A1 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

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

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