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Topic | Discussion | Learning Aids
| 15.1 THERMODYNAMIC SYSTEMS AND THEIR SURROUNDINGS A thermodynamic system is the collection of objects on which attention is being focused, and the surroundings are everything else in the environment. The state of a system is the physical condition of the system, as described by values for physical parameters, often pressure, volume, and temperature. |
Thermal equilibrium | 15.2 THE ZEROTH LAW OF THERMODYNAMICS Two systems are in thermal equilibrium if there is no net flow of heat between them when they are brought into thermal contact. |
Temperature | Temperature is the indicator of thermal equilibrium in the sense that there is no net flow of heat between two systems in thermal contact that have the same temperature. |
Zeroth law of thermodynamics | The zeroth law of thermodynamics states that two systems individually in thermal equilibrium with a third system are in thermal equilibrium with each other. |
| 15.3 THE FIRST LAW OF THERMODYNAMICS The first law of thermodynamics states that due to heat Q and work W, the internal energy of a system changes from its initial value of Ui to a final value of Uf according to |
First law of thermodynamics |

| (15.1)

Sign convention for Q and W | Q is positive when the system gains heat and negative when it loses heat. W is positive when work is done by the system and negative when work is done on the system. The first law of thermodynamics is the conservation-of-energy principle applied to heat, work, and the change in the internal energy. |
Function of state | The internal energy is called a function of state because it depends only on the state of the system and not on the method by which the system came to be in a given state. |
Quasi-static process | 15.4 THERMAL PROCESSES A thermal process is quasi-static when it occurs slowly enough that a uniform pressure and temperature exist throughout the system at all times. |
Isobaric process | An isobaric process is one that occurs at constant pressure. The work W done when a system changes at a constant pressure P from an initial volume Vi to a final volume Vf is |
Isobaric work |

| (15.2)

Isochoric process | An isochoric process is one that takes place at constant volume, and no work is done in such a process. |
Isothermal process | An isothermal process is one that takes place at constant temperature. |
Adiabatic process | An adiabatic process is one that takes place without the transfer of heat. |
Work done as the area under a pressure–volume graph | The work done in any kind of quasi-static process is given by the area under the corresponding pressure-versus-volume graph. |
| 15.5 THERMAL PROCESSES USING AN IDEAL GAS When n moles of an ideal gas change quasi-statically from an initial volume Vi to a final volume Vf at a constant Kelvin temperature T, the work done is |
Work done during an isothermal process |

| (15.3)

| When n moles of a monatomic ideal gas change quasi-statically and adiabatically from an initial temperature Ti to a final temperature Tf, the work done is |
Work done during an adiabatic process |

| (15.4)

Adiabatic change in pressure and volume | During an adiabatic process, and in addition to the ideal gas law, an ideal gas obeys the relation

| (15.5)

where is the ratio of the specific heat capacities at constant pressure and constant volume.
| 15.6 SPECIFIC HEAT CAPACITIES The molar specific heat capacity C of a substance determines how much heat Q is added or removed when the temperature of n moles of the substance changes by an amount :

| (15.6)

For a monatomic ideal gas, the molar specific heat capacities at constant pressure and constant volume are, respectively,
Specific heat capacities of a monatomic ideal gas |

| (15.7)

| (15.8)

| where R is the ideal gas constant. For a diatomic ideal gas at moderate temperatures that do not allow vibration to occur, these values are and . For any type of ideal gas, the difference between CPP and CV is

| (15.10)

Use Self-Assessment Test 15.1 to evaluate your understanding of Sections 15.1–15.6.

The second law of thermodynamics (heat flow statement) | 15.7 THE SECOND LAW OF THERMODYNAMICS The second law of thermodynamics can be stated in a number of equivalent forms. In terms of heat flow, the second law declares that heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. |
| 15.8 HEAT ENGINES A heat engine produces work from input heat that is extracted from a heat reservoir at a relatively high temperature. The engine rejects heat into a reservoir at a relatively low temperature. The efficiency e of a heat engine is |
Efficiency of a heat engine |

| (15.11)

Conservation of energy for a heat engine | The conservation of energy requires that |QH| must be equal to |W| plus |QC|:

| (15.12)

| By combining Equation 15.12 with Equation 15.11, the efficiency of a heat engine can also be written as

| (15.13)

Reversible process | 15.9 CARNOT’S PRINCIPLE AND THE CARNOT ENGINE A reversible process is one in which both the system and its environment can be returned to exactly the states they were in before the process occurred. |
Carnot’s principle | Carnot’s principle is an alternative statement of the second law of thermodynamics. It states that no irreversible engine operating between two reservoirs at constant temperatures can have a greater efficiency than a reversible engine operating between the same temperatures. Furthermore, all reversible engines operating between the same temperatures have the same efficiency. |
A Carnot engine | A Carnot engine is a reversible engine in which all input heat |QH| originates from a hot reservoir at a single Kelvin temperature TH and all rejected heat into a cold reservoir at a single Kelvin temperature TC. For a Carnot engine

| (15.14)

The efficiency eCarnot of a Carnot engine is the maximum efficiency that an engine operating between two fixed temperatures can have:
Efficiency of a Carnot engine |

| (15.15)

| 15.10 REFRIGERATORS, AIR CONDITIONERS, AND HEAT PUMPS Refrigerators, air conditioners, and heat pumps are devices that utilize work |W| to make heat |QC| flow from a lower Kelvin temperature TC to a higher Kelvin temperature TH. In the process (the refrigeration process) they deposit heat |QH| at the higher temperature. The principle of the conservation of energy requires that .
If the refrigeration process is ideal, in the sense that it occurs reversibly, the devices are called Carnot devices and the relation (Equation 15.14) holds.
Coefficient of performance (refrigerator or air conditioner) | The coefficient of performance of a refrigerator or an air conditioner is

| (15.16)

Coefficient of performance (heat pump) | The coefficient of performance of a heat pump is

| (15.17)

Change in entropy | 15.11 ENTROPY The change in entropy for a process in which heat Q enters or leaves a system reversibly at a constant Kelvin temperature T is

| (15.18)

where the subscript R stands for “reversible.”
The second law of thermodynamics (entropy statement) | The second law of thermodynamics can be stated in a number of equivalent forms. In terms of entropy, the second law states that the total entropy of the universe does not change when a reversible process occurs () and increases when an irreversible process occurs (). |
Unavailable work | Irreversible processes cause energy to be degraded in the sense that part of the energy becomes unavailable for the performance of work. The energy Wunavailable that is unavailable for doing work because of an irreversible process is

| (15.19)

where is the total entropy change of the universe and T0 is the Kelvin temperature of the coldest reservoir into which heat can be rejected.
Entropy and disorder | Increased entropy is associated with a greater degree of disorder and decreased entropy with a lesser degree of disorder (more order). |

Use Self-Assessment Test 15.2 to evaluate your understanding of Sections 15.7–15.11.

The third law of thermodynamics | 15.12 THE THIRD LAW OF THERMODYNAMICS The third law of thermodynamics states that it is not possible to lower the temperature of any system to absolute zero () in a finite number of steps. |

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