Mod 2
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Module-2 : Latent heat Latent Heat: Latent heat describes the amount of energy in the form of heat that is required for a material to undergo a change of phase. A solid consists of molecules that are tightly bound to each other by forces acting between them. Energy must be supplied in the form of heat to overcome these forces. As the bonding forces weaken, groups of molecules break free, and as more heat is supplied the solid changes into a liquid, in which small groups of molecules constantly break apart, and reform and groups slide freely past each other. While this is happening, the temperature of the substance remains unchanged. All of the heat energy is used in loosening the bonds between molecules. If still more energy is applied, it has the effect of making the groups of molecules move faster. When they move faster they strike harder against any object with which they come into contact. It is the speed of motion of molecules that a thermometer measures as temperature. Once a solid has melted to become a liquid, the application of additional heat raises the temperature of the liquid. When a liquid is cooled, its molecules lose energy and move more slowly, and the temperature of the liquid falls. When their energy falls to a certain level the molecules start bonding together. This requires less energy than moving about, and so heat energy is released as the liquid solidifies. The temperature of the substance remains unchanged, but the surrounding medium is warmed by the release of energy. For a phase change, the heat liberated or absorbed is given by
Q = ml − − − − − − − − − − − − − − − − − (1) where l is the latent heat of fusion (latent heat of melting) or latent heat of vaporization. How much heat does it take to 80 cal / gram absorbed 540 cal / gram absorbed get water to change state? If the water is at a temperature of 100 degrees C (that is, the Gas boiling point, or 212 degrees F) it Solid Water vapor Liquid Ice takes an additional 540 calories Water of heat to convert one gram of water from the liquid state to the vapor state. When the vapor 80 cal / gram released 540 cal / gram released converts to the liquid state, 540 calories of energy will be released per gram of water. If you are converting solid water (ice) to liquid water at 0 degrees C, it will require about 80 calories of heat to melt one gram of ice, and the 80 calories will be released when the liquid water is frozen to the solid state.
Latent Heat of Fusion: 1
Fusion is the change of state from solid to liquid. In the process of fusion, the molecule absorbs energy. This energy is latent heat. When a solid substance changes from the solid phase to the liquid phase, energy must be supplied in order to overcome the molecular attractions between the constituent particles of the solid. This energy must be supplied externally, normally as heat, and does not bring about a change in temperature. The units of heat of fusion are usually expressed as joules per mole (the SI units) or calories per gram or Btu per pound-mole
l fusion = 80 cal/gm or 334 kJ/kg The specific latent heat of fusion is defined as "The specific latent heat of fusion of a substance is the amount of heat required to convert unit mass of the solid into the liquid without a change in temperature." The specific latent heat of fusion of ice at 0 ºC, for example, is 334 kJ.kg -1. This means that to convert 1 kg of ice at 0 ºC to 1 kg of water at 0 ºC, 334 kJ of heat must be absorbed by the ice. Conversely, when 1 kg of water at 0 ºC freezes to give 1 kg of ice at 0 ºC, 334 kJ of heat will be released to the surroundings.
Latent Heat of Vaporization: Evaporation is the change of state from liquid to vapor. In the process of evaporation, the molecule absorbs energy. This energy is latent heat. How did you make the water evaporate? Probably you added heat. You might have set it out in the sun, or possibly put it over a fire. To make water evaporate, you put energy into it. The individual molecules in the water absorb that energy, and get so energetic that they break the hydrogen bonds connecting them to other water molecules. They become molecules of water vapor.
lvaporization = 540 cal/gm or 2260 kJ/kg The definition of the specific latent heat of vaporization is 'The specific latent heat of vaporization is the amount of heat required to convert unit mass of a liquid into the vapour without a change in temperature." For water at its normal boiling point of 100 ºC, the latent specific latent heat of vaporization is 2260 kJ.kg -1. This means that to convert 1 kg of water at 100 ºC to 1 kg of steam at 100 ºC, 2260 kJ of heat must be absorbed by the water. Conversely, when 1 kg of steam at 100 ºC condenses to give 1 kg of water at 100 ºC, 2260 kJ of heat will be released to the surroundings.
Heating / Cooling Curves: The diagram on the left shows the uptake of heat by 1 kg of water, as it passes from ice at -50 ºC to steam at temperatures above 100 ºC, affects the temperature of the sample.
2
A: Rise in temperature as ice absorbs heat. B: Absorption of latent heat of fusion. C: Rise in temperature as liquid water absorbs heat. D: Water boils and absorbs latent heat of vaporization. E: Steam absorbs heat and thus increases its temperature. The above is an example of a heating curve. One could reverse the process, and obtain a cooling curve. The flat portions of such curves indicate the phase changes.
