Problem 1 Type I thermocouple, input range = -210 to 1200 C (based on thermocouple table on carmen: files/homework) For parts a-f: reference junction maintained at temperature T, For part g: electronic reference junction (similar to AD594 used in lab - except that the AD594 also amplifies and linearizes). reference junction uncertainty = +0.05C (95%) display resolution = 0.01C. uncertainty of "measured junction = +/- 2.2C or +/-.75% (whichever is greater) a. The standard thermocouple circuit produces an emf of 41 mV for Tm=750 C. What is Tr? b. full scale output range (based on thermocouple table type J thermocouple) c. sensitivity (just a gross estimate based on the input range and output range, K = AV/AT) d. write the differential equation for the thermocouple (based on thermal model). Write the equation for the time constant and solve for its numerical value if the diameter is 0.001 m. Assume the thermocouple is spherical. For the convective heat transfer coefficient, h, use 100 W/mK for the surrounding air. For the density, P, and heat capacity, c, use the average value of the two metals: constantan and iron. e. Solve for the bandwidth: (Put the volume and surface area in terms of the radius of the thermocouple weld - assume it is spherical). f. how can you increase the bandwidth without changing thermocouple material, the heat transfer coefficient or A% (for the bandwidth calculation). g. What is the uncertainty of measuring the temperature if an electronic reference junction is used? Assume you're measuring 1200 C. Consider the overall uncertainty to be due to two terms: the uncertainty of the reference junction and the uncertainty of the "measured junction. Problem 1 Type I thermocouple, input range = -210 to 1200 C (based on thermocouple table on carmen: files/homework) For parts a-f: reference junction maintained at temperature T, For part g: electronic reference junction (similar to AD594 used in lab - except that the AD594 also amplifies and linearizes). reference junction uncertainty = +0.05C (95%) display resolution = 0.01C. uncertainty of "measured junction = +/- 2.2C or +/-.75% (whichever is greater) a. The standard thermocouple circuit produces an emf of 41 mV for Tm=750 C. What is Tr? b. full scale output range (based on thermocouple table type J thermocouple) c. sensitivity (just a gross estimate based on the input range and output range, K = AV/AT) d. write the differential equation for the thermocouple (based on thermal model). Write the equation for the time constant and solve for its numerical value if the diameter is 0.001 m. Assume the thermocouple is spherical. For the convective heat transfer coefficient, h, use 100 W/mK for the surrounding air. For the density, P, and heat capacity, c, use the average value of the two metals: constantan and iron. e. Solve for the bandwidth: (Put the volume and surface area in terms of the radius of the thermocouple weld - assume it is spherical). f. how can you increase the bandwidth without changing thermocouple material, the heat transfer coefficient or A% (for the bandwidth calculation). g. What is the uncertainty of measuring the temperature if an electronic reference junction is used? Assume you're measuring 1200 C. Consider the overall uncertainty to be due to two terms: the uncertainty of the reference junction and the uncertainty of the "measured junction