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Home , Ideal gas law

CHAPTER 12 The Laws of

Units

• The First Law of Thermodynamics • Thermodynamic Processes and the First Law • Human and the First Law • The Second Law of Thermodynamics – Introduction • Engines • Refrigerators, Air Conditioners, and Heat Pumps • and the Second Law of Thermodynamics • Order to Disorder • Unavailability of ; Heat Death • Evolution and Growth; “Time’s Arrow” • Statistical Interpretation of Entropy and the Second Law • Thermal Pollution and Global Warming

Thermodynamics is the name given to the study of processes in which energy is transferred as heat and as . A system is any object or set of objects and everything else will be referred to as its “environment”. A is one for which no enters or leaves (but energy may be exchanged with the environment). An open system mass may enter or leave (as well as energy). Many systems, including plants and animals, are open systems since they exchange materials (food, , waste products) with the environment. Many systems we study in physics are closed systems.

First Law of Thermodynamics

• The First Law of Thermodynamics tells us that the of a system can be increased by – Adding energy to the system – Doing work on the system • There are many processes through which these could be accomplished – As long as energy is conserved The internal energy of a system is defined as the sum total of all the energy of the of the system. We would expect that the internal energy of a system would be increased if work were done on the system, or if heat were added to it. Similarly the internal energy would be decreased if heat flowed out of the system or if work were done by the system on something else.

The change in internal energy of a closed system will be equal to the energy added to the system minus the work done by the system on its surroundings. UQW   This is the law of , written in a form useful to systems involving heat transfer.

1 Example 1: Using the first law: An amount of heat equal to 2500J is added to a system, and 1800J of work is done on the system. (a) What is the change in internal energy of the system? UQW  

UJJJJJ 2500  (  1800 )  2500  1800  4300 because 1800J done on the system equals -1800J done by the system. (b) What would be the internal energy change if 2500J of heat is added to the system and 1800J of work is done by the system? UQW  

Heat is still being added to the system, so Q = +2500J, but now the work is being done by the system. UJJJ 2500  1800  700

Work in Thermodynamic Processes – Assumptions

• Dealing with a • Assumed to be in thermodynamic equilibrium – Every part of the gas is at the same – Every part of the gas is at the same • law applies

Work in a

• The gas is contained in a cylinder with a moveable piston. • The gas occupies a V and exerts pressure P on the walls of the cylinder and on the piston.

• A is applied to slowly compress the gas – The compression is slow enough for all the system to remain essentially in thermal equilibrium • W = - P ΔV – This is the work done on the gas

• When the gas is compressed – ΔV is negative – The work done on the gas is positive • When the gas is allowed to expand – ΔV is positive – The work done on the gas is negative • When the volume remains constant – No work is done on the gas

2 Thermodynamic Processes and the First Law

An is one where the temperature does not change.

A process called an isothermal process (from the Greek meaning “same temperature”) is an idealized process that is carried out at constant temperature. If the system is an ideal gas, then PV = nRT, so for constant temperature PV = constant. Thus the process follows a curve as shown in the PV diagram

An is one where there is no heat flow into or out of the system.

An adiabatic process is one in which no heat is allowed to flow into or out of the system: Q = 0. This situation can occur if the system is extremely well insulated, or the process happens so quickly that heat – which flows slowly – has no time to flow in or out. In a diesel engine, the air-fuel mixture is rapidly compressed adiabatically by a factor of 15 or more; the temperature rise is so great that the mixture ignites spontaneously.

An (a) occurs at constant pressure; an isovolumetric one (b) at constant volume.

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An isobaric process is one in which the pressure is kept constant.

An isochoric or isovolumetric process is one in which the volume does not change.

If the pressure is constant, the work done is the pressure multiplied by the change in volume:

In an isometric process, the volume does not change, so the work done is zero.

If the pressure is kept constant during a process (isobaric), the work done is easily calculated. If the gas (to the right) expands slowly against the piston, the work done by the gas to raise the piston is the force F times the distance d. But the force is just the pressure P of the gas times the area A of the piston, F = PA thus, W Fd  PAd or W  P  V

For processes where the pressure varies, the work done is the area under the P-V curve.

Example 2: First law in isobaric and isochoric processes. An ideal gas is slowly compressed at a constant pressure of 2.0atm from 10.0L to 2.0L. This process is represented as the path B to D. Heat is then added to the gas, holding the volume constant, and the pressure and are allowed to rise until the temp reaches its original value (A to D).

4 (a) Calculate the total work done by the gas in the process BDA. The work is done only in the first part, the compression (BD).

