A cup of tea cools from ( 65.5^ C ) to ( 62.5^ C ) in one minute in a room at ( 22.5^ C ). How long will it take to cool from ( 46.5^ C ) to ( 40.5^ c ) in the same room?

Step-by-step solution

Given, cup of tea cools from 65.5^ C to 62.5^ C in 1 minute. Room temperature =22.5^ C We know that d T d t =k ( - ₀ ) (1) For 1st case : d T d t = 65.5-62.5 1 ~min = 3^ C 1 Also, - ₀= ( 65.5+62.5 2 )-22.5=64-22.5 - ₀=41.5^ C Now, substituting in Eq. (1), we get 3=k(41.5) k= 3 41.5 (2) For 2 nd case : d T d t = 46.5-40.5 t = 6^ C t Also, - ₀= ( 46.5+40.5 2 )-22.5=43.5-22.5 - ₀=21^ C Again, substituting in Eq. (1), we get 6 t =k 21 Substitute value of k from Eq. (2), we get 6 t = 3 41.5 21 t= 6 41.5 3 21 =3.9523