(Solved): The leads from a J-type thermocouple bead are inserted into a connector block as shown below. The ...

The leads from a J-type thermocouple bead are inserted into a connector block as shown below. The connector block temperature \( T_{\text {block }} \) is measured using a platinum RTD \( (\alpha=0.003927 \) \( { }^{\circ} \mathrm{C}^{-1} \) ) where \( R=1.18 \Omega \) (at \( \mathrm{T}_{\text {block }} \) ) and \( R_{\circ}=1.15 \Omega \) at \( T_{\circ}=25^{\circ} \mathrm{C} \). The open circuit voltage difference, \( \mathrm{V}_{a}-\mathrm{V}_{\mathrm{b}} \), is measured to be \( -1.52 \mathrm{mV} \). Calculate the thermocouple bead temperature \( T_{c} \). The copper wires are at \( T_{\text {block }} \) everywhere along their lengths. In addition, metal \( A \) is iron and metal \( \mathrm{B} \) is constantan. Hint: Generate an analytical solution using integrals of Seebeck coefficients. Compare your analytical solution with what was found to apply to a simple TC circuit.