One end of a copper rod of uniform cross-section and of length 1 . 5 m is kept in contact with ice at 0 ° C and the other end with water at 100 ° C . If the whole system is insulated from its surroundings, then at what distance from the end of the rod which is in contact with the steam, the temperature should be maintained at 200 ° C , so that in steady-state the rate of melting of ice be equal to the rate of product

Step-by-step solution

If the point is at a distance x from water at 100 o C, heat conducted to ice in time t, Q ice = KA 200 - 0 1.5 - x × t So ice melted by this heat m ice = Q ice L F = KA 80 200 - 0 1.5 - x × t Similarly heat conducted by the rod to the water at 100 o C in time t, Q water = KA 200 - 100 x t So steam formed by this heat m steam = Q water L V = KA 200 - 100 540 × x t According to given problem m ice = m steam , i.e., 200 80 1.5 - x = 100 540 × x or x = 6 58 m = 10.34 cm i.e., 200 o C temperature must be maintained at a