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heat capacity

heat capacity

- 1. Thermal Physics IBDP Topic 3.1 Thermal Concepts
- 2. Phases (States) of Matter Matter is defined as anything that has mass and occupies space. There are 4 states of matter • Solids, Liquids, Gases and Plasmas Most of the matter on the Earth is in the form of the first 3 whereas most of the matter in the Universe is in the plasma state.
- 3. Macroscopic • Macroscopic properties are all the observable behaviours of that material such as shape, volume, compressibility. • The many macroscopic or physical properties of a substance can provide evidence for the nature of that substance. TOK
- 4. Macroscopic Characteristics Characteristics Solid Liquid Gas Shape Volume Compressibility Diffusion Comparative Density
- 5. Macroscopic Characteristics Characteristics 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
- 6. Microscopic At the atomic level we consider the energy of the particles. The energy is in the form of: • Kinetic Energy, KE • Potential Energy, PE
- 7. Microscopic Characteristics Characteristics Solid Liquid Gas KE Vibrational Vibrational Rotational Some Translational Mostly Translational Higher Rotational Higher Vibrational PE High Higher Highest
- 8. Describe the Energy in… 1. Water running from a tap 2. Air in a room 3. Coffee in a cup
- 9. Solids Before the turn of the previous century it was thought that the content of a solid,determined its characteristics. It was what made diamonds hard, lead heavy and iron magnetic. The characteristics of a solid are due to its structure. That is, the arrangement of atoms within the material.
- 10. Solids To keep the atoms in the regular pattern (lattice) there are forces (electrical in nature) which bind them together. If the atoms get too close, the force becomes repulsive (between electrons in their outer shells). In solids, the thermal energy is very much smaller than the intermolecular binding energy and so, solids have specific macroscopic properties.
- 11. Solids maintain a fixed shape and, a fixed size. Even if a force is applied it does not readily change its shape, or volume. The result is that the atoms vibrate about a fixed position. Solids
- 12. Arrangement of Particles - 1 • Closely packed • Strongly bonded to neighbours • held rigidly in a fixed position • the force of attraction between particles gives them PE
- 13. Fluids • Liquids • Gases are both known as fluids because they FLOW.
- 14. Liquids The thermal energy (due to an increase in temperature) is greater allowing the atoms to move farther apart. The binding forces are less and the atoms are able to roll over each other. This gives rise to the macroscopic properties of liquids. Liquids do not maintain a fixed shape it takes the shape of the container. Like a solid, it is not readily compressible only a very large force can, significantly change its volume.
- 15. Arrangement of Particles - 2 • Still closely packed • Bonding is still quite strong • Not held rigidly in a fixed position and bonds can break and reform • PE of the particles is higher than a solid because the distance between the particles is higher
- 16. Gases The forces of attraction are so weak and the thermal energy is so high (due to another increase in temperature), the atoms do not even stay close together. They move very rapidly in a random manner filling the container and, occasionally colliding with one another.
- 17. Gases The speed at which the atoms are moving is so fast that when they do collide, the force of attraction is not strong enough to, keep them together and, they fly off in a new direction. A gas has neither a fixed shape nor a fixed volume it will expand to fill its container.
- 18. Arrangement of Particles - 3 • Widely spaced • Only interact significantly on closest approach or collision • Have a much higher PE than liquids because the particles are furthest apart
- 19. Plasma At extremely high temperatures such as those found in stars, atoms are ionised. The result is a collection of nuclei (ions) and electrons referred to as plasma.
- 20. Changes of State Add energy to ice and it turns to water. Add energy to water and it turns to steam. The state of matter depends upon its temperature and the pressure that is exerted upon it. To change state, a transfer of energy is required. A substance can undergo changes of state or phase changes at different temperatures.
- 21. Changes of State - 2 The moving particle theory can be used to explain the microscopic behaviour of these phase changes. When the solid is heated the particles of the solid vibrate at an increasing rate as the temperature is increased the vibrational KE of the particles increases.
- 22. Changes of State - 3 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 the particles and over time all the solid particles are changed to a liquid. The PE of the system increases as the particles move apart.
- 23. Changes in State - 4 As the heating continues the temperature of the liquid rises due to an increase in the vibrational, rotational and translational 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 and escape into the gaseous state. The PE increases. Continued heating at the boiling point provides the energy for all the particles to change.
- 24. Heating Curve Solid Liquid Gas Solid - liquid phase change Liquid - gas phase change Temp / oC Time /min
- 25. Changes of State GASSOLID LIQUID Freezing/solidification vaporisation condensation melting sublimation Thermal energy given out Thermal energy added
- 26. Sublimation This is the process whereby a solid changes directly into a vapour without passing through the liquid phase. Carbon dioxide will do this at atmospheric pressure.
