13. INCIDENCIA EN POLÍTICAS PÚBLICAS
18.1. RELATORÍA DEL TALLER PARTICIPATIVO CON ACTORES CLAVE
A calorimeter is a useful piece of equipment for investigations in Thermal Physics because it allows masses at different temperatures to be mixed with minimum energy loss to the surroundings. It is used for direct and indirect methods in determining the specific heat capacity of a substance. (The name of the instrument is derived from the Imperial unit, the calorie.)
copper vessel heating coil liquid thermometer stirrer lagging joulemeter
Figure 310 Calorimeter being used to measure the heating effect of a current
Figure 310 illustrates the use of a calorimeter to determine the specific heat capacity of a liquid, in this case water. The heating coil is used to convert electrical energy to thermal energy. The electrical energy can be measured by a joulemeter or by using a voltmeter/ammeter circuit. The duration of time of electrical input is noted.
The thermal energy gained by the calorimeter cup and the water is equal to the electrical energy lost to the calorimeter cup and water.
Electrical energy lost =
V × I × t = [m × c × ΔT]calorimeter cup + [m × c × ΔT]water where V is the potential difference across the heating coil in volts V and I is the current in the amperes, A.
The specific heat capacity, c, of the calorimeter cup is obtained from published values. The other quantities are recorded and the specific heat capacity of the water is calculated.
In calorimeter investigations, heat losses to the surroundings need to be minimised. It is normal to polish the calorimeter cup to reduce loss of heat due to radiation. The calorimeter is also insulated with lagging materials
such as wool or polystyrene to reduce heat loss due to conduction and convection.
After the power supply is switched off, the temperature should continue to rise for a period, and then level out for an infinite time. However, heat is lost to the surroundings, and the maximum temperature that could be achieved, in theory, is never reached. Instead appreciable cooling occurs. One method used to estimate the theoretical maximum temperature is to use a cooling correction
curve as shown in Figure 311.
{Note that cooling correction is not required in the syllabus but is included for possible extended essays.}
t 2t 3t A 1 A2 θ θ2 Δθ Δθ A1 A2 ---×θ = θ1 θ3= θ2+Δ θ θ3 , so that θ2–θ1 = ( ) (= correction) T e m p era tu re , °C Time, minutes actual curve theoretical curve room temp
Figure 311 Graph of cooling correction.
A cooling correction is based on Newton’s Law of Cooling. It states that the rate of loss of heat of a body is proportional to the difference in temperature between the body and its surroundings (excess temperature). A full explanation of this Law will not be given. If the power supply is switched off at time 2t minutes, then the temperature should continue to be recorded for a further t minutes. The correction to the temperature θ can be obtained from the graph as shown. The final temperature, θ3, is then given as the final
temperature of the thermometer plus the correction θ.
Another direct electrical method used to determine the specific heat capacity of a metal is shown in Figure 312. An immersion heater is placed into a metal block. The hole for the heater is lubricated with oil to allow even heat transmission. The electrical energy lost to the block is recorded for a given period of time and the specific heat of the metal is calculated. Cooling correction is more important in this case because the temperatures under which the investigation is carried out could be much higher than was the case when using a calorimeter.
C
ORE
metal block thermometer lagging V A Low voltage supply immersion heaterFigure 312 Electrical method using an immersion heater and a metal block
A common indirect method to determine the specific heat capacity of a solid and liquids is called the method of
mixtures. In the case of a solid, a known mass of the solid
is heated to a certain temperature, and then transferred to a known mass of liquid in a calorimeter whose specific heat capacity is known. The change in temperature is recorded and the specific heat of the solid is calculated from the results obtained. In the case of a liquid, a hot solid of known specific heat is transferred to a liquid of unknown specific heat capacity.
Example
A block of copper of mass 3.0 kg at a temperature of 90 °C is transferred to a calorimeter containing 2.00 kg of water at 20 °C. The mass of the copper calorimeter cup is 0.210 kg. Determine the final temperature of the water.