W P  V (2.0 x 105 N / m 2 )(2.0 x 10 3 m 3  10.0 x 10 3 m 3 )

3 1.6xJ 10 From D to A no work is done (V 0) ; so the total work done by the gas is 1.6xJ 103 , where the minus means that 1.6xJ 103 of work is done on the gas.

(a) Calculate the total heat flow into the gas. Since the temperature at the beginning and at the end of the process is the same, there is no change in internal energy U 0 Since Q is negative it means that 1600J of heat flows out of the gas.

Human Metabolism and the First Law

The metabolic rate is the rate at which internal energy is transformed in the body.

A great many energy-transforming processes occur within an organism, and they are referred to as metabolism. We can apply the first law of thermodynamics, UQW  

To an organism, work W is done by the body in its various activities, and if this is not to result in a decrease in body’s internal energy (and temperature), energy must somehow be added to compensate. The body’s internal energy is not maintained by a heat flow of heat Q into the body.

Normally, the body is at a higher temperature than its surroundings, so heat flows out of the body. Its source of energy is the internal energy (chemical and potential) stored in foods. In an open system, such as an animal, internal energy itself can flow into or out of the system. The intake of food increases the total internal energy U in the body. This energy eventually goes into work and heat flow from the body according to the first law.

5 The Second Law of Thermodynamics – Introduction

The absence of the process illustrated above indicates that conservation of energy is not the whole story. If it were, movies run backwards would look perfectly normal to us!

The second law of thermodynamics is a statement about which processes occur and which do not. There are many ways to state the second law; here is one: Heat can flow spontaneously from a hot object to a cold object; it will not flow spontaneously from a cold object to a hot object.

Heat Engines

It is easy to produce using work, but how does one produce work using thermal energy? This is a ; mechanical energy can be obtained from thermal energy only when heat can flow from a higher temperature to a lower temperature. We will discuss only engines that run in a repeating cycle; the change in internal energy over a cycle is zero, as the system returns to its initial state. The high temperature reservoir transfers an amount of heat QH to the engine, where part of it is transformed into work W and the rest, QL, is exhausted to the lower temperature reservoir. Note that all three of these quantities are positive. The basic idea behind any heat engine is that mechanical energy can be obtained from thermal energy only when heat is allowed to flow from a high temperature to a low temperature. In the process, some of the heat can then be transformed to mechanical work. The high and low temperatures are called the operating temperatures of the engine.

A steam engine is one type of heat engine.

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Steam engines are of two types, each making use of steam heated by combustion of coal, oil, or gas (or nuclear energy). In the reciprocating type the heated steam passes through the intake valve and expands against a piston, forcing it to move. In a steam turbine everything is essentially the same, except that the reciprocating piston is replaced by rotating turbine that resembles a paddlewheel with many sets of blades. Most electricity today is generated by using steam turbines.

The internal combustion engine is a type of heat engine as well.

In an internal combustion engine, the high temperature is achieved by burning the gasoline-air mixture in the cylinder itself. The efficiency of the heat engine is the ratio of the work done to the heat input:

Using conservation of energy to eliminate W, we find:

7 The heat input QH must equal the work done plus the heat that flows out at the low temperature

QL .

Example 3: Car efficiency An automobile engine has an efficiency of 20% and produces an average of 23,000J of mechanical work per second during operation. How much heat is discharged from this engine per second?

QL WJ23,000 5 1 e  0.80 e W/ QHH Q    1.15 x 10 J QH e 0.20

54 QLH0.80 Q  (0.80)(1.15 x 10 J )  9.2 x 10 J

The engine discharges 9.2x 104 J / s 92,000 watts

Sadi Carnot

• 1796 – 1832 • French Engineer • Founder of the science of thermodynamics • First to recognize the relationship between work and heat

Heat Engines

The Carnot engine was created to examine the efficiency of a heat engine. It is idealized, as it has no friction. Each leg of its cycle is reversible. The consists of: • Isothermal expansion • Adiabatic expansion • Isothermal compression • Adiabatic compression

8 Carnot Cycle

Carnot Cycle, A to B

• A to B is an isothermal expansion at temperature Th • The gas is placed in contact with the high temperature reservoir • The gas absorbs heat Qh • The gas does work WAB in raising the piston

Carnot Cycle, B to C • B to C is an adiabatic expansion • The base of the cylinder is replaced by a thermally nonconducting wall • No heat enters or leaves the system • The temperature falls from Th to Tc • The gas does work WBC

