Isothermal and Adiabatic Processes & Heat Engines

Vocabulary flashcards covering isothermal and adiabatic processes, heat engines, the second law of thermodynamics, Carnot efficiency, Clausius' theorem, and related historical/experimental concepts.

Quasistatic process

A process performed sufficiently slowly so that the system remains in equilibrium throughout the entire process and passes seamlessly from one equilibrium state to the next, each differing by an infinitesimal change in system parameters.

Isothermal expansion

An expansion of a system that occurs at constant temperature, resulting in $ΔT = 0$ and $ΔU = 0$ for an ideal gas.

Adiathermal

Meaning 'without flow of heat'; a system bounded by adiathermal walls is thermally isolated.

Adiabatic process

A thermodynamic change or expansion that is both adiathermal (no heat flow, $d\bar{Q} = 0$) and reversible.

Adiabatic lapse rate

The rate of decrease of temperature with height in an atmosphere given by $\frac{\text{d}T}{\text{d}z} = -\frac{M_{\text{molar}}g}{C_p}$, which equals $9.7\,\text{K/km}$ for dry air.

Clausius' statement of the second law of thermodynamics

'No process is possible whose sole result is the transfer of heat from a colder to a hotter body.'

Kelvin's statement of the second law of thermodynamics

'No process is possible whose sole result is the complete conversion of heat into work.'

Heat engine

A system operating a cyclic process that converts heat into work.

Carnot cycle

A thermodynamic cycle consisting of two reversible adiabats and two reversible isotherms for an ideal gas, operating between two heat reservoirs at temperatures $T_{\text{h}}$ and $T_{\ell}$.

Efficiency of a heat engine

The ratio of work output to heat input, defined as $\eta = \frac{W}{Q_{\text{h}}}$.

Efficiency of a Carnot engine

The efficiency of a Carnot engine operating between hot reservoir temperature $T_{\text{h}}$ and cold reservoir temperature $T_{\ell}$, given by $\eta_{\text{Carnot}} = \frac{T_{\text{h}} - T_{\ell}}{T_{\text{h}}} = 1 - \frac{T_{\ell}}{T_{\text{h}}}$.

Carnot's theorem

'Of all the heat engines working between two given temperatures, none is more efficient than a Carnot engine.'

Efficiency of a refrigerator

The ratio of heat extracted from the cold reservoir to work input, defined as $\eta = \frac{Q_{\ell}}{W}$, which for a Carnot refrigerator is $\eta_{\text{Carnot}} = \frac{T_{\ell}}{T_{\text{h}} - T_{\ell}}$.

Efficiency of a heat pump

The ratio of heat added to the hot reservoir to work input, defined as $\eta = \frac{Q_{\text{h}}}{W}$, which for a Carnot heat pump is $\eta_{\text{Carnot}} = \frac{T_{\text{h}}}{T_{\text{h}} - T_{\ell}}$.

Clausius' theorem

States that for any closed cycle, $\oint \frac{d\bar{Q}}{T} \le 0$, where equality necessarily holds for a reversible cycle.

Rüchhardt's apparatus

An experimental apparatus consisting of a ball of mass $m$ oscillating inside a tube of cross-sectional area $A$ connected to a gas container of volume $V$, used to measure $\gamma$.

Historical steam and gas engines

Early engine designs including (a) Hero's engine (rotational steam toy), (b) Newcomen's engine (atmospheric steam piston engine), and (c) Stirling's engine (operated by repeated heating and cooling of a sealed gas).

Otto cycle

The four-stroke cycle used in internal combustion engines with efficiency $1 - r^{1-\gamma}$, where $r = \frac{V_1}{V_2}$ is the compression ratio.

Thermal reservoir

A body sufficiently large that it has an effectively infinite heat capacity, allowing heat to be continuously added or extracted without changing its temperature.

Perpetual motion machine of the second kind

A hypothetical machine that produces the exact same amount of energy as it uses and continues running indefinitely by converting all waste heat back into mechanical work, violating the second law of thermodynamics.