Question
Find the thermo-emf developed in a copper-silver thermocouple when the junctions are kept at $0^\circ$C and $40^\circ$C. Use the data in table.
 
Metal with
a
b
lead (Pb)
$\mu\text{V}/^\circ\text{C}$
$\mu\text{V}/^\circ(\text{C})^2$
Aluminium
-0.47
0.003
Bismuth
-43.7
-0·47
Copper
2.76
0·012
Gold
2.90
0.0093
Iron
16.6
-0.030
Nickel
19.1
-0.030
Platinum
-1.79
-0.035
Silver
2.50
0.012
Steel
10.8
-0.016
 

Answer

$\text{E}=\text{a}_{\text{AB}}\theta+\text{b}_{\text{AB}}\theta^2$
$\text{a}_{\text{CuAg}}=\text{a}_{\text{CuPb}}-\text{b}_{\text{AgPb}}$
$=2.76-2.5=0.26\mu\text{v}/^\circ\text{C}$
$\text{b}_{\text{CuAg}}=\text{b}_{\text{CuPb}}-\text{b}_{\text{AgPb}}$
$=0.012-0.012\mu\text{vc}=0$
$\text{E}=\text{a}_{\text{AB}}\theta=(0.26\times40)\mu\text{V}$
$=1.04\times10^{-5}\text{V}$

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