Answer:
steady state temperature =88.7deg C
t=time within 1 deg C of it steady state is 8.31s
Explanation:
A 1 m long wire of diameter 1mm is submerged in an oil bath of temperature 25-degC. The wire has an electrical resistance per unit length of 0.01 Ω/m. If a current of 100 A flows through the wire and the convection coefficient is 500W/m2K, what is the steady state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature within 1-degC of the steady state value? The density of the wire is 8,000kg/m3, its heat capacity is 500 J/kgK and its thermal condu
The diameter of the wire is known to be=1mm
properties=
The density of the wire is 8,000 kg/m3,
heat capacity is 500 J/kgK
themal conductivity is 20W/m.K
electrical resistance per unit length of 0.01 Ω/m
from lump capavity method
500*(2.5*10^-4)/20
0.006<0.1
we know also, to find steady state temperature
Dh(T-Tinf)=
make T the subject of the equation , we have
T=25+
T=88.7 degC
rate of chnage in temperature
dT/dt=
at t=o and integrating both sides
we have
t=8.31s
steady state temperature =88.7deg C
t=time within 1 degC of it steady stae is 8.31s
is the Coulomb's constant. If we substitute the numbers, we find (we can ignore the negative sign of the electron charge, since we are interested only in the magnitude of the force)