10 points to who can answer this Conductivity Physics Question?

Question

A cylinder with a piston is filled with ideal gas. The gas temperature is held at 350 K. The cylinder is heated by an oven through a square metal rod connected between the oven and the cylinder. The rod has sides d = 2 cm and length L = 1.8 m.

a) If the oven is held at 600 K, and the heat current conducted through the metal rod is 28 W, find the thermal conductivity (k) of the metal in the rod ( ans in W/m K )

(b) For a larger cylinder at 350 K, a heat current of 50 W is needed. If we use the same metal rod to conduct heat, find the oven temperature in Kelvin that will maintain the necessary heat current.

THANKS.... part A is correct....

but I still need help on B... it's is not going thru as correct.... :-\

i was instructed to use the same equation used for part a... for b.... but i cant come up with the right answer.. 600 isn't quite right

Answer 1

(a) Let the thermal conductivity of the metal in the rod be k (W/m•K).
28W = k*(0.02m)^2*(600K - 350K)/1.8m...(1)
k = 504
(b) Let the required oven temperature be T (K).
50W = k*(0.02m)^2*(T K - 350K)/1.8m....(2)
(2)/(1) we get:
50/28 = (T-350)/250
T = 350+250*50/28 = 796 (K).