copper resistance thermometer - temperature

scholio

1. The problem statement, all variables and given/known data

a piece of copper wire (rho_20 = 1.7*10^-8 ohm-m) is being used as a resistance thermometer.At 20 degrees celsius, the wire is known to have a resistance of 170 ohms. when the wire is immersed in a hot oil bath, its resistance increases to 173.4 ohms. if the temperature coefficient of resistivity is 10^-3, what is the temperature of the oil?

assume that expansion of the copper negligible

2. Relevant equations

current density J = nqv_d where n is electron density, q is charge, v_d is drift velocity

J = sigma*E where sigma is conductivity, E is electric field

J = E/rho where rho is resistivity

3. The attempt at a solution

i really don't know where to start, is the 'temperature coefficient of resistivity' the same as rho?

what equation do i use that relates temperature to resistance/rho? does it have anything to do with work, as work and heat have the same unit, joules?

help appreciated..

rl.bhat

is the 'temperature coefficient of resistivity' the same as rho?
No. Go through any text book or Hyper Physics site. You will get the relation between the resistance of the conductor and change in temperature of the conductor.
All your relevant equations are irrelevant!!

scholio

okay found the equation:

R = R_reference [1 + alpha(T - T_reference)]
173.4 = 170( 1 + 10^-3(T - 20)]
(173.4/170) - 1 + 0.02 = 10^-3T
0.04/(10^-3) = T
T = 40 degrees celsius

http://www.allaboutcircuits.com/vol_1/chpt_12/6.html

Redbelly98

Looks good.

FYI on units, the temperature coefficient of resistivity is 10^-3 per degree C,
or 10^-3 / C.