Plotting a cooling curve

Have you ever observed what happens when a hot cup of milk is left on the table? After some time, it cools down and reaches room temperature or the temperature of its external surroundings. This happens due to the heat exchange between the surroundings and the cup of milk. If we plot a graph of temperature and time, it is observed that at starting, the cooling is fast and then gradually starts decreasing as the temperature of systems. 

A hot body loses its heat by emitting radiation to its surroundings. This loss rate depends upon the difference in temperature between the surroundings and the body. Sir Issac Newton was the first to give a formula for calculating material temperature after it loses heat. The cooling curve of a substance is obtained when a graph is drawn against the change of temperature and the time when the substance is allowed to cool.

Cooling curve

The cooling curve of the mixture is used in the preparation of alloys in exact proportions as cooling can be constructed for pure metals. The temperature at which they form a molten state and then solidify can be clearly noted by these curves obtained by the change in phase.

As we know, all pure metals have a definite melting point and freezing point. Therefore, the graph obtained for the pure metals is a horizontal straight line.

When the mixture of metals is added, there are no sharp points. There is always a range of temperature that is noted when they are cooled or heated. 

The cooling curve for the solidification of eutectic alloy (mixed molten state) shows two stages of solidification. As this alloy exhibits a definite melting and freezing point, these temperatures are called eutectic temperatures.

Study material notes on plotting a cooling curve?

Heat: It is a form of energy that is transferred between objects or systems that varies the temperature of the system or the object. The flow of heat energy is always from higher temperature to lower temperature.

Heat capacity: It is the amount of heat required to change the temperature of 1 mole of a substance by 1℃.

Specific heat capacity: It is the amount of heat required to change the temperature of 1 gram of a substance by 1℃. 

The formula of specific heat capacity: Q = mC ∆t

Here, Q = quantity of heat absorbed by a body

m = mass of the body

∆t = Rise in temperature

C = Specific heat capacity of a substance 

Its SI unit is J kg-1 K-1.

The slope formed in the cooling curve depends on heat capacity, change in temperature, and the thermal conductivity of the substance. When more heat is required to change the temperature of the substance, it cools slower, and the gradient of the curve decreases. When the substance has a higher thermal conductivity, the faster the heat is transferred, so the substance cools faster. Liquids have the highest heat capacity among all the phases.

Interpretation of the cooling curve 

The temperature difference between the surroundings and the object decreases as the object cools; therefore, the lines are curved. Because the temperature differential between the surroundings and the object decreases as the object cools, the lines are curved. This slows down the pace at which heat is transmitted out of the substance, slowing down the cooling process.

For most pure substances, phase transitions occur at particular temperatures. The temperature remains constant during the phase transition because the energy produced by new bonds in the substance neutralises the cooling.

Phase transitions appear as horizontal lines as a result of this. Phase transitions of mixtures occur over a wide temperature range; therefore, instead of a flat segment, the cooling curves of mixtures undergo a gradient change during a phase transition.

Newton’s law of cooling

According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the excess in the temperature of the body and its surroundings.

Rate of cooling ∝ ΔT 

or

it can be written as 

– dTdt = k( T – Ts)   ( We put a negative sign here because the temperature of the body is decreasing in this case, where we have considered the temperature of the surroundings to be lower than that of the body)

Where,

T is the temperature of the body at time t and

Ts is the temperature of the surrounding,

k is the constant that depends truly on the area and nature of the surface of the system under examination.

The greater the difference in temperature between the system and surroundings, the more the heat transfer will be there. Newton’s law of cooling formula can be expressed as:

T(t)  = Ts + ( To – Ts ) e-kt 

where

T (t) is the temperature of the body at time t 

Ts is the temperature of the surroundings

k is constant

To is the temperature of the body initially

t is the time

Conclusion:

To plot the cooling curve, first, we had to understand the concept of heat energy, specific heat capacity, and how the thermal conductivity takes place between objects and the surrounding. The next step was to understand Newton’s law of cooling, which gave a specific equation to understand how the increase or decrease in temperature modifies the graph.

Later in this article, we understood how to set up Newton’s cooling apparatus and how to carry out the experiment. The result obtained from the experiment is then plotted as a graph.

Interpretation of the graph is important to understand the whole concept of the cooling curve. The cooling curve of pure substances and mixtures play an important role in metallurgy, as in separating the metals from ores and minerals and also for making alloys.