The ends a and b of a rod l'' cm long have their temperature kept at c ο 30 and c ο 80 , until steady state conditions prevail. the temperature of the end b is suddenly reduced to c ο 60 and that of a is increased to c ο 40 . find the temperature distribution in the rod after time t. also show that the temperature at the midpoint of the rod remains unaltered for all time, regardless of the material of the rod.
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