11. IMPACTOS Y RESULTADOS
11.2. DESCRIPCIÓN DE LOS IMPACTOS DE LA EMPRESA
James Prescott Joule (1818-1889) conducted a series of
brilliant experiments between 1842 and 1870 that proved beyond doubt that heat was a type of energy – internal energy – of the particles of matter. The caloric theory lost popularity very quickly.
Joule was the son of a wealthy brewer in Manchester, UK.
Because of his wealth, he never worked for a living. His experiments were performed in a laboratory that he built at his own expense while he was in his twenties. He became interested in ways to develop more efficient engines that were driving various components of the brewing process. Encouraged by the work of Count Rumford and others, he began to investigate whether mechanical work could produce heat.
Joule performed a variety of experiments and he refined
and elaborated his apparatus and his techniques. In one of his first experiments, he used a falling weight to drive a small electric generator. The current produced heated a wire that was immersed in a definite mass of water, and the change in temperature was noted. He reasoned that the work done as the weight decreases its gravitational potential energy should be equivalent to the heat energy gained by the water. In another experiment he mounted a large container filled with air into a tub of water. When the air was compressed, the temperature of the gas increased. He measured the amount of work needed to compress the gas and the amount of heat energy given to the water as a result of compression.
Perhaps Joule’s most famous experiment consisted of a paddlewheel mounted inside a cylinder of water that was driven by falling weights as shown in Figure 301. He wanted to see if one could raise the temperature of the water simply by turning the paddles. He repeated this experiment many times continually improving the apparatus and refining his analysis of the data. For example, he took great care to insulate the container so that no heat was lost to the surroundings, and he developed his own thermometer so
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that he could measure the temperature with a precision of a fraction of a degree. moving vanes xed vanes calorimeter ywheel handles to pulley with weights attached to pulley with weights (containing water) spindle attached
Figure 301 Schematic diagram of Joule’s paddlewheel experiment.
Joule arranged the vanes of the paddlewheel so that they would not interfere with the particles of water set in motion. He didn’t want to bruise or damage the water particles so that they might “bleed” heat.
In 1849 he published his results in which he reported
“…the quantity of heat produced by friction of bodies, whether solid or liquid, is always proportional to the quantity of [energy] expended.”
“…the quantity of heat capable of increasing the temperature of a pound of water by 1 ° Fahrenheit requires for its evolution the expenditure of a mechanical energy represented by the fall of 772 pound through the distance of one foot”.
Joule found that about 4.2 joules of work would yield one calorie of heat or that the quantity of heat required to raise the temperature of one gram of water by 1 °C is one calorie.
A modern day value for the mechanical equivalent of heat is 4.18605 joules = 1 calorie.
The experiments proved beyond doubt that mechanical work can produce heat and as such no caloric fluid can be created or destroyed. Furthermore, Joule reasoned that the temperature increase must be related to the energy of the microscopic motions of the particles.
Finally, a paradigm shift in our way of reasoning had again proved that science is not the ultimate truth.
Example
Calculate the mechanical equivalent of heat for Joule’s paddlewheel experiment if a mass of 2.0 kg falls through a height of 100 m, and increases the temperature of 10 g of water by 46.8 °C.
Solution
Work done by the falling mass is given by
W = Ep = mgΔh
= 2.0 kg × 9.8 m s-2 × 100 m
= 1.96 × 10 3 J
Heat energy produced is given by
Q = m × c × ΔT
= 10 g × 1 cal × 46.8 °C
= 4.68 × 102 calories
Mechanical equivalent of heat is given by W Q --- 1.96 10 3 J × 4.68 ×102cal --- = = 4.19 J cal-1
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3.1.1 State that temperature determines the direction of thermal energy transfer between two objects.
3.1.2 State the relation between the Kelvin and Celsius scales of temperature.
3.1.3 State that the internal energy of a
substance is the total potential energy and random kinetic energy of the molecules of the substance.
3.1.4 Explain and distinguish between the macroscopic concepts of temperature, internal energy and thermal energy (heat).
