4.9: The Second Law of Thermodynamics (Summary)
Key Terms
| Carnot cycle | cycle that consists of two isotherms at the temperatures of two reservoirs and two adiabatic processes connecting the isotherms |
| Carnot engine | Carnot heat engine, refrigerator, or heat pump that operates on a Carnot cycle |
| Carnot principle | principle governing the efficiency or performance of a heat device operating on a Carnot cycle: any reversible heat device working between two reservoirs must have the same efficiency or performance coefficient, greater than that of an irreversible heat device operating between the same two reservoirs |
| Clausius statement of the second law of thermodynamics | heat never flows spontaneously from a colder object to a hotter object |
| coefficient of performance | measure of effectiveness of a refrigerator or heat pump |
| cold reservoir | sink of heat used by a heat engine |
| disorder | measure of order in a system; the greater the disorder is, the higher the entropy |
| efficiency (e) | output work from the engine over the input heat to the engine from the hot reservoir |
| entropy | state function of the system that changes when heat is transferred between the system and the environment |
| entropy statement of the second law of thermodynamics | entropy of a closed system or the entire universe never decreases |
| heat engine | device that converts heat into work |
| heat pump | device that delivers heat to a hot reservoir |
| hot reservoir | source of heat used by a heat engine |
| irreversibility | phenomenon associated with a natural process |
| irreversible process | process in which neither the system nor its environment can be restored to their original states at the same time |
| isentropic | reversible adiabatic process where the process is frictionless and no heat is transferred |
| Kelvin statement of the second law of thermodynamics | it is impossible to convert the heat from a single source into work without any other effect |
| perfect engine | engine that can convert heat into work with 100%100% efficiency |
| perfect refrigerator (heat pump) | refrigerator (heat pump) that can remove (dump) heat without any input of work |
| refrigerator | device that removes heat from a cold reservoir |
| reversible process | process in which both the system and the external environment theoretically can be returned to their original states |
| third law of thermodynamics | absolute zero temperature cannot be reached through any finite number of cooling steps |
Key Equations
| Result of energy conservation | \(W=Q_h−Q_c\) |
| Efficiency of a heat engine | \(e=\frac{W}{Q_h}=1−\frac{Q_c}{Q_h}\) |
| Coefficient of performance of a refrigerator | \(K_R=\frac{Q_c}{W}=\frac{Q_c}{Q_h−_Q}\) |
| Coefficient of performance of a heat pump | \(K_P=\frac{Q_h}{W}=\frac{Q_h}{Q_h−Q_c}\) |
| Resulting efficiency of a Carnot cycle | \(e=1−\frac{T_c}{T_h}\) |
| Performance coefficient of a reversible refrigerator | \(K_R=\frac{T_c}{T_h−T_c}\) |
| Performance coefficient of a reversible heat pump | \(K_P=\frac{T_h}{T_h−T_c}\) |
| Entropy of a system undergoing a reversible process at a constant temperature | \(ΔS=\frac{Q}{T}\) |
| Change of entropy of a system under a reversible process | \(ΔS=S_B−S_A=∫^B_AdQ/T\) |
| Entropy of a system undergoing any complete reversible cyclic process | \(∮dS=∮\frac{dQ}{T}=0\) |
| Change of entropy of a closed system under an irreversible process | \(ΔS≥0\) |
| Change in entropy of the system along an isotherm | \(\lim_{T→0}(ΔS)_T=0\) |
Summary
4.2 Reversible and Irreversible Processes
- A reversible process is one in which both the system and its environment can return to exactly the states they were in by following the reverse path.
- An irreversible process is one in which the system and its environment cannot return together to exactly the states that they were in.
- The irreversibility of any natural process results from the second law of thermodynamics.
4.3 Heat Engines
- The work done by a heat engine is the difference between the heat absorbed from the hot reservoir and the heat discharged to the cold reservoir, that is, \(W=Q_h−Q_c\).
- The ratio of the work done by the engine and the heat absorbed from the hot reservoir provides the efficiency of the engine, that is, \(e=W/Q_h=1−Q_c/Q_h\).
4.4 Refrigerators and Heat Pumps
- A refrigerator or a heat pump is a heat engine run in reverse.
- The focus of a refrigerator is on removing heat from the cold reservoir with a coefficient of performance \(K_R\).
- The focus of a heat pump is on dumping heat to the hot reservoir with a coefficient of performance \(K_P\).
4.5 Statements of the Second Law of Thermodynamics
- The Kelvin statement of the second law of thermodynamics: It is impossible to convert the heat from a single source into work without any other effect.
- The Kelvin statement and Clausius statement of the second law of thermodynamics are equivalent.
4.6 The Carnot Cycle
- The Carnot cycle is the most efficient engine for a reversible cycle designed between two reservoirs.
- The Carnot principle is another way of stating the second law of thermodynamics.
4.7 Entropy
- The change in entropy for a reversible process at constant temperature is equal to the heat divided by the temperature. The entropy change of a system under a reversible process is given by \(ΔS=∫^B_AdQ/T\).
- A system’s change in entropy between two states is independent of the reversible thermodynamic path taken by the system when it makes a transition between the states.
4.8 Entropy on a Microscopic Scale
- Entropy can be related to how disordered a system is—the more it is disordered, the higher is its entropy. In any irreversible process, the universe becomes more disordered.
- According to the third law of thermodynamics, absolute zero temperature is unreachable.