Question

One end of an insulated metal rod is maintained at 100 ∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. The rod has a length of 75.0 cm and a cross-sectional area of 1.05 cm2 . The heat conducted by the rod melts a mass of 8.35 g of ice in a time of 15.0 min .

Answer 1

the power transmitted is P = dQ/dt = (m*Lf)/dt

m is the mass of the ice = 8.35 g

Lf is the latent heat of meting of ice into water = 334 j/g

dt= 15*60 = 900 s

then P= dQ/dt = (8.35*334)/(900) = 3.09 J/s

power per unit area is P/A = 3.09 /(1.05*10^-4) = 29428.57 W/m^2

and also temparature gradient is dT/dx = 100/0.75 = 133.34 K/m

then thermal conductivity K = (P/A)/(dT/dx) = 29428.57/133.3 = 220.8 W/(m*K)