experiment_Problem - 39th International Physics Olympiad -...

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