Your boss asks you to classify some of the components in a temperature measurement system. The system consists of a thermocouple and an analog-digital conversion (ADC) device. The thermocouple has a linear response from 0 to 70°C. Over this range, its minimum output voltage is 0 V and its maximum output voltage is 3.649 mV. The ADC device has 8 bits and two possible input ranges +5 mV and ±5 V. You can assume that the ADC rounding process operates in the same manner as we discussed in class. a. Determine the resolution voltage and its related uncertainty of the ADC for both input ranges b. Determine the sensitivity of the thermocouple c. You set a water bath to a 57°C temperature and place the thermocouple in the bath. i. What do you expect the thermocouple voltage to read? ii. Based off both ADC input ranges, what do you expect the ADC output voltage to read? iii. How can you explain the difference in values? iv. Which input range is optimal for this measurement scenario? d. Based on the previous step and the lower ADC input range: If you didn't know the bath temperature and only knew the ADC voltage, what temperature would you say the bath is set to?

Explanation:

1) Resolution and uncertainty of both ADC ranges

a) Resolution (for +/- 5 mV range) = 5 mV / 2n where n = number of bits of ADC

Resolution = 5 mV / 28 = 5 mV / 256 = 0.0195 mV    1

uncertainty (for +/- 5 mV range) = +/- 0.5*resolution = +/- 0.5*0.0195 mV = 0.00975 mV       2

b) Resolution (for +/- 5 V range) = 5 V / 2n where n = number of bits of ADC

Resolution = 5 mV / 28 = 5 V / 256 = 0.0195 V = 19.5 mV    3

uncertainty (for +/- 5 mV range) = +/- 0.5*resolution = +/- 0.5*19.5 mV = 9.75 mV       4

2)Thermocouple sensitivity = ( Maximum output voltage - Minimum Output voltage) / (Maximum Temperature - Minimum Temperature)

Thermocouple sensitivity = (3.649mv - 0 ) / (70 - 0) = 0.0521 mV / Deg.C           5

This is the required Thermocouple sensitivity

3) Water bath temperature is given as 57 deg.C

Hence voltage read by Thermocouple = Sensitivity*57 = 0.0521*57 mV = 2.9697 mV    6

4)We need to use ADC with a range of +/- 5 mV range as ADC with +/- 5 V range can not do measurement as it's resolution is higher than output voltage.

ADC will measure voltage as 2.9695 mV                    7

energy can cross the boundaries of a closed system in the form of heat and mass

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