Solution
The thermal energy gained by the water and the calorimeter cup will be equal to the thermal energy lost by the copper. That is, [mcΔT]copper = [mcΔT]calorimeter cup + [mcΔT]cup
We also have that,
Thermal energy lost by the copper
= (3.0 kg) (3.85 × 102 J kg -1 K -1) (90.0 –Tf) K
Thermal energy gained by the water
= (2.0 kg) (4.18 × 103 J kg -1 K -1) (Tf – 20.0) K
Thermal energy gained by the cup
= (0.21 kg) (9.1 × 102 J kg -1 K -1) (Tf – 20.0) K 1.04 × 105 – 1.155 × 103 Tf = (8.36 × 103 Tf – 1.67 × 105) +(1.91 × 102 Tf – 3.82 × 103) That is, – 9.71 × 103 Tf = – 2.75 × 105 Giving Tf = 28.3 °C
The final temperature of the water is 28 °C
Exercise 3.2 (a)
1. The amount of thermal energy required to raise the temperature of 1.53 × 103g of water from 15 K
to 40 K is
A. 1.6 × 107 J
B. 1.6 × 105 J
C. 4.4 × 107 J
D. 4.4 × 105 J
2. The specific heat capacity of a metal block of mass
m is determined by placing a heating coil in it, as
shown in the following diagram.
The block is electrically heated for time t and the maximum temperature change recorded is Δθ. The constant ammeter and voltmeter readings during the heating are I and V respectively. The electrical energy supplied is equal to VIt.
C
ORE
metal block thermometer lagging V A Low voltage supply immersion heaterThe specific heat capacity is best calculated using which one of the following expressions?
A. c = VI mΔ
θ
B. c = θ Δ m VI C. c =θ
Δ m VIt D. c = VIt mΔθ
3. 5.4 × 106 J of energy is required to heat a 28 kg
mass of steel from 22 °C to 450 °C. Determine the specific heat capacity of the steel.
4. Liquid sodium is used as a coolant in some nuclear reactors. Describe the reason why liquid sodium is used in preference to water.
5. 6.00 × 102 kg of pyrex glass loses 8.70 × 106 J of
thermal energy. If the temperature of the glass was initially 95.0 °C before cooling, calculate is its final temperature.
(Take the specific heat capacity of pyrex glass to be 8.40 × 10 2 J kg -1 K-1)
6. A piece of wood placed in the Sun absorbs more thermal energy than a piece of shiny metal of the same mass. Explain why the wood feels cooler than the metal when you touch them.
7. A hot water vessel contains 3.0 dm3 at 45 °C.
Calculate the rate that the water is losing thermal energy (in joules per second) if it cools to 38 °C over an 8.0 h period.
8. Determine how many joules of energy are released when 870 g of aluminium is cooled from 155 °C to 20 °C.
9. If 2.93 × 106 J is used to raise the temperature of
water from 288 K to 372 K, calculate the mass of water present.
10. 1.7 mJ of energy is required to cool a 15 kg mass of brass from 400 °C to 25 °C. Determine the specific heat capacity of brass.
11. A piece of iron is dropped from an aeroplane at a height of 1.2 km. If 75% of the kinetic energy of the iron is converted to thermal energy on impact with the ground, determine the rise in temperature.
12. If 115 g of water at 75.5 °C is mixed with 0.22 kg of water at 21 °C, determine the temperature of the resulting mixture.
13. Describe an experiment that would allow you to determine the specific heat capacity of a metal.
(i) Sketch the apparatus.
(ii) Describe what measurements need to be made and how they are obtained. (iii) State and explain the equation used to
calculate the specific heat capacity of the metal.
(iv) Describe 2 main sources of error that are likely to occur in the experiment.
(v) Is the experimental value likely to be higher or lower than the theoretical value, if the experiment was carried out in a school laboratory? Explain your answer.
14. A heating fluid releases 4.2 × 107 Jkg-1 of heat as it
undergoes combustion. If the fluid is used to heat 250 dm3 of water from 15 °C to 71 °C, and the
conversion is 65% efficient, determine the mass of the heating fluid that will be consumed in this process.
15. A large boulder of 125 kg falls off a cliff of height 122 m into a pool of water containing 120 kg of water. Determine the rise in temperature of the water. Assume that no water is lost in the entry of the boulder, and that all the heat goes to the water.
16. A thermally insulated container of water is dropped from a large height and collides inelastically with the ground. Determine the height from which it is dropped if the temperature of the water increases by 1.5 °C.
C
ORE
17. A piece of copper is dropped from a height of 225 m. If 75% of its kinetic energy is converted to heat energy on impact with the ground, calculate the rise in temperature of the copper. (Use the table of specific heat capacities to find the value for copper).
