Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are pla

Question

Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end as shown in the figure. Their thermal conductivities are kA = 339 J/(s m K) and kB = 837 J/(s m K). The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K

Two bars, A and B. each of length 2-0 m and cross sectional area 1.0 m^2, are placed end to end as shown in the figure Their thermal conductivities are kA = 339 J/(s .m. K) and kB = 837 J/(s .m. K). The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. Which one of the following statements is true concerning the above situation? A. For a given time t. the amount of heat transferred through bar A is the same as that through B. B. For a given time 4 the amount of heat transferred through bar A is smaller than that through B. C. For a given time the amount of heat transferred through bar A is less than that through B D. The time for a quantity of heat Q to pass through bar A is less than that for B. E. Time is not a factor in determining the quantity of heat conducted through these bars.

Explanation / Answer

Rate of heat transfer through a bar of length l and area of cross section A ; When the temperature difference between its ends is T = kTA/l

As in this case both rods have same A and L; The rate of heat flow (Q/t) depends on kT

But heat cannot accumulate at any point. Hence the rate at which heat enters the junction of the two bars must be same as the rate at which heat leaves the junction.
The junction attains such a tempreture which keeps the heat flow same in both the bars.

Hence the 1st option will be true.
For a given time t, amount of heat transfered through A will be same as B

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