Question

A vessel full of hot water is kept in a room and it cools from $80$${}^o$C to $75$${}^o$C in $T_1$ minutes, from $75$${}^o$C to $70$${}^o$C in $T_2$ minutes and from $70$${}^o$C to $65$${}^o$C in$T_3$ minutes. Then :

• A. $T_1=T_2=T_3$
• B. $T_1>T_2>T_3$
• C. $T_1<T_2=T_3$
• D. $T_1<T_2<T_3$

Answer 1

Answer: (D)

$T_1<T_2<T_3$

According to Newton's cooling law, rate of cooling is directly proportional to the temperature difference between body and surrounding. Also more is the rate of cooling, faster it cools i.e. takes lesser time. Here although all three steps of cooling have equal temperature differences[5${}^{0}C$], still the absolute temperature difference with surrounding goes on decreasing, which decreases the rate of cooling and increases time of cooling.