# Calorimetry (Heat Transfer) Revision Notes

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13.4Calorimetry (Heat Transfer)

In these revision notes for Calorimetry (Heat Transfer), we cover the following key points:

• How does the process of heat transfer occur?
• What does the general law of calorimetry say?
• Which are the four methods of heat transfer?
• What is a calorimeter used for?
• How can we calculate the rate of heat transfer in each of the four methods of heat transfer?

## Calorimetry (Heat Transfer) Revision Notes

The general law of calorimetry (heat exchange) states that:

During a heat exchange process between two objects of a thermodynamic system, the heat released by the hottest object is entirely gained by the coldest object if the system is isolated from the surroundings.

Mathematically, we can write

Qreleased by the hot object=Qgained by the cold object

or

m1 × c1 × (t1-tf ) = m2 × c2 × (tf-t2 )

where m1 is the mass of the hottest object, c1 is its specific heat capacity, t1 is the initial temperature of the hottest object, m2 is the mass of the coldest object, c2 is its specific heat capacity, t2 is the initial temperature of the coldest object and tf is the final (common) temperature after the heat exchange process is done.

A calorimeter is an insulated container used to measure the specific heat capacity of an unknown solid by means of heat exchange approach. The only difference with the case in which two liquids are mixed lies in the fact that the materials in a calorimeter do not mix to obtain a homogenous mixture but they remain two distinct materials even after the thermal equilibrium is established (when both materials reach the same temperature). The rest is the same.

Heat is transferred from one place to another through four basic methods:

### a) Conduction

By definition, conduction is the method of heat transfer through the collision of particles.

In simpler words, conduction is the heat flow between objects through direct contact.

Not all object conduct the heat equally. Some materials conduct heat better than the others. As explained earlier, such materials as known as good conductors of heat. For example, most metals are good conductors of heat.

On the other hand, some materials conduct very poorly the heat. They are known as bad (poor) conductors of heat. Wood, glass, cork, plastics, air, vacuum etc., are all bad conductors of heat.

There is a mathematical equation, which allows us to calculate the rate of heat flow through a solid. Thus, the heat rate (heat per unit time) flowing through a solid object of surface A and thickness d during which the temperature changes from T1 to T2 is

Q/t = K × A × (T2 - T1)/d

where K is a quantity known as the coefficient of thermal conduction, measured in [W/m × K]. It depends on the characteristics of material.

### b) Convection

By definition, convection is the method of heat transfer through the circulation of fluid itself.

This process involves both heat and matter transfer. Obviously, matter must be present during convection.

There are two types of convection: natural and forced convection. Coastal breeze is an example of natural convection, while electric fan is an example of forced convection.

We can find the rate of heat flow through convection using the equation

Q/t = k × A × (T2 - T1 )

where k is the coefficient of thermal convection measured in [W/m2K] and A is the area involved.

Radiation is the third method of heat transfer. By definition, radiation is the method of heat transfer by means of electromagnetic waves.

Most radiation comes to Earth from the Sun. Radiation does not involve any matter transfer; it only transfers energy. Also, matter presence is not necessary in this process, as most radiation travels through vacuum.

When radiation falls on an object, it is partly reflected, partly transmitted and partly absorbed. The absorbed heat causes the molecules of the object to vibrate more than before, so it becomes hot.

Some objects emit radiation more than the others; they are known as black bodies.

The radiation energy per unit time from a black body is proportional to the fourth power of the absolute temperature and can be expressed with Stefan-Boltzmann Law as

Q/t = σ × T4 × A

where σ is a quantity known as Stefan-Boltzmann constant. It has a value of 5.6703 × 10-8 W/m2K4. T is the absolute temperature of the black body in Kelvin degree and A is the area of the emitting body.

For objects other than ideal black bodies ("gray bodies") the Stefan-Boltzmann Law can be expressed as

Q/t = ε × σ × T4 × A

where ε is a dimensionless quantity between 0 and 1 (one for black bodies) called emissivity coefficient of the object.

When a hot object of temperature TH radiates heat energy to its cool surroundings of temperature TC, the rate of net radiation heat loss can be expressed as

Q/t = ε × σ × (TH4-TC4 ) × AH

where AH is the area of the hot emitting body.

### d) Evaporation

Evaporation is not a proper method of heat transfer but sometimes it is regarded as the fourth method of heat transfer. By definition, evaporation is a method of heat transfer through heat removal from a hot body by means of change in state of a covering liquid.

This is because the most energetic particles of liquid (for example sweat) get some heat energy from the object they cover (for example our body) to make themselves pass in gaseous state and as a result, they leave the body surface.

Refrigerators and air conditioners use liquids with low boiling points to produce cooling effect through evaporation.

The rate of heat flow through evaporation by a human body is calculated through the equation

Q/t = h × A × (ps-p0)

where h is the coefficient of heat transfer through evaporation, A is the area of the human body, ps is the pressure of water vapour near the skin and p0 is the pressure of water vapour in the environment air. The pressure of the water vapour near the surface of the skin depends on the humidity of the environment and the degree of sweating.

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