- 27. Evaporation The process of evaporation is a change from the liquid state to the gaseous state which occurs at a temperature below the boiling point. The Moving Particle (Kinetic) theory can be applied to understand the evaporation process.
- 28. Explanation - evaporation A change of state from liquid to gas that takes place at the surface of the liquid. • The temperature of any body is related to the mean kinetic energy of its molecules. As the molecules move in a random manner, some molecules may collide. Some may lose kinetic energy and some may collide and increase kinetic energy, enough to overcome the attractive forces of their neighbouring molecules.
- 29. As the higher kinetic energy molecules have escaped, the mean kinetic energy of the liquid has been reduced. This means the liquid left behind has been cooled and there is a corresponding temperature drop. This is the principle used by evaporative air conditioners and perspiration.
- 30. Cooling Condensation is the opposite process to evaporation. This is the cooling of a gas to a liquid. When water vapour molecules collide with a cold can of Coke, giving up sufficient kinetic energy, they condense into a liquid.
- 31. Cooling Condensation is a warming process. The kinetic energy lost by the gas molecules warms the surface that they strike. A steam burn is more dangerous than a boiling water burn at the same temperature. Steam gives up energy when it condenses to the liquid that wets the skin.
- 32. Temperature At a macroscopic level, temperature is the degree of hotness or coldness of a body as measured by a thermometer. Temperature is a property that determines the direction of thermal energy transfer between two bodies in contact. Are you a good thermometer? TOK
- 33. Thermal Equilibrium Thermal equilibrium occurs when the temperature of 2 bodies, that are in contact, are the same. Heat will flow from the warmer body to the colder body until the two objects reach the same temperature. They will then be in Thermal Equilibrium.This is how a thermometer works
- 34. Thermometers Nearly all matter expands when its temperature increases and conversely contracts when temperature decreases. A thermometer uses the expansion and contraction of a liquid in a glass capillary tube with a scale to measure the expansion or contraction. What other examples can you think of?
- 35. Thermometer - scales A temperature scale is constructed by taking two fixed, reproducible temperaturas. The upper fixed point is the boiling point of pure water at atmospheric pressure. The lower fixed point is the melting point of pure ice at atmospheric pressure.
- 36. Use the idea of thermal equilibrium to explain 1. Why kitchen floors are generally cold to bare feet during winter 2. Why hot water bottles are used in winter 3. Why carpet feels warmer than wood 4. Why do car windows fog in winter
- 37. Temperature - Microscopic At a microscopic level, temperature is related to the random motion of the atoms or molecules in a substance. In an ideal gas temperature is a measure of the average kinetic energy per molecule associated with its movement in the substance.
- 38. Temperature is not a measure of the total kinetic energy of the atoms or molecules in a substance. There is twice as much kinetic energy in 2 litres of boiling water than in 1 litre. The temperature is however the same in both containers as the mean kinetic energy of the atoms or molecules is the same.
- 39. Internal Energy The Internal (thermal) energy of a body is the total energy associated with the thermal motions of the particles. It can comprise of both kinetic and potential energies associated with particle motion: Kinetic energy arises from the translational and rotational motions, Potential energy arises from the forces between the molecules.
- 40. What can change a system? Heat and work can change the state of the system but they are not a property of the system. They are not characteristic of the state itself but rather they are involved in the thermodynamic process that can change the system from one state to another.
- 41. Heat Touch a hot saucepan an energy is transferred to your hand as the saucepan is warmer than your hand. If however you touch ice, energy is transferred from your hand to the ice. Thermal energy is always transferred from a hotter substance to a cooler one.
- 42. Heat - 2 The term heat represents energy transfer due to a temperature difference and occurs from higher to lower temperature regions. Most people tend to believe that all matter contains heat. All matter contains a number of forms of energy but not heat.
- 43. Heat - 3 Heat is the transfer of energy from a body with higher temperature to one of lower temperature. Once the energy is transferred it ceases to be heat. It becomes kinetic energy.
- 44. Heat will not necessarily flow from a body with more total molecular kinetic energy to one with less total molecular kinetic energy. A bowl of warm water has much more total molecular kinetic energy than a red hot bolt. If the red hot bolt is immersed into the warm water heat will flow according to temperature difference.
