A cup of tea cools from `65.5^@`C to `62.55^@C` in one minute is a room at `225 .^@C.` How long will the same cup of tea take to cool from `46.5^@C` to `40.5^@C` in the same room ? (Choose the nearest value in min).

Options

A. 1
B. 2
C. 3
D. 4

Answer

D

Explanation

According to Newton.s law of cooling `(T_(1) - T_(2))/(t) = K [(T_(1) +T_(2))/(2) - T_(S)]`
For the first case `(65.5 - 62.5)/(1) = K [(65.5 + 62.5)/(2) - 22.5]`
or `3= K (64-22.5) = K(41.5)` …(i)
For the second case, `(46.5 - 40.5)/(t) = K [(46.5 + 40.5)/(2) -22.5]`
or `(6)/(t) = K (43.5-22.5) = K(21)` ...(ii)
Divide (i) by (ii), we get
`(t)/(2) = (41.5)/(21) ~~ 2 or t =4` min