18. 5kg of lead shot is poured into a cylindrical cardboard tube 2.0 m long. The ends of the tube are sealed, and the tube is inverted 50 times. The temperature of the lead increases by 4.2 °C. If the specific heat of lead is 0.031 kcal kg-1 °C-1,
determine the number of work units in joules that are equivalent to the heat unit of 1 kilocalorie.
3.2.3 PHASE
STATES
An understanding of thermal energy is based upon a theory called the moving particle theory or kinetic theory (for gases) that uses models (Figure 314) to explain the structure and nature of matter. The basic assumptions of this moving particle theory relevant to thermal energy are:
• all matter is composed of extremely small particles • all particles are in constant motion
• if particles collide with neighbouring particles, they conserve their kinetic energy
• a mutual attractive force exists between particles
solid liquid gas
Figure 314 Arrangement of particles in solids, liquids and gases
An atom is the smallest neutral particle that represents an element as displayed in a periodic table of elements. Atoms contain protons, neutrons and electrons and an array of other sub-atomic particles. Atomic diameters are of the order of magnitude 10–10 m. Atoms can combine to form
molecules of substances. In chemistry, the choice of the terms e.g. ‘atoms, molecules, ions’ are specific to elements and compounds. In physics, the word ‘particle’ is used to describe any of these specific chemistry terms at this stage of the course.
As previously mentioned, evidence for the constant motion of particles can be gained from observation of what is known as Brownian Motion. If pollen grains from flowers
are placed on water and observed under a microscope, the pollen grains undergo constant random zig-zag motion. The motion becomes more vigorous as the thermal energy is increased with heating. A Whitley Bay smoke cell uses smoke in air to achieve the same brownian motion. In both cases, the motion is due to the smaller particles striking the larger particles and causing them to move.
The large number of particles in a volume of a solid, liquid or gas ensures that the number of particles moving in all directions with a certain velocity is constant over time. There would be no gaseous state if the particles were losing kinetic energy.
A mutual attractive force must exist between particles otherwise the particles of nature would not be combined as we know them. Further explanation of this assumption will be given later in this topic.
Matter is defined as anything that has mass and occupies space. There are four states of matter which are also called the four phases of matter – solids, liquids, gases and plasma. Most matter on Earth is in the form of solids, liquids and gases, but most matter in the Universe is in the plasma state. Liquids, gases and plasma are fluids.
A plasma is made by heating gaseous atoms and molecules to a sufficient temperature to cause them to ionise. The resulting plasma consists then of some neutral particles but mostly positive ions and electrons or other negative ions. The Sun and other stars are mainly composed of plasma.
The remainder of this chapter will concentrate on the other three states of matter, and their behaviour will be explained in terms of their macroscopic and microscopic characteristics of which some are given in Figures 315 and 316.
Characteristic Solid Liquid Gas
Shape Definite Variable Variable Volume Definite Definite Variable
Compressibility Almost Incompressible Very slightly Compressible Highly Compressible Diffusion Small Slow Fast
Comparative
Density High High Low
Figure 315 Some macroscopic characteristics of solids, liquids and gases
Macroscopic properties are all the observable behaviours of that material such as shape, volume and compressibility.
C
ORE
The many macroscopic or physical properties of a substance can provide evidence for the nature and structure of that substance.
Characteristic Solid Liquid Gas
Kinetic energy Vibrational
Vibrational Rotational Some translational Mostly translational Higher rotational Higher vibrational Potential energy High Higher Highest Mean molecular
Separation (r0) r0 r0 10r0
Thermal energy
of particles (ε) < ε /10 < ε > ε /10 > ε Molecules per m3 1028 1028 1025
Figure 316 Some microscopic characteristics of solids, liquids and gases
Microscopic characteristics help to explain what is happening at the atomic level, and this part of the model will be interpreted further at a later stage.
The modern technique of X-ray diffraction that will be studied in detail in a later chapter has enabled scientists to determine the arrangement of particles in solids. The particles are closely packed and each particle is strongly bonded to its neighbour and is held fairly rigidly in a fixed position to give it definite shape in a crystalline lattice. Some patterns are disordered as is the case for ceramics, rubber, plastics and glass. These substances are said to be amorphous. The particles have vibrational kinetic energy in their fixed positions and the force of attraction between the particles gives them potential energy.
