Power and Temperature Question?

Question

A toaster using a Nichrome heating element operates on 120V. When it is switched on at 20.0 Celsius, the heating element carries an initial current of 1.35A. A few seconds later the current reaches the steady value of 1.23A.

a) What is the final temperature of the element? The average value of the temperature coefficient of resistivity for Nichrome over the temperature range is 4.5*10^-4 (1/Celsius).

b) What is the power dissipated in the heating element initially?

c) What is the power dissipated in the heating element when the current reaches a steady value?

Appreciate the help :)

Answer 1

A. Rf/Ri = Ii/If = (1+4.5E-4)^ΔT
log(li/lf) = log(1+4.5E-4) * ΔT
ΔT = log(1.35/1.23)/log(1.00045) = 206.9 C
Final T = 20 + 206.9.
The problem writers might be expecting a "linear" answer. This assumes that Rf/Ri-1 = ΔT*4.5E-4. In that case,
ΔT = (Ii/If-1)/4.5E4 = (1.35/1.23-1)/4.5E-4 = 216.8 C and
Final T = 20 + 216.8
B., C. I'm guessing you can do these.