Respuesta :
Answer:
a) what is the steady-state temperature of the wire?
83.67°C
b) From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value?
8.31s
Explanation:
a) what is the steady-state temperature of the wire?
From the above question we are given the following values:
Oil bath temperature = 15°C.
Diameter of wire = 1mm
Converting to m(meter)
1 mm = 0.001m
The wire has an electrical resistance per unit length of Re′= 0.01 Ω/m. Current of I= 96 A
Convection coefficient is h= 500 W/m²·K,
Temperature in steady state formula =
Temperature + I² × Re' /π × D × h
= 25°C + 96² × 0.01/π × 0.001 × 500
= 25°C + 92.16/1.5707963268
= 25°C + 58.670878232
= 83.670878232°C
≈ 83.67°C
b)From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value?
For question b, we are given the following values
rho= 8000 kg/m3, c= 500 J/kg·K, and k= 20 W/m·K
Formula
= Exp( -4 × h/rho × c × k)
=Exp(- 4 × 500 W/m²·K)/8000 kg/m³ ×
500 J/kg·K × 20 W/m·K
= 8.31s
