Changing end temperatures assume that the ends of the bar in Probs. 5 9 have been

Question:

Changing end temperatures assume that the ends of the bar in Probs. 5 – 9 have been kept at 100oC for a long time. Then at some instant, call it t = 0, the temperature at x = L is suddenly changed to 0oC and kept at 0oC, whereas the temperature at x = 0 is kept at 100oC. Find the temperature in the middle of the bar at t = 1, 2, 3, 10, 50 sex. First guess then calculate.