In liquids the particles are still closely packed and the bonding between particles is still quite strong. However, they are not held as rigidly in position and the bonds can break and reform. This infers that the particles can slowly and randomly move relative to each other to produce variable shape and slow diffusion. Particles in a liquid have vibrational, rotational and some translational kinetic energy due to their higher mean speeds. The potential energy of the particles in a liquid is somewhat higher than for a solid because the spacing between the particles is large.
In gases the particles are widely spaced and the particles only interact significantly on collision or very close approach. Because of the rapid random zig-zag motion of the particles, a gas will become dispersed throughout any
container into which it is placed. Diffusion (the spreading out from the point of release) can occur readily. Gases are compressible because the particles are widely spaced at a distance much greater than the size of the particles. The much higher mean speeds are due to an increased translational kinetic energy of the particles. Gases have a much higher potential energy than liquids because the particles are much further apart.
3.2.4 THE
PROCESSOFPHASE
CHANGES
A substance can undergo changes of state or phase changes at different temperatures. Pure substances (elements and compounds) have definite melting and boiling points which are characteristic of the particular pure substance being examined. For example, oxygen has a melting point of -218.8 °C and a boiling point of -183 °C at standard atmospheric pressure.
The heating curve for benzene is illustrated in Figure 317. A sample of benzene at 0°C is heated in a closed container and the change in temperature is graphed as a function of time. The macroscopic behaviour of benzene can be described using the graph and the microscopic behaviour can be interpreted from the macroscopic behaviour.
SO L I D L I Q U I D G AS L iquid-gas phase change Solid-liquid phase change Temperature /°C
H eating time /min melting point boiling point 5.5°C 80°C
Figure 317 Heating curve for benzene.
When the solid benzene is heated the temperature begins to rise. When the temperature reaches 5.5 °C the benzene begins to melt. Although heating continues the temperature of the solid – liquid benzene mixture remains constant until all the benzene has melted. Once all the benzene has melted the temperature starts to rise until the liquid benzene begins to boil at a temperature of 80 °C. With continued heating the temperature remains constant until all the liquid benzene has been converted to the gaseous state. The temperature then continues to rise as the gas is in a closed container.
C
ORE
3.2.5 MOLECULARBEHAVIOURAND
PHASECHANGES
The moving particle theory can be used to explain the microscopic behaviour of these phase changes. When solid benzene is heated the particles of the solid vibrate at an increasing rate as the temperature is increased. The vibrational kinetic energy of the particles increases. At the melting point a temperature is reached at which the particles vibrate with sufficient thermal energy to break from their fixed positions and begin to slip over each other. As the solid continues to melt, more and more particles gain sufficient energy to overcome the forces between particles and over time all the solid particles change to a liquid. The potential energy of the system increases as the particles begin to move. As heating continues the temperature of the liquid rises due to an increase in the vibrational, rotational and part translational kinetic energy of the particles. At the boiling point a temperature is reached at which the particles gain sufficient energy to overcome the inter- particle forces present in the liquid benzene and escape into the gaseous state. Continued heating at the boiling point provides the potential energy needed for all the benzene molecules to be converted from a liquid to a gas. With further heating the temperature increases due to an increase in the kinetic energy of the gaseous molecules due to the larger translational motion.
3.2.6 EVAPORATIONANDBOILING
When water is left in a container outside, exposed to the atmosphere, it will eventually evaporate. Mercury from broken thermometers has to be cleaned up immediately due to its harmful effects. Water has a boiling point of 100 °C and mercury has a boiling point of 357 °C. Yet they both evaporate at room temperature.
The process of evaporation is a change from the liquid state to the gaseous state that occurs at a temperature below the boiling point.
The moving particle theory can be applied to understand the evaporation process. A substance at a particular temperature has a range of kinetic energies. So in a liquid at any particular instant, a small fraction of the molecules will have kinetic energies considerably greater then the average value. If these particles are near the surface of the liquid, they may have enough kinetic energy to overcome the attractive forces of neighbouring particles and escape from the liquid as a vapour. Now that the more energetic particles have escaped, the average kinetic energy of the
remaining particles in the liquid has been lowered. Since temperature is proportional to the average kinetic energy of the particles, a lower kinetic energy implies a lower temperature, and this is the reason why the temperature of the liquid falls as evaporative cooling takes place. Another way of explaining the temperature drop is in terms of latent heat. As a substance evaporates, it needs thermal energy input to replace its lost latent heat of vaporisation and this thermal energy can be obtained from the remaining liquid and its surroundings.
A substance that evaporates rapidly is said to be a volatile