Question

One end of an insulated metal rod is maintained at 100ºC, and the other end is maintained at 0ºC by an ice-water mixture. The rod is 60.0 cm long and has a cross-section area of 1.25 cm2. The heat conducted by the rod melts 8.50 g of ice in 10.0 minutes. Find the thermal conductivity of the metal rod.

Answer 1

Given: T₁ = 100c ; T₂ = 0c ; L = 60 cm ; A = 1.25 cm² ; m= 8.50g ; t=10 min.

Goal: thermal conductivity (K)

Solution:

we know that thermal conductivity is the ratio of energy flux to the temperature gradient.

The pwer transmittewd can be given as :

P = E/t = [latent heat of melting water](m/t)

= [334 J/g](8.50 g)/(10*60 s)

= 4.73 J/s

Energy flux can be given as :

E = P/ A = (4.73 J/s)/(1.25 *10^-4 m²)

= 37853.33 J/sm²

Temperature gradient can be computed as:

T/L = ( 100 k)/0.60 m = 166.67 K/m

Thermal conductivity :

K = E/ (T/L) = (37853.33)/(166.67) = 227.12 W/mK