Heat Calculation:
2g of ice at - 6 OC
+
Add 2x2.1x6 J
Q= mCΔT = 25.2 J
↓ 2g of ice at - 0 OC
+
Add 2x336 J
Q= mL = 672 J
↓ 2g of water at - 0 OC
+
Add 2x4.2x100 J
Q= mCΔT = 840 J
↓ 2g of water at - 100 OC
+
Add 2x2260 J
↓ 2g of steam at 100 OC
3
Q= mL
Problem Sheet 1. One kilogram of ice at -15 oC is heated until the whole of it evaporates. How much heat is required? Latent heat of fusion of ice = 80 cal/gm and that of steam = 540 cal/gm. 2. Calculate the energy released when (i) 20 g water at 100 °C and (ii) 20 g of steam at 100 °C are each spilt on the hand. Take the specific heat capacity of water to be 4200 J kg –1 K –1 and the specific latent heat of vaporization of water to be 2.2 MJ kg–1. Assume that the temperature of the skin is 33 °C. 3. It takes 15 minutes for an electric kettle to heat a certain quantity of water from 0 oC to the boiling point 100 o C. It requires 80 minutes to turn all the water at 100 oC into steam. Determine the latent heat of steam. 4. A refrigerator converts 60 g of water at 25 oC into ice at -30 oC in one hour. Determine the quantity of heat removed per minute. (Specific heat of ice = 0.5) 5. (i) How much heat is needed to take ice of mass m = 720 g at -10 oC to a liquid state at 15 oC? (ii) If we supply the ice with a total heat only 210 kJ, what then is the final state of the water? 6. In a cold storage ice melts at the rate of 3 kg per hour when the external temperature is 28 oC. Find the minimum power output of the motor used to run the refrigerator just to prevent melting of ice. 7. In an industrial process 10 kg of water per hour is to be heated from 20 0 C to 80 0 C.To do this, steam at 150 0 C is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at 900 C. How many kg of steam is required per hour? Specific heat of steam= 1cal /gm, Latent heat of steam =540 cal/gm 8. An aluminium container of mass 100 gm contains 200 gm of ice at -200C.Heat is added to the system at the rate of 100 calories per seconds. What is the temperature of the system after 4 minutes? Specific heat of aluminium = 0.2 cal g-1(=0C)-1 9. A lead bullet at 100 0 C strikes a steel plate and melts. What was its minimum speed? Specific heat of lead =0.03, latent heat = 5cal/gm and melting point = 327 0 C. The heat produced is shared equally between the plate and the bullet. 10. An ice cube at 00C is dropped into ground and melts to water at 0 0C.If all the kinetic energy of the ice went into heating it, from what height did it fall? 11. When a falling hailstone is at a height of 2.0 km its mass is 2.50 g. What is its potential energy? Assuming that all of this potential energy is converted to latent heat during the fall, calculate the mass of the hailstone on reaching the ground. Take the specific latent heat of fusion of ice to be 3.36 × 10 5 J kg–1 and the acceleration due to gravity to be 9.81 ms–2.
4
Q = ml − − − − − − − − − − − − − − − − − (1) where l is the latent heat of fusion (latent heat of melting) or latent heat of vaporization. How much heat does it take to 80 cal / gram absorbed 540 cal / gram absorbed get water to change state? If the water is at a temperature of 100 degrees C (that is, the Gas boiling point, or 212 degrees F) it Solid Water vapor Liquid Ice takes an additional 540 calories Water of heat to convert one gram of water from the liquid state to the vapor state. When the vapor 80 cal / gram released 540 cal / gram released converts to the liquid state, 540 calories of energy will be released per gram of water. If you are converting solid water (ice) to liquid water at 0 degrees C, it will require about 80 calories of heat to melt one gram of ice, and the 80 calories will be released when the liquid water is frozen to the solid state.
Latent Heat of Fusion: 1
Fusion is the change of state from solid to liquid. In the process of fusion, the molecule absorbs energy. This energy is latent heat. When a solid substance changes from the solid phase to the liquid phase, energy must be supplied in order to overcome the molecular attractions between the constituent particles of the solid. This energy must be supplied externally, normally as heat, and does not bring about a change in temperature. The units of heat of fusion are usually expressed as joules per mole (the SI units) or calories per gram or Btu per pound-mole
l fusion = 80 cal/gm or 334 kJ/kg The specific latent heat of fusion is defined as "The specific latent heat of fusion of a substance is the amount of heat required to convert unit mass of the solid into the liquid without a change in temperature." The specific latent heat of fusion of ice at 0 ºC, for example, is 334 kJ.kg -1. This means that to convert 1 kg of ice at 0 ºC to 1 kg of water at 0 ºC, 334 kJ of heat must be absorbed by the ice. Conversely, when 1 kg of water at 0 ºC freezes to give 1 kg of ice at 0 ºC, 334 kJ of heat will be released to the surroundings.
