Question 19.1: A 0.0100 m diameter copper bus bar is maintained at a consta...
A 0.0100 \text{m} diameter copper bus bar is maintained at a constant temperature of 20.0°\text{C} and is subjected to a voltage gradient of 1.00 \text{V/m}. Determine the Peltier heat flow, \dot{Q}_P. The Seebeck coefficient for the copper is α_\text{cu} = 3.50 × 10^{−6} \text{V/K}, and its resistivity is ρ_e = 5.00 × 10^{−9} ohm meters.
The Peltier heat flow is given by Eq. (19.33) as
π = \frac{\dot{Q}_P}{I} = αT (19.33)
\dot{Q}_P = πI = (αT)I
where
I = AJ_E = \frac{A}{ρ_e} (- \frac{dϕ}{dx})
Here, −dϕ/dx = \text{voltage gradient} = 1.00 \text{V/m}, so
I = \frac{(π/4) (0.0100 \text{m})^2 (1.00 \text{V/m})}{5.00 × 10^{−9} \text{Ω gm}} = 1.57 × 10^4 \text{V/Ω} = 1.57 × 10^4 \text{A}
Then
\dot{Q}_P = (3.50 × 10^{−6} \text{V/K}) (20,0 + 273.16 \text{K}) (1.57 × 10^4 \text{A}) = 16.2 \text{V.A} = 16.2 \text{W}