An insulated container is filled with a mixture of water and ice at $t_{c} = 0 ° C .$ Another container is filled with water that is continuously boiling at $t_{h} = 100 ° C .$ In a series of experiments, the containers are connected by various thick rods that pass through the walls of container. The rod is insulated in such a way that there is no heat loss to surrounding. In experiment 1, a copper rod is used, and the ice melts in $T_{1} = 20 m i n .$ In experiment 2, a steel rod of same cross-section and length is used and the same amount of ice melts in $T_{2} = 60 minutes .$ Now if both the rods are connected in series, find the time (in minutes) in which same amount of ice shall melt.

Question

An insulated container is filled with a mixture of water and ice at $t_{c} = 0 ° C .$ Another container is filled with water that is continuously boiling at $t_{h} = 100 ° C .$ In a series of experiments, the containers are connected by various thick rods that pass through the walls of container. The rod is insulated in such a way that there is no heat loss to surrounding. In experiment 1, a copper rod is used, and the ice melts in $T_{1} = 20 m i n .$ In experiment 2, a steel rod of same cross-section and length is used and the same amount of ice melts in $T_{2} = 60 minutes .$ Now if both the rods are connected in series, find the time (in minutes) in which same amount of ice shall melt.

Accepted Answer

The rate at which heat is transferred by a single rod is given by P=QT=KA(th−tc)L In series Ps= A(th−tc)L1K1+L2K2   or  1Ps=1P1+1P2 We have T1=QP1,T2=QP2  and T=QP ∴    QP=QP1+QP2=T1+T2=80 min.

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