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Carnot Cycle, C to D

• The gas is placed in contact with the cold temperature reservoir at temperature Tc • C to D is an isothermal compression • The gas expels energy QC • Work WCD is done on the gas

Carnot Cycle, D to A

• D to A is an adiabatic compression • The gas is again placed against a thermally nonconducting wall – So no heat is exchanged with the surroundings • The temperature of the gas increases from TC to Th • The work done on the gas is WCD

Heat Engines

For an ideal reversible engine, the efficiency can be written in terms of the temperature:

From this we see that 100% efficiency can be achieved only if the cold reservoir is at , which is impossible. Real engines have some frictional losses; the best achieve 60-80% of the Carnot value of efficiency.

Example 4: Steam engine efficiency. A steam engine operates between 500o C and 270o C . What is the maximum possible efficiency of the engine? First change the temperature to .

TKTK773 and 543 HL

543K exideal 1   0.30( 100%)  30% 773K The exhaust temperature is still high, 270o C .

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Example 5: A phony claim? An engine manufacturer makes the claim that their heat input per second of their engine is 9.0kJ at 375K. The heat output per second is 4.0kJ at 225K. Is this possible? QQ 9.0kJ 4.0 kJ exHL  0.56( 100%)  56% Q9.0 kJ H The maximum possible efficiency is given by Carnot as:

TTHL 375KK 225 exideal   0.40( 100%)  40% TKH 375

At normal temperatures, a 100% efficient engine is not possible. Only if the exhaust temperature were at absolute zero could 100% efficiency be obtained. Reaching absolute zero is a practical (as well as theoretical) impossibility. Thus no device is possible whose sole effect is to transform a given amount of heat completely into work.

Refrigerators, Air Conditioners, and Heat Pumps

These appliances can be thought of as heat engines operating in reverse. By doing work, heat is extracted from the cold reservoir and exhausted to the hot reservoir.

Refrigerator performance is measured by the coefficient of performance (COP):

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A heat pump can heat a house in the winter:

Example 5: Heat Pump A heat pump has a coefficient of performance of 3.0 and is rated to do work at 1500W. (a) How much heat can be added to a room per second?

Q COPxW (3.0)(1500 J )  4500 J H It can pour heat into the room at a rate of 4500J per second or at a rate of 4500W.

(b) If the heat pump were turned around to act as an air conditioner in the summer, what would you expect its coefficient of performance to be, assuming all else stays the same?

QQWJJJLH  4500  1500  3000 The coefficient of performance as an air conditioner would be Q 3000J COP L   2.0 WJ1500

Lord (1824-1907)

British Physicist and Mathematician. Born William Thomson in Belfast, Kelvin was the first to propose the use of an absolute scale of temperature. His study of Carnot’s theory led to the idea that energy cannot pass spontaneously from a colder object to a hotter; this principle is known as the second law of thermodynamics.

12 Entropy and the Second Law of Thermodynamics

Definition of the change in entropy S when an amount of heat Q is added:

Another statement of the second law of thermodynamics: The total entropy of an never decreases.

Rudolf Clausius (1822-1888)

German physicist born with the name Rudolf Gottlieb was one of the founders of thermodynamics. By his restatement of Sadi Canot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis.

Example 6: Entropy change in melting. An ice cube of mass 60-g is taken from a storage compartment at 0o C and placed in a paper cup. After a few minutes, exactly half of the mass of the ice cube has melted, becoming water at 0o C . Find the change in entropy of the ice/water. The heat required to melt 30g of ice is found from the of fusion.

Q mL (30 g )(79.7 cal / g )  2400 cal Q2400 cal S    8.8 cal / K TK273

Order to Disorder

Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law: Natural processes tend to move toward a state of greater disorder. Example: If you put milk and sugar in your coffee and stir it, you wind up with coffee that is uniformly milky and sweet. No amount of stirring will get the milk and sugar to come back out of .

Another example: when a tornado hits a building, there is major damage. You never see a tornado approach a pile of rubble and leave a building behind when it passes. Thermal equilibrium is a similar process – the uniform final state has more disorder than the separate temperatures in the initial state.

13 Unavailability of Energy; Heat Death

Another consequence of the second law: In any natural process, some energy becomes unavailable to do useful work.

If we look at the universe as a whole, it seems inevitable that, as more and more energy is converted to unavailable forms, the ability to do work anywhere will gradually vanish. This is called the heat death of the universe.

