The First Law of Thermodynamics

Vocabulary flashcards covering key definitions, principles, formulas, and process relations from the lecture notes on the First Law of Thermodynamics.

First law of thermodynamics

The law of energy conservation stating that energy can neither be created nor destroyed and is conserved in a system; it relates the total energy stored in a system to energy transferred via heat and work.

Constant-volume specific heat ($C_v$)

The energy required to raise the temperature of $1\,\text{kg}$ of a substance by $1\,^{\circ}\text{C}$ in an isochoric process, defined mathematically as $C_v = \left(\frac{\partial u}{\partial T}\right)_v$.

Specific heat transfer ($q$)

The amount of heat transfer per unit mass of a substance, given by $q = \frac{Q}{m}$ with units of $\text{kJ/kg}$.

Boundary work

The mechanical work associated with the expansion or compression of a gas performed at the boundary between a system and its surroundings.

Specific boundary work ($w$)

The boundary work done by or on a unit mass of a substance, expressed in units of $\text{kJ/kg}$ or $\text{J/kg}$.

Polytropic process

An expansion or compression process that includes heat transfer, described by the relation $P\mathbb{V}^n = \text{constant}$ or $Pv^n = \text{constant}$, where $n$ is the dimensionless polytropic exponent.

Isobaric process

A thermodynamic process occurring at constant pressure ($P = \text{constant}$), corresponding to a polytropic exponent of $n = 0$.

Isothermal process

A thermodynamic process occurring at constant temperature ($T = \text{constant}$), corresponding to a polytropic exponent of $n = 1$ for an ideal gas.

Isochoric process

A thermodynamic process occurring at constant volume ($v = \text{constant}$), corresponding to a polytropic exponent of $n = \infty$.

Polytropic boundary work ($n \neq 1$)

The boundary work expression valid for both real and ideal gases undergoing a polytropic process where the exponent is not equal to one: ${_1W_2} = \frac{P_2\mathbb{V}_2 - P_1\mathbb{V}_1}{1 - n}$.

Isothermal boundary work for ideal gases ($n = 1$)

The boundary work expression valid specifically for ideal gases in a constant-temperature process: ${_1W_2} = mRT\ln\left(\frac{\mathbb{V}_2}{\mathbb{V}_1}\right) = mRT\ln\left(\frac{P_1}{P_2}\right)$.

First law of thermodynamics for closed systems

The statement that the change in internal energy equals net heat added to the system minus net work done by the system: $\Delta U = U_2 - U_1 = {_1Q_2} - {_1W_2}$.

Control volume (Open system)

A thermodynamic system that always exchanges mass with its surroundings, and may exchange energy with its surroundings in the form of heat and work across its open boundary.

Enthalpy ($H$)

A property essential for energy analysis in open systems, related to mass and specific enthalpy by the equation $H = mh$, with units in $\text{kJ}$ or $\text{J}$.

Constant-pressure specific heat ($C_p$)

The energy required to raise the temperature of $1\,\text{kg}$ of a substance by $1\,^{\circ}\text{C}$ in an isobaric process, defined mathematically as $C_p = \left(\frac{\partial h}{\partial T}\right)_p$.

Specific heat approximation for solids and liquids

The thermodynamic relation for incompressible substances where $C_p \approx C_v$, leading to the approximation $\Delta h \approx \Delta u \approx C_p(T_2 - T_1)$.

Mass flow rate ($\dot{m}$)

The amount of mass flowing through a cross-sectional area per unit of time, defined as $\dot{m} = \frac{dm}{dt} = \rho\dot{\mathbb{V}} = \rho V_{\text{avg}, n}A$, in units of $\text{kg/s}$.

Volume flow rate ($\dot{\mathbb{V}}$)

The volume of fluid passing through a cross-sectional area per unit of time, defined as $\dot{\mathbb{V}} = \frac{d\mathbb{V}}{dt} = \dot{m}v = V_{\text{avg}, n}A$, in units of $\text{m}^3\text{/s}$.

Steady-flow energy equation

The energy conservation expression for an open system operating under steady flow conditions: $\dot{Q}_{cv} + \sum \dot{m}_i \left(h_i + \frac{1}{2}V_i^2 + gz_i\right) = \dot{W}_{cv} + \sum \dot{m}_e \left(h_e + \frac{1}{2}V_e^2 + gz_e\right)$.