Latent Heat of Vaporization: Evaporation is the change of state from liquid to vapor. In the process of evaporation, the molecule absorbs energy. This energy is latent heat. How did you make the water evaporate? Probably you added heat. You might have set it out in the sun, or possibly put it over a fire. To make water evaporate, you put energy into it. The individual molecules in the water absorb that energy, and get so energetic that they break the hydrogen bonds connecting them to other water molecules. They become molecules of water vapor.
lvaporization = 540 cal/gm or 2260 kJ/kg The definition of the specific latent heat of vaporization is 'The specific latent heat of vaporization is the amount of heat required to convert unit mass of a liquid into the vapour without a change in temperature." For water at its normal boiling point of 100 ºC, the latent specific latent heat of vaporization is 2260 kJ.kg -1. This means that to convert 1 kg of water at 100 ºC to 1 kg of steam at 100 ºC, 2260 kJ of heat must be absorbed by the water. Conversely, when 1 kg of steam at 100 ºC condenses to give 1 kg of water at 100 ºC, 2260 kJ of heat will be released to the surroundings.
Heating / Cooling Curves: The diagram on the left shows the uptake of heat by 1 kg of water, as it passes from ice at -50 ºC to steam at temperatures above 100 ºC, affects the temperature of the sample.
2
A: Rise in temperature as ice absorbs heat. B: Absorption of latent heat of fusion. C: Rise in temperature as liquid water absorbs heat. D: Water boils and absorbs latent heat of vaporization. E: Steam absorbs heat and thus increases its temperature. The above is an example of a heating curve. One could reverse the process, and obtain a cooling curve. The flat portions of such curves indicate the phase changes.
Heat Calculation:
2g of ice at - 6 OC
+
Add 2x2.1x6 J
Q= mCΔT = 25.2 J
↓ 2g of ice at - 0 OC
+
Add 2x336 J
Q= mL = 672 J
↓ 2g of water at - 0 OC
+
Add 2x4.2x100 J
Q= mCΔT = 840 J
↓ 2g of water at - 100 OC
+
Add 2x2260 J
↓ 2g of steam at 100 OC
3
Q= mL
Problem Sheet 1. One kilogram of ice at -15 oC is heated until the whole of it evaporates. How much heat is required? Latent heat of fusion of ice = 80 cal/gm and that of steam = 540 cal/gm. 2. Calculate the energy released when (i) 20 g water at 100 °C and (ii) 20 g of steam at 100 °C are each spilt on the hand. Take the specific heat capacity of water to be 4200 J kg –1 K –1 and the specific latent heat of vaporization of water to be 2.2 MJ kg–1. Assume that the temperature of the skin is 33 °C. 3. It takes 15 minutes for an electric kettle to heat a certain quantity of water from 0 oC to the boiling point 100 o C. It requires 80 minutes to turn all the water at 100 oC into steam. Determine the latent heat of steam. 4. A refrigerator converts 60 g of water at 25 oC into ice at -30 oC in one hour. Determine the quantity of heat removed per minute. (Specific heat of ice = 0.5) 5. (i) How much heat is needed to take ice of mass m = 720 g at -10 oC to a liquid state at 15 oC? (ii) If we supply the ice with a total heat only 210 kJ, what then is the final state of the water? 6. In a cold storage ice melts at the rate of 3 kg per hour when the external temperature is 28 oC. Find the minimum power output of the motor used to run the refrigerator just to prevent melting of ice. 7. In an industrial process 10 kg of water per hour is to be heated from 20 0 C to 80 0 C.To do this, steam at 150 0 C is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at 900 C. How many kg of steam is required per hour? Specific heat of steam= 1cal /gm, Latent heat of steam =540 cal/gm 8. An aluminium container of mass 100 gm contains 200 gm of ice at -200C.Heat is added to the system at the rate of 100 calories per seconds. What is the temperature of the system after 4 minutes? Specific heat of aluminium = 0.2 cal g-1(=0C)-1 9. A lead bullet at 100 0 C strikes a steel plate and melts. What was its minimum speed? Specific heat of lead =0.03, latent heat = 5cal/gm and melting point = 327 0 C. The heat produced is shared equally between the plate and the bullet. 10. An ice cube at 00C is dropped into ground and melts to water at 0 0C.If all the kinetic energy of the ice went into heating it, from what height did it fall? 11. When a falling hailstone is at a height of 2.0 km its mass is 2.50 g. What is its potential energy? Assuming that all of this potential energy is converted to latent heat during the fall, calculate the mass of the hailstone on reaching the ground. Take the specific latent heat of fusion of ice to be 3.36 × 10 5 J kg–1 and the acceleration due to gravity to be 9.81 ms–2.
4