3.1.5 Define the mole and molar mass.
3.1.6 Define the Avogadro constant.
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3.1.1 TEMPERATUREANDTHERMAL
ENERGY
TRANSFER
Everyone seems to have a feel for the concept of heat because there is so much talk in everyday conversation of how hot or how cold it is. We endure the seasons of the year wanting either to cool our bodies or heat up our surroundings. We are aware of how difficult it was for our ancestors to keep warm, and our present dwellings are designed and insulated to suit the climate. Our consumption of electrical and chemical energy for heating and other purposes is a continual concern. We have become aware that increased global warming could spell the end of the world, as we know it.
But what is the difference between heat and temperature in physics? They are definitely not the same physical quantity. If you fill a cup and a dish with hot water at the same temperature, and then place ice cubes into each, the dish full of hot water can melt more ice cubes than the cup of hot water even though the water in each was at the same temperature. The dish containing the larger amount of hot water has a greater mass of water as well as a greater amount of heat or thermal energy. A greater mass infers a greater number of water molecules and more thermal energy infers that these molecules would have a greater overall amount of energy. We cannot see the interaction
of the water molecules at the microscopic level because we cannot see atoms. However, we can observe and monitor the temperature change by using a macroscopic temperature-measuring device.
Thermal energy is a measure of the kinetic and potential
energy of the component particles of an object and is measured in joules. Heat is the thermal energy that is absorbed, given up or transferred from one object to another.
Temperature is a scalar quantity that gives an indication of
the degree of hotness or coldness of a body. Alternatively, temperature is a macroscopic property that measures the average kinetic energy of particles on a defined scale such as the Celsius or Kelvin scales. The chosen scale determines the direction of thermal energy transfer between two bodies in contact from the body at higher
temperature to that of lower temperature. Eventually,
the two bodies will be in thermal equilibrium when they acquire the same temperature in an isolated system. It will be deduced later in this text that thermal energy cannot be transferred from a body at lower temperature to that of higher temperature.
3.1.2 TEMPERATURESCALES
There is no instrument that directly measures the amount of thermal energy a body gives off or absorbs. A property that varies with temperature is called a thermometric property. This property can be used to establish a temperature scale and construct a thermometer. Thermometers are made using the thermometric properties of a substance such as the expansion of a liquid, the electrical resistance of a wire.
A typical laboratory thermometer as shown in Figure 302 contains a liquid such as mercury or coloured alcohol. The expansion of alcohol is six times greater than mercury. Alcohol thermometers are safer and can be used at lower temperatures than mercury which turns to a solid below -38.9 °C. Its disadvantage is that it boils above 78.5 °C. To make the thermometer sensitive, it has a narrow bore tube and a large bulb. The bulb is made of thin glass so that heat can be transferred quickly between the bulb liquid and the material being observed. There is a vacuum above the thermometer liquid and it can move easily along the glass bore.
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100°C 0 °C mercury or alcohol thin glass bulb glass stem capillary tube vacuumFigure 302 Typical laboratory thermometer
A clinical thermometer as shown in Figure 303 does not need the temperature range of a laboratory thermometer. It is designed so that the maximum temperature remains constant after the patient’s temperature is taken. It has a small constriction to stop the mercury flowing back into the bulb. The mercury is then shaken back into the bulb after the temperature has been taken.
35 36 37 38 39 40 41 42
Figure 303 A Clinical Thermometer
In order to calibrate these thermometers, two fixed points are used to define the standard temperature interval. The ice point (the lower fixed point) marked at 0 °C is the temperature of pure ice at standard atmospheric pressure and is in thermal equilibrium with the liquid in the bulb. The steam point (the upper fixed point) marked at 100 °C is the temperature of steam at standard atmospheric pressure and is in thermal equilibrium with the liquid in the bulb. The scale between these values is marked with even spaces. The Celsius temperature scale named after the Swedish astronomer Anders Celsius (1701-1774) is constructed in such a manner.
