Question

A bucket full of hot water cools from ${75^o}C$to ${70^o}C$ in time ${T_1}$ from ${70^o}C$to ${65^o}C$in time ${T_2}$and from ${65^o}C$to ${60^o}C$in time${T_3}$, 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

In order to answer this question, we need to have knowledge about thermal properties of matter. Thermal properties of matter tells us about how an object reacts when it is subjected to heat. Thus, from the properties of matter we also come to know how cooling of a body depends.

Complete Step-By-Step Solution:
Thermal properties of matter deals with the temperature of the matter. Now, we know matter is defined as anything that has mass and occupies a space. Temperature is one of the physical properties that is related to matter.
Thermal properties of a substance are defined by parameters such as thermal resistance, thermal conductance, Thermal conductivity and Thermal transmittance.
Thermal resistance determines the heat insulation property of a material. With increase in value thermal resistance, the amount of heat loss decreases.
Thermal conductance on the other hand determines the ability of the body to transfer heat.
Thermal conductivity is defined as the ability of the material to conduct heat.
Thermal transmittance is defined as the rate at which heat is transferred from one substance to another.
All these quantities implies that the hotter the body, the lesser time it takes to cool time. Among the temperatures given the maximum temperature is${75^o}C$, and it cools to ${70^o}C$. Thus it takes the least time.
Therefore, the order in which it cools is given as ${T_1} < {T_2} < {T_3}$

Thus, option (C) is correct.

Note:
The basic property of matter states that if the temperature of a body increases, volume of it decreases. This is referred to as thermal expansion.