The temperatures of a liquid drops from 365 K to 361 K in 2 min. The time during which the temperature of the liquid drops falls from 344 K to 342. K, when room temperature is at 293 K iş

Options

A. 84 s
B. 72 s
C. 66 s
D. 60 s

Answer

A

Explanation

By Newton.s law of cooling
`ms (( theta_(2) - theta_(1)))/(t) = K ((theta_(2) + theta_(1))/(2) - theta_(0))`
`ms ((365 -361 ))/(2) = K ((365 +361)/(2)-293)`
`implies ms xx (4)/(2) = K xx 70`
`implies 2ms = 70 K`
Again `ms ((344 -342))/(t)= K ((344+342)/(2)-293)`
`implies ms xx (2)/(t) = K (50)`
`implies (2ms)/(t) = 50 K`
From Eqs (i) and (ii) 70 , `(K)/(t) = 50 `K
`implies t = (7)/(5) ` min
`t = (7)/(5) xx 60 s = 84 s `