- 45. Temperature scale Temperature is measured in degrees Celsius (oC) or Kelvin (K) (the absolute scale). Where Temp in K = Temp in oC + 273(.15) Temp in K is known as the absolute temperature
- 46. Heat Capacity/Thermal Capacity When different substances undergo the same temperature change they can store or release different amounts of energy. The temperature change that occurs when a substance absorbs heat depends on the amount of the substance. In order to quantify heat we must specify the amount of the substance.
- 47. Heat Capacity The calorie is defined as: The amount of heat required to raise the temperature of 1 g of water by 1oC. A kilocalorie is the heat required to raise the temperature of 1 kg of water by 1oC. The S.I. unit of heat is the same as all other forms of energy - the Joule (J). 1 calorie = 4.187 J.
- 48. Heat Capacity - 2 Heat capacity = Q / T in JK-1 Q = the change in thermal energy in joules T = the change in temperature in Kelvin Defined as the amount of energy to change the temperature of a body by unit temperature and applies to a specific BODY.
- 49. Heat Capacity - 3 A body with a high heat capacity will take in thermal energy at a slower rate than a substance with a low heat capacity because it needs more time to absorb a greater quantity of thermal energy. They also cool more slowly because they give out thermal energy at a slower rate.
- 50. Specific Heat Capacity Why is it that when fried in the same way for the same time, you can eat fried mushrooms but fried tomatoes burns your tongue? Why is it that a pizza can be just right but the pineapple is always much hotter?
- 51. The answer lies in the fact that different substances have different capacities for storing heat. Put a litre of water in a saucepan and heat, it may take a few minutes to boil. Put a metal knife on the same hotplate and it will reach the same temperature much more quickly. If we were given 1g of both iron and water, we would have a different number of molecules of different type and mass in each sample. Specific Heat Capacity - 2
- 52. Water uses energy to increase the rotation of molecules, internal vibration and bond stretching. Iron atoms use the energy to increase the translational kinetic energy. This means it takes 8 times the amount of heat to raise 1g of water by 1 oC than it does for iron. (The more water in the food the hotter it will seem) Specific Heat Capacity - 3
- 53. Specific Heat Capacity - 4 Defined as the quantity of heat required to raise the temperature of a unit mass of a substance by 1 degree is known as the specific heat capacity. Unit mass is normally 1kg, and unit temperature rise is normally 1K Specific Heat Capacity = Q / (mT) in J kg -1 K-1 where m is the mass of the material
- 54. We use the symbol c for specific heat capacity so the equation becomes: Q = mcT For an object made of one specific material then Heat Capacity = m x Specific Heat Capacity Water has a specific heat of 4180 joules/kgoC. This means it takes 4180 J of energy to raise the temperature of 1kg of water by 1oC.
- 55. Specific Heat Capacity - 5 Unit masses of different substances contain different numbers of molecules of different types of different masses If the same amount of internal energy is added to each unit mass it is distributed amongst the molecules.
- 56. Specific Heat capacity - 6 The average energy change of each molecule will be different for each substance. Therefore, the temperature changes will be different. So the specific heat capacities will be different.
- 57. Question How much heat energy would be required to raise the temperature of 5 kg of water from 19oC to 44oC?
- 58. Solution • m = 5 kg • c = 4200 J/kgoC • Ti = 19oC • Tf = 44oC • Q = mcT • Q = 5 x 4200 x (44 -19) • Q = 5.25 x 105 J
- 59. Question 2 If 40 000 J of heat are provided to 4 kg of water at 20oC, what final temperature will be achieved?
- 60. Solution • Q = 40 000 J • m = 4 kg • c = 4200 J/kgoC • Ti = 20oC • Q = mcT • 4 x 104 = 4 x 4200 x (Tf - 20) • Tf = (4 x 104/4 x 4200) + 20 • Tf = 22.4oC
- 61. Methods of finding the S.H.C The specific heat capacity can be found in two ways: • Direct • Indirect
- 62. 1. SHC of Liquids Thermometer Calorimeter Heating coil Liquid Insulation Stirrer To joulemeter or voltmeter and ammeter
- 63. Calculations - Liquids Electrical Energy input is equal to the thermal energy gained by the liquid and the calorimeter – this is the assumption that we are making Work done = V x I x t Energy gained by liquid = ml cl Tl Energy gained by calorimeter = mc cc Tc
- 64. Calculations - Liquids -2 Using conservation of energy Electrical energy in = thermal energy gained by liquid + thermal energy gained by calorimeter V I t = ml cl Tl + mc cc Tc The only unknown is the specific heat capacity of the liquid.
