Heat

Chapter 5 Heat



Chapter contents



5.1 Aim 27


5.2 Introduction 27


5.3 Heat energy and temperature 27


5.3.1 Temperature scales 28

5.3.2 Units of heat energy, specific heat capacity and thermal capacity 28

5.4 Transfer of heat 29


5.4.1 Conduction 29

5.4.2 Convection 29

5.4.3 Radiation 30

5.4.3.1 Black-body radiation 31

5.5 Thermal expansion 31


5.6 Evaporation and vaporization 32


Further reading 32



5.1 Aim


This chapter considers heat as a transfer of energy. Links between heat and temperature are established. The mechanisms of transferring heat are also established.



5.2 Introduction


We are familiar with the feelings of hot and cold; indeed, we are crucially dependent on our bodily temperature staying within a very limited range in order to survive. Compared to the vast ranges of temperature which exist across the universe, our experience of ‘hot’ and ‘cold’ is very limited indeed.



Insight


In fact, we are better at noticing ‘hotter’ or ‘colder’ than we are at determining an absolute value of ‘hot’ or ‘cold’. This can easily be shown from a simple experiment for which you require a bowl of hot water, a bowl of cold water and two bowls of tepid water. Place the right hand in the bowl of hot water and the left hand in the bowl of cold water and leave them in position for about 2 minutes. Now transfer both hands to the bowls of tepid water. You will note that this water feels cold to the right hand and warm to the left hand. This shows that we are better at detecting changes in temperature than we are at detecting absolute values of temperature.


In order to investigate heat further, we must use objective measures of heat and cold, as described in the following sections.



5.3 Heat energy and temperature


When heat is given to a body, its atoms or molecules are given increased kinetic energy in the form of increased lattice vibration (this is the reason why substances expand when heated). A body whose atoms have a higher kinetic energy than those of another body is said to be hotter or at a higher temperature. If two bodies are placed in contact, then heat will be transferred from the hotter body to the cooler body by collisions between the molecules at the point of contact. The molecules of the cooler body receive a net increase in kinetic energy and so its temperature rises. The molecules of the hotter body have lost kinetic energy and so its temperature falls. This process continues until the two bodies are at the same temperature when no further exchange of energy takes place. The bodies are now in a state of thermal equilibrium. Notice that the thermal energy is always transferred from the body at the higher temperature to the body at the lower temperature, irrespective of the size of the bodies. Also note that the temperature existing at thermal equilibrium will always lie somewhere between the initial temperatures of the two bodies.



Insight


If a body is made to give away thermal energy, then the lattice (the bound framework of a solid or semisolid) vibrations of its atoms or molecules will decrease. It is logical to assume that there must be a temperature at which no lattice vibration exists. As all movement of molecules ceases to exist at this temperature, this is the lowest temperature that we can attain. This temperature is known as absolute zero and will be further discussed in the next section.



5.3.1 Temperature scales


There are two temperature scales used in modern physics: Celsius (also called centigrade) and kelvin. The Celsius scale is defined as 0°C at the temperature of melting ice, and 100°C at the temperature of boiling water at an atmospheric pressure of 1.01 × 105 newtons per square metre (76 mm of mercury). On this scale, the temperature of absolute zero (see previous Insight) is approximately −273.15°C. This temperature is zero on the kelvin scale (0 K) while the temperature of melting ice is 273.15 K. From this, we can see that the units of temperature are the same on both scales but the scales have different starting points, i.e. one unit on the Celsius scale is equivalent to one unit on the kelvin scale. Note that temperature on the kelvin scale does not have the degree symbol in front of the K. It is a convenient approximation to assume that 0°C=273 K, so that the simple conversion formula may be used:



Equation 5.1 image



where T is temperature.



5.3.2 Units of heat energy, specific heat capacity and thermal capacity


If heat is given to a body, then its molecules will have a higher kinetic energy and its temperature will rise. Hence, it is convenient to express a quantity of heat in terms of the temperature change it produces in a given body. Consider the situation where we wish to apply an amount of energy, Q, which will raise the temperature of a body by 1 kelvin unit (for simplicity, assume that this does not change the state of the body, i.e. it does not change from a solid to a liquid). This will be affected by the mass and the type of material of the body. It also seems logical to assume that we would need twice the amount of heat to raise the temperature of the body by 2 kelvin units. If we take all these factors together, we can write the equation:



Equation 5.2 image



where Q is the heat energy required to raise the temperature of a body of mass m from T1 to a temperature T2. The factor c is approximately constant for a particular material and is known as the specific heat capacity of the material. We can rearrange Equation 5.2 to get:



Equation 5.3 image



so that c, the specific heat capacity, is in units of c joules per kilogram per kelvin (J.kg−1.K−1). Specific heat capacity can be defined thus:



Definition


The specific heat capacity of a body is the energy in joules required to raise the temperature of 1 kilogram of the body by 1 kelvin unit.


The specific heat capacity of a substance is thus unique to that substance and it allows us to predict the behaviour of different masses of the same substance.



Example


The specific heat capacity of water is about it 4.2 (J.kg−1.K−1). How much heat energy is required to raise a mass of 10 g of water from 280 K to 285 K? (Remember that the unit of energy is the joule and the unit of mass is the kilogram.)


Using Equation 5.2, we have:



image




In the situations considered so far, we have considered the amount of heat required to raise the temperature of 1 kg of the material. Another unit of heat energy, which is useful in practice, is the thermal capacity.



Definition


The thermal capacity of a body is the heat energy in joules which is required to raise the temperature of the body by 1 kelvin unit.

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Mar 6, 2016 | Posted by in GENERAL RADIOLOGY | Comments Off on Heat

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