An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figure

In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.

In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.

In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.

In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.

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  • A

    The value of $t_{10}$ is $100$ minutes

  • B

    The value of $t_{10}$ is $50$ minutes

  • C

    The value of $t_{20}$ is $32$ minutes

  • D

    The value of $t_{20}$ is $8$ minutes

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