The temperature of a liquid drops from 365 K to 361 K in 2 minutes . Find the time during which temperature of the liquid drops from 344 K to 342 K.Temperature of room is 293 K

Options

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

Answer

A

Explanation

From Newton's law ofcooling,
`(dT)/(dt) = -k(T-T_(0))`
`rArr``int_(365)^(361) (dT)/(T-T_(0)) = -k int_(0)^(120) dt`
`rArr``In ((361-293)/(365 - 293)) = -k (120-0)`
`k= 4.76 xx 10^(-4)`
To cool from 344 K to 342 K
`int_(344)^(342)(dT)/(T- 293) = -k int_(l_(1))^(l_(2)) dt`
`rArr``In((342 - 293)/(344 - 293)) = - (4.76 xx 10^(-4))(t_(2)-t_(1))`
`rArr``t_(2)-t_(1) = 84 s`