An insulated container is filled with ice at `0^(@)C,` and another container is filled with water that is continuously boiling at `100^(@)C.` In series of experiments, the container connected by various, thick metal rods that pass through the walls of container as shown in the figure-4.46.
In the experiment- I: A copper rod is used and all ice melts is 20 minutes.
In the experiment - II: A steel rod of identical dimensions is used and all melts in 80 minutes.
In the experiment-III: Both the are used in parallel all ice melts in `t_(10)` minutes.
In the cxperiment-IV: Both rods are used in parallel all ice melts in `t_(20)`

Options

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 16 minutes
D. The value of `t_(20)` is 8 minutes

Answer

A, C

Explanation

`p_(1)=(K_(1)A(100-0))/(L)`
As `Q=P_(1)t_(1)`
`implies P_(2)=(K_(2)A(100-0))/(L)`
As `Q=P_(2)t_(2)`
`implies P_(3)=(P_(1)P_(2))/(P_(1+P_(2)))=((Q)/(t_(1))xx(Q)/(t_(2)))/((Q)/(t_(1))+(Q)/(t_(2)))=(Q)/(t_(1)+(t_(2)))`
and `Q=P_(3)(t_(1)+t_(2))`
`implies t_(10)=t_(1)+t_(2)=100min`
`implies P_(2)=P_(1)+P_(2)=(Q)/(t_(1))+(Q)/(t_(2))=(Q(t_(1)+t_(2)))/(t_(1)t_(2))`
`implies Q=P_(4)((t_(1)t_(2))/(t_(1)+t_(2)))`
`implies t_(20)=(t_(1)t_(2))/(t_(1)+t_(2))=(20xx80)/(100)=16 min`