Perpetual Motion Machines

• A perpetual motion machine would operate continuously without input of energy and without any net increase in entropy • Perpetual motion machines of the first type would violate the First Law, giving out more energy than was put into the machine • Perpetual motion machines of the second type would violate the Second Law, possibly by no exhaust • Perpetual motion machines will never be invented

14 CHAPTER 13 – 14 – 15 TEMPERATURE – HEAT – THERMODYNAMICS CONCEPTS

1. A temperature reading of absolute zero for a system would mean that the system’s internal energy is at a minimum.

2. As the absolute temperature of a gas increases, the average kinetic energy of the gas molecules increases.

3. For object A to have a higher absolute temperature than object B, object A must have a higher average internal kinetic energy.

4. The minimum average kinetic energy of the molecules in a substance occurs at a temperature of 0 K.

5. The minimum internal energy of an object would occur at a temperature of -273oC.

6. The graph on the right represents the relationship between the temperature of a gas and the average kinetic energy of the molecules of the gas. The temperature represented at point X is approximately -273oC.

7. The graph that best shows the relationship between the average kinetic energy of a sample of gas and the absolute temperature of the gas is D.

8. The graph that best represents the relationship between the average kinetic energy of the molecules of an ideal gas and the absolute temperature of the gas is C.

15 9. The graph that best represents the relationship between the Kelvin temperature scale and the Celsius temperature scale is A.

10. Two metal blocks are placed in an insulated container. If there is a net flow of heat between the blocks, they must have different initial temperatures.

11. The graph on the right represents the temperature of 2.0 kg of a material as a function of the heat added to the substance. During the BC and DE intervals shown is when the average of the molecules of the material increasing

12. The sum of the kinetic and potential of an object’s molecules is called the object’s internal energy.

13. The internal energy of water depends on its temperature, mass, and .

14. A crystalline solid at a temperature below its melting point is heated at a constant rate to a temperature above its melting point. The graph that best represents the average internal kinetic energy of the substance as a function of heat added is B.

15. The graph that best represents the relationship between the heat absorbed (Q) by a solid and its temperature (T) is B.

16 16. Rock salt is thrown on icy pavement to make roadways safer for driving in winter. This process works because the dissolved salt lowers the freezing point of water.

17. Compared to the freezing point of pure water, the freezing point of a salt-water solution is lower.

18. When a block of ice at zero degrees Celsius melts, the ice absorbs from its environment. As the ice is melting, the temperature of the block remains the same.

19. Water with the highest boiling point occurs in diagram C.

20. Increasing the external pressure on a sample of water will increase its boiling point and decrease its freezing point.

21. When a car is driven over snow, the snow under the tires may melt because the pressure of the tires lowers the melting point of the snow.

22. As pressure is applied to a snowball, the melting point of the snow decreases.

23. The graph to the right represents the variation in temperature as 1.0 kg of a gas, originally at 200oC, loses heat at a constant rate of 2.0 kJ per minute and eventually becomes a solid at room temperature. The phase has the greatest specific heat.

24. Molecules transfer energy through collisions is a statement consistent with the kinetic theory of ideal .

26. Pressure is a characteristic of a gas sample that results from the collision of gas molecules with the walls of its container.

25. According to the , an ideal gas of low has relatively large distances between molecules.

27. According to kinetic theory, pressure exerted by a gas is caused by the collision of gas molecules with the walls of the container.

28. As the number of gas molecules in a rigid container at constant temperature is increased, the pressure on the walls of the container increases.

17 29. As the pressure of a fixed mass of a gas is increased at constant temperature, the density of the gas increases.

30. As the absolute temperature of a fixed mass of an ideal gas is increased at constant pressure, the volume occupied by the gas increases.

31. If the pressure of a fixed mass of an ideal gas is doubled at a constant temperature, the volume of the gas will be halved.

32. The graph that best represents the relationship between pressure (P) and absolute temperature (T) for a fixed mass of an ideal gas in a rigid container is C.

33. The graph that best represents the relationship between volume and absolute temperature for an ideal gas at constant pressure is C.

34. A quantitative measure of the disorder of a system is called entropy.

35. In an ideal gas, entropy is a measure of the disorder of the molecules.

36. When a student drops a beaker, it shatters, spreading randomly shaped pieces of glass over a large area of the floor. According to the second law of thermodynamics, the measure of the disorder of this system is known as entropy.

37. According to the second law of thermodynamics, the phenomenon that will most likely occur is the universe will steadily become more disordered.

38. According the second law of thermodynamics, as time passes, the total entropy in the universe increases.

39. Gas to liquid is the phase change that represents a decrease in entropy.

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40. In order to double the average speed of the molecules in a given sample of gas, the temperature (measured in Kelvin’s) must quadruple.