Although thermometers constructed using thermometric properties are useful for everyday use, they are not accurate enough for scientific work. Unfortunately, two thermometers constructed using different thermometric properties do not necessarily agree with each other as they do not vary linearly over large temperature ranges. (They are of course in agreement at the lower and upper fixed
points). For example, different thermometers will give different values for the boiling point of zinc (907 °C).
The standard fundamental temperature scale in the SI system is denoted by the symbol T. and is measured in Kelvin, K. It is the thermodynamic temperature scale used in scientific measurement.
The lower fixed point is absolute zero and is assigned a value of 0 K. This is the point where molecular vibrations become a minimum – the molecules have minimum kinetic energy but molecular motion does not cease. The upper fixed point is the triple point of water. This is the temperature at which saturated water vapour, pure water and melting ice are all in equilibrium. For historical reasons, it is assigned a value of 273.16 K.
T in K = T in °C + 273.16
Exercise 3.1 (a)
1. At room temperature, an iron rod feels cooler when held in the hand than wood held in the same wood held in the same hand. This is because:
A. thermal energy tends to flow from the metal to the wood
B. wood has a higher specific heat capacity than the iron rod
C. wood has a lower specific heat capacity than the iron rod
D. the iron rod conducts thermal energy better than the wood
2. Explain the difference between heat and temperature.
3. If you were travelling to Antarctica, deduce what would be the better thermometer to take – mercury or alcohol?
4. State one advantage and one disadvantage of a
i. mercury in glass thermometer ii. constant volume thermometer.
5. The triple point of water is 273.16 K. Express this as a Celsius temperature.
6. Determine the ice point and the steam point of pure water on the Kelvin scale?
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7. Define absolute zero.
8. If normal body temperature is 37.0 °C, what is it on the thermodynamic temperature scale?
3.1.3 HEATANDINTERNAL
ENERGY
Thermal energy of a system is referred to as internal energy - the sum total of the potential energy and the random kinetic energy of the molecules of the substance making up the system.
The potential energy is due to
• the energy stored in bonds called bond energy • intermolecular forces of attraction between particles.
The bond energy is a form of chemical potential energy. It becomes significant in chemistry when a chemical reaction occurs, and bonds are broken and formed.
The intermolecular forces of attraction between particles is due to the electromagnetic fundamental force since the gravitational force is too small to be of any significance.
Figure 304 indicates how the intermolecular electro- magnetic force F between particles varies with the distance
r between their centres.
At distances greater than r0 (less than 2.5 × 10-10 m)
attraction takes place, and at distances closer than r0 the particles repel. At r0 the particles are in equilibrium. Any displacement from the equilibrium position results in a simple harmonic oscillation of a particle or molecule.
r0 re p u ls io n at tr ac ti o n
solid and liquid phase
10r0 gaseous phase nuclear separation, r / m Force, F / N + –
Figure 304 Force versus separation of particles
Figure 305 shows the relationship between the potential energy and the separation r of two molecules. At 0 K, the average separation of particles centres is r0 and the overall force is zero. This is the point of minimum potential energy. Work will need to be done to move the particles apart and there will be an increase in potential energy.
r0 equilibrium separation gas liquid separation, r / m P o te n ti al ener g y, U/ J solid + – ε
minimum potential energy = –ε
Figure 305 Potential energy versus separation of particles
Work done = force × distance = F × r = change in potential energy
∴ F = Δ E p
____ r
In other words, the gradient of the potential energy curve at any point on the curve gives the force that must be applied to hold the molecules at that separation. We can classify the phases according to the sizes of the energy ε.
When less than __ 10ε, the vibrations occur about fixed positions and the particles are in the solid phase. When approximately equal to __ 10ε, the particles have sufficient energy to partly overcome the attractive forces and melting occurs.
When greater than __ 10ε, a liquid can form. When greater than ε, the particles have sufficient energy to leave the liquid and form a gas.
The kinetic energy is mainly due to the translational, rotational and vibrational motion of the particles as depicted in Figure 306.
Vibrational
kinetic energy kinetic energyRotational kinetic energyTranslational