- 65. 2. SHC of Solids Insulation Thermometer Heating coil Solid Insulation To joulemeter or voltmeter and ammeter
- 66. Calculations - Solids Again using the conservation of energy. Electrical Energy input is equal to the thermal energy gained by the solid Electrical energy = V x I x t Energy gained by solid = ms cs Ts V x I x t = ms cs Ts The only unknown is the specific heat capacity of the solid.
- 67. Question 3 How much water could be boiled using an immersion heater that draws a 5A current in 15 minutes from room temperature (20oC)?
- 68. Solution • VIt = mcT • m = Vit/cT • m = (240 x 5 x 15 x 60)/(4200 x (100 -20)) • m = 1.08 x 106/3.36 x 105 • m = 3.2 kg
- 69. Question 4 A person wants to make 4, 250ml cups of hot coffee. If they were to use an electric kettle 240 V that used 1500W, how long would it take to boil the minimum amount of water from 25oC)?
- 70. Solution • P = VI and VIt = mcT • Pt = mcT • t = mcT/P • t = (4 x 0.25) x 4200 x (100 - 25)/1500 • t = (1 x 4200 x 75)/1500 • t = 315000/1500 • t = 210 s (or 3½ min)
- 71. 3. Method of mixtures In the case of solid, a known mass of solid is heated to a known temperature (usually by immersing in boiling water for a period of time). Then it is transferred to a known mass of liquid in a calorimeter of known mass.
- 72. The change in temperature is recorded and from this the specific heat capacity of the solid can be found. Energy lost by block = Energy gained by liquid and calorimeter. mb cb Tb = mw cw Tw + mc cc Tc the SHC of water and the calorimeter are needed.
- 73. Apparatus Heat Thermometer Beaker Boiling Water Block Thermometer Calorimeter Water Block Insulation
- 74. Question 5 Ten silver spoons, each with a mass of 30g, are removed from a pan of boiling water, quickly dried, and then placed in a pan of water at room temperature (20oC). The pan contains 500g of water. The temperature rises to 23oC. What is the specific heat capacity of silver?
- 75. Solution • (mcT)silver = (mcT)water • (0.03 x 10) x cs x (100 - 23) = 0.5 x 4200 x (23 - 20) • c x 0.3 x 77 = 2100 x 3 • 23.1c = 6300 • c = 6300/23.1 • c = 270J/kgoC
- 76. Question 6 Determine the final temperature of a 0.2 kg mass of hot coffee at 90oC contained in a foam- insulating cup if 0.1 kg of cold water at 10oC is poured into it? Assume the specific heat capacity of coffee is 4000 J/kgoC.
- 77. Solution • cwater = 4200 J/kgoC • ccoffee = 4000 J/kgoC • m2 = 0.1 kg • T2i = 10oC • m1 = 0.2 kg • T1i = 90oC Qgained = Qlost m1ccoffeeT1 = m2cwaterT2 0.2 x 4000 x (90 - Tf)=0.1 x 4200 x (Tf - 10) 72000 - 800 Tf = 420 Tf -4200 1220 Tf = 76200 Tf = 62.5oC
- 78. Question 7 What will be the final temperature reached when a 250 g rod of copper (ccopper = 385 J/kgoC) is taken from a beaker of boiling water and plunged into 100g of water at 20oC contained in another beaker?
- 79. Solution • m1 = 0.25 kg • c1 = 385 J/kgoC • T1i = 100 oC • m2 = 0.1 kg • c2 = 4200 J/kgoC • T2i = 20 oC Qgained = Qlost m1c1T1 = m2c2T2 0.25 x 385 x (100- Tf)=0.1 x 4200 x (Tf - 20) 9625 - 96.25 Tf = 420 Tf - 8400 516.25 Tf = 18025 Tf = 34.9oC
- 80. Vaporisation Evaporation takes place at the surface of a liquid. A change of state from liquid to gas can also take place within the liquid. The gas that forms beneath the surface occurs as bubbles which move up and out into the surrounding air. This is also called boiling. The pressure of the bubbles within the bubble must be great enough to resist the pressure of the liquid water.
- 81. Does evaporation always happen at same speed? Evaporation can be increased by • Increasing temperature (more particles have a higher KE) • Increasing surface área (more particles closer to the surface) • Increasing air flow above the Surface (gives the particles somewhere to go to)
- 82. Latent Heat The thermal energy which a particle absorbs in melting, vaporising or sublimation or gives out in freezing, condensing or sublimating is called Latent Heat because it does not produce a change in temperature. During a change of state, there is no change in temperature until all of the substance has changed state.
