Glossary of engineering

${\displaystyle y'+P(x)y=Q(x)y^{n}\,}$

${\displaystyle n}$

${\displaystyle n\neq 0}$

${\displaystyle n\neq 1}$

${\displaystyle k={\frac {R}{N_{\text{A}}}}.}$.

${\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}$

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} T}}={\frac {L}{T\,\Delta v}}={\frac {\Delta s}{\Delta v}},}$

${\displaystyle \mathrm {d} P/\mathrm {d} T}$

${\displaystyle L}$

${\displaystyle T}$

${\displaystyle \Delta v}$

${\displaystyle \Delta s}$

${\displaystyle \oint {\frac {\delta Q}{T_{surr}}}\leq 0,}$

where ${\displaystyle \delta Q}$ is the infinitesimal amount of heat absorbed by the system from the reservoir and ${\displaystyle T_{surr}}$ is the temperature of the external reservoir (surroundings) at a particular instant in time. In the special case of a reversible process, the equality holds.[103] The reversible case is used to introduce the entropy state function. This is because in a cyclic process the variation of a state function is zero. In words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir.[104] Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around.[105] The generalized "inequality of Clausius"[106]

${\displaystyle dS>{\frac {\delta Q}{T_{surr}}}}$

${\displaystyle 1~{\text{C}}=1~{\text{A}}\cdot 1~{\text{s}}}$

Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

${\displaystyle 1~{\text{C}}=1~{\text{F}}\cdot 1~{\text{V}}}$

The coulomb is equivalent to the charge of approximately 6.242×10¹⁸ (1.036×10⁻⁵ mol) protons, and −1 C is equivalent to the charge of approximately 6.242×10¹⁸ electrons.

${\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}}$,

where k_e is Coulomb's constant (k_e ≈ 9×10⁹ N m² C⁻²), q₁ and q₂ are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).

• an applied force (the deformation energy in this case is transferred through work) or
• a change in temperature (the deformation energy in this case is transferred through heat).

The first case can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or torsion (twisting).

${\displaystyle \rho ={\frac {m}{V}}}$

${\displaystyle w(x)}$

${\displaystyle V(x)=-\int w(x)\,dx}$

The internal moment M(x) is the integral of the internal shear:

${\displaystyle M(x)=\int V(x)\,dx}$ = ${\displaystyle -\int [\int w(x)\ \,dx]dx}$

The angle of rotation from the horizontal, ${\displaystyle \theta }$, is the integral of the internal moment divided by the product of the Young's modulus and the area moment of inertia:

${\displaystyle \theta (x)={\frac {1}{EI}}\int M(x)\,dx}$

Integrating the angle of rotation obtains the vertical displacement ${\displaystyle \nu }$:

${\displaystyle \nu (x)=\int \theta (x)dx}$.

96485.33212... C mol⁻¹.[164]

This constant has a simple relation to two other physical constants:

${\displaystyle F\,=\,eN_{A}}$

where

e = 1.602176634×10⁻¹⁹ C;[165]

N_A = 6.02214076×10²³ mol⁻¹.[166]

• If two non-collinear members meet in an unloaded joint, both are zero-force members.
• If three members meet in an unloaded joint of which two are collinear, then the third member is a zero-force member.

Reasons for Zero-force members in a truss system

• These members contribute to the stability of the structure, by providing buckling prevention for long slender members under compressive forces
• These members can carry loads in the event that variations are introduced in the normal external loading configuration.