A body is heated to a temperature 40 ° C and kept in a chamber maintained at 20 ° C . If the temperature of the body decreases to 36 ° C in 2 minutes, then the time after which the temperature will further decrease by 4 ° C, is

Question

A body is heated to a temperature 40 ° C and kept in a chamber maintained at 20 ° C . If the temperature of the body decreases to 36 ° C in 2 minutes, then the time after which the temperature will further decrease by 4 ° C, is, 2 minutes, 2 minutes 33 seconds, 2 minutes 55 seconds, 3 minutes

MARKS App · Accepted Answer

Rate of cooling, dθ dt = - k θ - θ 0 From 40 ° C to 36 ° C , θ 1 = 40 + 36 2 = 38 ° C dθ dt 1 = 4 2 = 2 ° C min - 1 From 36 ° C to 32 ° C , θ 2 = 36 + 32 2 = 34 ° C dθ dt 2 = 4 t d θ d t 1 d θ d t 2 = k θ 1 – θ 0 k θ 2 – θ 0 ⇒ 4 2 4 t = 38 - 20 34 - 20 ⇒ t = 2 min 33 s

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