## Monday, June 10, 2019

### Unizor - Physics4Teens - Energy - Heat - Heat & Temperature

Notes to a video lecture on http://www.unizor.com

Heat and Temperature

Specific Heat Capacity

Let's discuss the relationship between heat and temperature.
From the unscientific standpoint these two concepts are almost identical. Heating an object results in increase of its temperature. Increasing a temperature of an object constitutes its heating.
Yet, from the strictly scientific viewpoint these two concepts are different.

Heat is energy of some specific type, that can be transferred from one object to another, while temperature is an average kinetic energy of molecules of an object.
The same amount of heat, transferred into different objects, will result in different growth of their temperatures, depending on many factors, like mass, chemical composition, state etc. of these objects. Analogy of this is that same amount of fuel in different cars results in achieving very different speeds and, therefore, different kinetic energies in different cars, even if the gas pedal is pushed all the way down for all cars. It's just because cars are different and their internal structure converts fuel into movement differently.

It has been experimentally observed that to increase a temperature of an isolated object of a unit mass by a unit of temperature is independent (within reasonable level of precision) of the initial temperature of an object, but depends only on the type of object's material, composition, state etc. In other words, amount of heat needed to increase a temperature of 1 kg of water from 20°C to 21°C is the same as from 50°C to 51°C. If, instead of water, we take copper, the amount of heat, needed to increase its temperature from 20°C to 21°C, will be the same as to increase it from 50°C to 51°C, but different than that for water.

The above experimental fact allowed to establish a concept of specific heat capacity for each material as an amount of heat required to increase the temperature of a unit of mass of this material (1 kg in SI) by a unit of temperature (1°C or 1°K in SI).

Thus, specific heat capacity of water is, as we know, one kilocalorie per kilogram per degree - 1 kcal/(kg·°K), that is about 4184 joules per kilogram per degree - 4183 J/(kg·°K).
For copper the specific heat capacity is 385 J/(kg·°K).
Gold has the specific heat capacity of 129 J/(kg·°K).
Uranium's specific heat capacity is 116 J/(kg·°K).
Cotton's specific heat capacity is 1400 J/(kg·°K).
Hydrogen's specific heat capacity is 14304 J/(kg·°K).
Generally speaking, but not always, more dense, more solid materials have less specific heat capacity than less dense or liquids, which have, in turn, less specific heat capacity than gases.

Knowing specific heat capacityC of material of an object and its mass m, we can easily determine amount of energy ΔQneeded to heat it up by ΔTdegrees:
ΔQ = C·m·ΔT
Inversely, knowing the amount of heat supplied, we can determine an increase in temperature:
ΔT = ΔQ/(C·m)
Notice, that increment of temperature ΔT and increment of heat energy ΔQ can be both positive or both negative, which means that an object, that has increased its temperature, has increased (gained, consumed) energy, and the object that decreased its temperature, has decreased (lost, released) energy.

Change of State

Consider specific heat capacity of ice and water:
Ice: 2090 J/(kg·°K)
Water: 4183 J/(kg·°K)
Both these substances exist at temperature about 0°C=273°K. That means that we can heat 1 kg of ice up to 0°C spending 2090 joules per each degree of temperature, but to increase the temperaature of the water around 0°C we have to spend 4183 joules per each degree. But, while ice is melting into water, which takes some time, both states, solid and liquid, exist side by side and the temperature of the water will not rise while the ice is not completely melted, we have to spend heat energy just on melting without actually changing the temperature of a substance, that remains around 0°C during the melting process.

This experimental observation leads us to believe that, while graduate change of temperature for any specific state of matter linearly depends on the amount of heat supplied, change of state (like melting or freezing, or evaporating etc.) brings an element of non-linearity to this dependency.
More precisely, the temperature, as a function of amount of heat supply, in case of an object going through transformation of state from solid to liquid, looks like this (for better view, right click on the picture and open it in another tab of a browser):

As seen on this graph, supplying heat to ice will increase its temperature proportionally to amount of heat supplied.
Then, when the temperature reaches 0°C, ice will start melting and new heat will not change the temperature of ice/water mix, but will be used to change the state of matter from solid (ice) to liquid (water).

This process of melting consumes heat without increasing the temperature until all ice is melted. Such a transformation of state that requires supply of heat energy is called endothermic.
Then, when the process of melting is complete, and all ice is transformed into water, the temperature of water will start increasing, as the new heat is supplied, but with a different coefficient of linearity relatively to the heat than in case of ice, since water's specific heat capacity is different than that of ice.
The graph above is characteristic to any heating process, where the transformation of the state of matter is involved. It is relatively the same for transforming liquid to gas (evaporation) or solid to gas (sublimation).

In case of a reversed transformation from liquid to solid (freezing) or gas to liquid (condensation) or gas to solid (deposition) the heat energy must be taken away from a substance. It is the same amount in absolute value as was needed to supply to solid to melt it into liquid or to liquid to vaporise it into gas, or to solid to vaporize it into gas. So, in case of freezing, condensation or deposition we deal with the process of decreasing heat energy of a substance. Such a process is called exothermic.

Amount of heat energy needed to transform a substance from one state to another is also experimentally determined and, obviously, depends on a substance, its mass and a kind of transformation it undergoes.
For example, melting of 1 kg of ice requires 333,000 joules of heat energy to be supplied. The same amount of heat energy should be extracted from the water at 0°C to freeze it into ice.