41. The temperature of an ideal gas increases from 2oC to 4oC while remaining at constant pressure. The volume of the gas increases slightly.

42. Both the pressure and volume of a given sample of an ideal gas double. This means that its temperature in Kelvin’s must quadruple.

43. If the pressure acting on an ideal gas at constant temperature tripled, its volume is reduced to one-third.

44. A container is filled with a mixture of and oxygen gases. A thermometer in the container indicates that the temperature is 22oC. The helium molecules have the greater average speed because they are less massive.

45. A container is filled with a mixture of helium and oxygen gases. A thermometer in the container indicates that the temperature is 22oC. The helium and oxygen have the same kinetic energy because the temperatures are the same.

46. Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen, compared to hydrogen is the same.

47. Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the oxygen molecules are moving at ¼ the speed.

48. A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. The average speed of the molecules in the sample does not change.

49. The number of molecules in one of a substance is the same for all substances.

50. The surface water temperature on a large, deep lake is 3oC. A sensitive temperature probe is lowered several meters into the lake. The probe will record a temperature warmer than 3oC.

51. Super saturation occurs in air when the relative is 100% and the temperature decreases.

52. If you double both the pressure and absolute temperature of an ideal gas, the volume of the gas will not change.

53. According to Boyle’s Law, PV=constant for a given temperatures. As a result, an increase in volume corresponds to a decrease in pressure. This happens because the molecules strike the container wall less often.

54. A container holds N molecules of an ideal gas at a given temperature. If the number of molecules in the container is increased to 2N with no change in temperature or volume, the pressure in the container remains constant.

55. The average molecular kinetic energy of a gas can be determined by knowing only the temperature of the gas.

56. It is well known fact that water has a higher specific than iron. Now, consider equal of water and iron that are initially in thermal equilibrium. The same amount of heat, 30 , is added to each. They are no longer in thermal equilibrium; the iron is warmer.

57. A chunk of ice (T = -20oC) is added to a thermally insulated container of cold water (T = 0oC). In the container some of the water freezes and the chunk of ice becomes larger.

58. A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat capacity of aluminum is more than double that of Copper. Without knowing the mass of each it is impossible to tell which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium.

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59. A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat capacity of aluminum is more than double that of Copper. Both experience the same size gain or loss of heat during the time the system takes to reach thermal equilibrium.

60. Phase changes occur as the temperature remains the same.

61. Turning up the flame under a pan of boiling water causes the water to boil away faster.

62. If you double the absolute temperature of an object, it will radiate energy 16 times faster.

63. Convection can occur only in and gases.

64. By the radiation heat transfer mechanism does the sun, warm the earth.

65. By the conduction heat transfer mechanism does one end of an iron , become hot when the other end is placed in a flame.

66. If you double the thickness of a wall built from a homogeneous material, the rate of heat loss for a given temperature difference across the thickness will become one-half its original value.

67. When a vapor condenses heat energy leaves the substance.

68. Evaporation of moisture from the skin extracts heat from the body. This best explains why sweating is important to humans in maintaining suitable body temperature.

69. The internal energy of an ideal gas depends on its temperature.

70. The process shown to the right on the p – V graph is an isobaric expansion.

71. The process shown to the right on the p – V graph is isochoric.

72. The process shown above on the T – V graph is an isothermal compression.

73. A gas is allowed to expand at constant pressure as heat is added to it. This process is isobaric.

74. A gas is confined to a rigid container that cannot expand as heat energy is added to it. This process is isochoric.

75. A gas is expanded to twice its original volume with no change in its temperature. This process is isothermal.

76. A gas is quickly compressed in an isolated environment. During the event, the gas exchanged no heat with its surroundings. This process is adiabatic.

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77. When the first law of thermodynamics, QUW   , is applied to an ideal gas that is taken through an isothermal process, U 0 .

78. When the first law of thermodynamics, , is applied to an ideal gas that is taken through an adiabatic process, Q  0 .

79. An ideal gas is compressed to one-half its original volume during an isothermal process. The final pressure of the gas increases to twice its original pressure.

80. When water freezes, the entropy of the water decreases.

81. Heat will transfer naturally from a hot reservoir to a cold reservoir.

82. The second law of thermodynamics leads us to conclude that disorder in the universe is increasing with the passage of time.

83. If the theoretical efficiency of a Carnot engine is to be 100%, the heat sink must be at absolute zero.

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