Question

A small metal bar, whose initial temperature was 30°C, is dropped into a large container of boiling water. Its temperature was 33° after 1 second. How long will it take the bar to reach 90°C?

Answer 1

giren that Page - 1) Given initial tompornlue - 30 we know that <(t) = C(l) + [co) - < (c] cY - find T= ? en c(t) is general solution of the single time constant system. givenc (0) = 3 R ((d) = 1000 (d) = Daopped in to a large boeting water. to 1 sec, c(t) = 33°C 33 = 100+30–100) etyt → 33 = 100+(-70] e 'lt → 33 = 100- 70.e.' → -67 = -702-17 ett - 0.9571 - + --log(0.9571) H+ = +0.04 384) = = 0,04384 T = 22.81021989€ T. 22.81 sec.

Now (Page 2 -7 when C(+) = qoc 90 = 100- 70 e 22.81 + 10 =+ 70 e +/22.81 eta.81 -0.142 tt 28.91 =71.951 (t = 44.50) sec