A pan filled with hot food cools from ( 94^ C ) to ( 86^ C ) in ( 2 ) minutes. When the room temperature'is ( 20^ C ). How long will it cool from ( 74^ C ) to ( 66 ^ C ) ?

Step-by-step solution

Given, food cools from ( 94^ C ) to ( 86^ C ) in ( 2 ) minutes; room temperature ( =20^ C ) Now, ( d T d t =k ( - ₀ ) ) For ( 1 ) st case, ( d T d t = 94-86 2 = 8 2 =4^ ) and ( ( - ₀ )= (94+86) 2 -20^ =70^ ) ( 4=k ) to ( k= 4 70 ) For ( 2 ) nd case, ( d T d t = 74-66 t = 8 t ) and ( - ₀= (74+66) 2 -20=50^ ) ( 8 t = 4 70 50 ) ( t= 8 70 4 50 =2.8 ) Thus, food cools from ( 74^ C ) to ( 66^ C ) in ( 2.8 ) minutes