Thermodynamics

The One Thing

Thermodynamics describes how energy is transferred as heat and work and how these transfers change the state of a system. Its laws establish energy conservation, the direction of spontaneous processes, and the maximum possible efficiency of heat engines.

Reactions, Processes and Experiments

Key Terms

• Thermodynamic system: A specified portion of the universe selected for study.
• Surroundings: Everything outside the thermodynamic system that can interact with it.
• Thermodynamic state: The condition of a system described by variables such as pressure, volume, temperature, and amount of substance.
• State variables: Properties whose values depend only on the present state of the system, such as pressure, volume, temperature, and internal energy.
• Path functions: Quantities whose values depend on the process followed between two states, such as heat and work.
• Thermal equilibrium: A condition in which systems in contact have the same temperature and no net heat flows between them.
• Zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
• Heat: Energy transferred between systems because of a temperature difference; it is represented by $Q$.
• Work: Energy transferred when an external force causes a displacement or when a gas expands or is compressed; for a quasistatic process, $W=\int PdV$.
• Internal energy: The total microscopic kinetic and potential energy of the particles forming a system; it is represented by $U$.
• First law of thermodynamics: Energy is conserved: $Q=\Delta U+W$, where $W$ is work done by the system.
• Equation of state: A relation connecting the state variables of a system; for an ideal gas, $PV=nRT$.
• Isothermal process: A process at constant temperature. For an ideal gas, $\Delta U=0$, so $Q=W$.
• Adiabatic process: A process in which no heat is exchanged with the surroundings, so $Q=0$ and $\Delta U=-W$.
• Isobaric process: A process carried out at constant pressure.
• Isochoric process: A process carried out at constant volume; since $\Delta V=0$, the work done is zero.
• Cyclic process: A process in which the system returns to its initial state, making the net change in internal energy zero.
• Second law of thermodynamics: Heat naturally flows from a hotter body to a colder body, and no heat engine can convert all absorbed heat completely into work.
• Reversible process: An ideal process that can be reversed so that both the system and surroundings return exactly to their initial states.
• Irreversible process: A real process involving effects such as friction, finite temperature differences, turbulence, or free expansion, which cannot be exactly reversed.
• Heat engine: A device that absorbs heat from a high-temperature reservoir, performs work, and rejects some heat to a low-temperature reservoir.
• Efficiency of a heat engine: The fraction of heat absorbed from the source that is converted into work: $\eta =W/Q_H=1-Q_C/Q_H$.
• Refrigerator: A device that uses external work to transfer heat from a low-temperature reservoir to a high-temperature reservoir.
• Coefficient of performance: For a refrigerator, $\mathrm{COP}=Q_C/W$, where $Q_C$ is heat removed from the cold reservoir.
• Carnot engine: An ideal reversible heat engine operating between two temperatures through two isothermal and two adiabatic processes.
• Carnot efficiency: The maximum possible efficiency of an engine working between source temperature $T_H$ and sink temperature $T_C$: $\eta =1-T_C/T_H$, with temperatures measured in kelvin.
• Heat capacity: The heat required to raise the temperature of a body by one kelvin: $C=Q/\Delta T$.
• Molar heat capacities: Heat capacities represented by $C_v$ at constant volume and $C_p$ at constant pressure.
• SI unit of energy: The joule (J), the SI unit of heat, work, and energy.
• Kelvin temperature: The absolute temperature scale required in thermodynamic efficiency formulas: $T(K)=t(°C)+273.15$.

Easily Confused

• State variables and path functions: State variables depend only on the initial and final states, whereas path functions depend on the process followed; internal energy is a state variable, while heat and work are path functions.
• Heat and internal energy: Heat is energy transferred because of a temperature difference, whereas internal energy is energy stored microscopically within the system.
• Isothermal and adiabatic processes: An isothermal process has constant temperature and, for an ideal gas, $\Delta U=0$; an adiabatic process has $Q=0$, so its temperature may change.
• Isobaric and isochoric processes: An isobaric process has constant pressure, whereas an isochoric process has constant volume and therefore zero work.
• Reversible and irreversible processes: A reversible process can restore both system and surroundings exactly to their initial states; an irreversible process cannot.
• Heat engine and refrigerator: A heat engine converts part of absorbed heat into work, whereas a refrigerator uses work to transfer heat from a cold reservoir to a hot reservoir.
• First law and second law: The first law expresses conservation of energy but does not determine heat-flow direction; the second law establishes the natural direction of heat flow and the impossibility of 100-percent heat-engine efficiency.
• Heat-engine efficiency and refrigerator coefficient of performance: Efficiency measures the fraction of $Q_H$ converted into work, whereas COP measures $Q_C$ removed per unit of work supplied.
• Carnot efficiency and practical-engine efficiency: Carnot efficiency is the maximum possible efficiency between two temperatures; a practical engine operating between those temperatures has efficiency less than or equal to Carnot efficiency.
• Constant-pressure work and constant-volume work: At constant pressure, $W=P(V_2-V_1)$; at constant volume, $\Delta V=0$, so $W=0$.

What Gets Asked

• Define a thermodynamic system, surroundings, state, state variables, and path functions; marks are lost by treating heat or work as state variables.
• Apply the first law using the stated sign convention: $Q=\Delta U+W$, where work done by the system is positive; reversing this convention without explanation changes the result.
• Identify isothermal, adiabatic, isobaric, isochoric, and cyclic processes from their defining conditions; common errors include assigning $Q=0$ to an isothermal process or non-zero work to an isochoric process.
• Calculate work from a pressure-volume process using $W={\int }_{V_1}^{V_2}PdV$, $W=P(V_2-V_1)$ for constant pressure, or the area on a pressure-volume diagram; the enclosed cycle area represents net work.
• Calculate heat-engine or Carnot efficiency using $\eta =W/Q_H=1-Q_C/Q_H$ or $\eta =1-T_C/T_H$; temperatures must be converted to kelvin using $T(K)=t(°C)+273.15$.
• Explain why no heat engine can be 100 percent efficient and why real engines are less efficient than or equal to a Carnot engine operating between the same two temperatures; the required rejected heat and the role of irreversibility must be stated.