Question

1) A cylindrical copper rod of length 2 m and cross-sectional area of 5 cm^2 is insulated to prevent heat loss through its surface. The ends are maintained at a temperature difference of 100 C by having one end in a water-ice mixture and the other in a boiling water/steam mixture. If you initially have 10 g of ice on the one end and lots of steam on the other, how long does it take to melt the ice?

2) How long would it take to melt the ice in the previous problem if the rod were 0.8 m of Cu and 0.8 m of iron?

Answer 1

Given is:-

Lenght of the copper rod L=2m

Cross sectional area A = 5cm^2 or

Temperature difference  

K_copper = 401 W/m-K

Now the rate at which the energy is conducted along the rod is

by plugging all the values in above equation, we get

Therefore the rate at which the ice melts at the cold end is

L_f for copper is  

by plugging all the values we get

Thus the time taken for 10g ice to melt is

Therefore the 10grams ice will take approx 333 seconds to melt due to heat conduction.

Part-b

For 0.8 m long copper rod

and

Thus time taken is

Thus time taken to melt 10gm ice by 0.8 m copper rod is approximately 133 seconds