- 83. Latent Heat - 2 If we study boiling water and steam that are both at 100oC, they both have the same average kinetic energy. The molecules in steam however, has much more potential energy as they are free to move and are not held together. When water turns to steam, no temperature rise is observed as the energy absorbed goes into increasing the potential energy.
- 84. Water Let us look at what happens when 1.0 kg of water is heated from -20oC where it is ice, until it has become steam at 100oC at 1 atm pressure (1.01 x 105Pa). As heat is added, its temperature increases at the rate of about 1oC for every 2.1 kJ of heat added to the ice. When the temperature reaches 0 oC, the temperature stops rising even though heat is still added. When 2100 J have been added, all the ice has turned to water and temperature is still 0 oC.
- 85. Water - 2 The energy required to change 1 kg of a substance from the solid to liquid state is called the latent heat of fusion (Lf). This also refers to the amount of heat released when a liquid is turned to solid. For water, the Lf = 3.34 x 105 J. The water will now increase in temperature at the rate of 1 oC for every 4.2 kJ of heat added. When the temperature reaches 100 oC, the temperature again remains constant until all of the water is turned to steam.
- 86. Water - 3 The energy required to change 1 kg of a substance from the liquid to gaseous state is called the latent heat of vaporisation (Lv). This also refers to the amount of heat released when a gas is turned to liquid. The heat required to change the state of a substance can also be expressed mathematically. Q = mL
- 87. Definition The quantity of heat energy required to change one kilogram of a substance from one phase to another, without a change in temperature is called the Specific Latent Heat of Transformation. Latent Heat = Q / m in J kg -1
- 88. Types of Latent Heat • Fusion • Vaporisation • Sublimation The latent heat of fusion of a substance is less than the latent heat of vaporisation or the latent heat of sublimation.
- 89. Questions When dealing with questions think about • where the heat is being given out • where the heat is being absorbed • try not to miss out any part
- 90. Question How much heat is required to convert 40 g of ice to water at 0oC?
- 91. Solution Q = mL Q = (4 x 10-2) x (3.34 x 105) Q = 1.3 x 104 J absorbed
- 92. Question 2 Water at 95oC is mixed with an equal mass of ice at 0oC. Find the final temperature achieved.
- 93. Solution Energy lost by water cooling = Energy gained by ice melting + Energy gained by ice warming mcT = mLf + mcT m x 4200 x (95 - Tf) = (m x (3.34 x 105)) + ((m x 4200 x (Tf - 0))
- 94. divide both sides by m. 399000 - 4200 Tf = 334000 + 4200 Tf 8400 Tf = 65000 Tf = 7.7 oC
- 95. Question 3 A large polystyrene pot contains 2 kg of water at 20oC. Steam at 100oC is blown into the water and the temperature reaches 50oC. Find the mass of steam used.
- 96. Solution • m2 = ? • Ti = 100oC • Tf = 50oC • Lv = 2.26 x 106 J kg-1 • m1 = 2 kg • c = 4200 J kg-1 oC-1 • Ti = 20oC • Tf = 50oC
- 97. m1cT = m2Lv + m2cT 2 x 4200 x 30 = m2 x (2.26 x 106) + m2 x 4200 x 50 m2 = (2 x 4200 x 30)/(2.26x106 + 4200 x 50) m2 = 0.1 kg
- 98. Methods of finding Latent Heat To find the latent heat of a substance similar methods are used as for specific heat capacity. The latent heat of fusion of ice can be found by adding ice to water in a calorimeter.
- 99. Apparatus Block of ice Thermometer Calorimeter Water Block of ice Insulation
- 100. The change in temperature is recorded and from this the latent heat of fusion of the ice can be found Energy gained by block melting = Energy lost by liquid and calorimeter mb Lb = mw cw Tw + mc cc Tc the SHC of water and the calorimeter are needed.
- 101. Latent Heat of Vaporisation Insulation Thermometer Heating coil Liquid in Calorimeter To joulemeter or voltmeter and ammeter
- 102. The initial mass of the liquid is recorded The change in temperature is recorded for heating the liquid to boiling The liquid is kept boiling The new mass is recorded Energy supplied by heater = energy to raise temperature of liquid + energy use to vaporise some of the liquid (The calorimeter also needs to be taken in to account. V I t = ml clTl+ me Le + mc ccTc
- 103. Question 4 A 200W immersion heater is used to raise the temperature of water to its boiling point. The heater is left on for 4 minutes after the water boils. What mass of water will be boiled off in this time?
- 104. Solution mLv = Pt m x 2.26 x 106 = 200 x 240 m = 200 x 240/(2.26 x 106) m = 2.12 x 10-2 kg

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