General Engineering and Applied Sciences Formulas

GENERAL ENGINEERING AND APPLIED SCIENCES FORMULAS (GEAS) CHEMISTRY Law of definite proportion = % element = (mass element/total mass compound) *100 Boyles Law (P1)(V1)=(P2)(V2) Charles law (V1)/(T1)=(V2)/(T2) Gay-Lussac Law (P1)/(T1)=(P2)/(T2) Combined Gas Law (P1)(V1)/(T1)=(P2)(V2)/(T2) *Always in Kelvin Avogadros Law (V1)/(n1)=(V2)/(n2) ; (R1)/(M1)=(R2)/(M2) *V=volume, n=number of moles, R=gas constant, M=molecular weight Idea gas law PV=nRT *R is constant 27 in calculator = 8.314 J/mol.K = 0.0821 L.atm/mol.K Daltons Partial pressure P(total)=P1+P2+P3…. Grahams law of effusion (rate B)/(rate A) = (√mw A)/( √mw B) = (√Ma)/( √Mb) Molefraction (X) (X) Solute= (solute in MOL)/(solute in MOL + solvent in MOL) (X) Solvent=(solvent in MOL)/(solute in MOL + solvent in MOL) *solvent in MOL=(No. of solution/mass of the solution) Molarity=(n)/(V) *1gram=1mol=6.022x10^23 amu atoms Molality=(moles solute)/(mass solvent in Kg) Normality=(no. of eq. solute)/(solutions in Liter) *no. of eq. solute=(grams)/(eq. weight) *eq. weight=(molecular weight)/(H+ or OH- or No. of POS/NEG charges) Density=(P)/(R)(T) *P=pressure, R=gas constant, T=temperature RMS of molecular mass= √(3(R)(T)/(molarity) Molar Heat Q(system)=Q(cal)+Q(rxn)=0 *burned=heat released *empirical formula divide the subscript by 2 *1 atm=760 torr PHYSICS Frictional force (F)=(µ)(N) Coef. Of kinetic friction (µk)=(F)/(N) Coef. Of static friction (µs)=F(max)/(N) Velocity=(Distance)/(Time) Centripetal Force (Fc) = (m)(Vt)^2/(r) *m=mass, Vt=tangential velocity, r=radius of the curvature *magnitude centripetal=magnitude of centrifugal Universal Gravitational Force = (G)(m1)(m2)/(s)^2 *G= constant no. 39 (N)(m)^2/(kg)^2, m=mass, s=distance of the 2 object Work=(Force)(Distance) Potential Energy=(W)(h) *W=(m)(g), h=height Kinetic Energy = (1/2)(m)(v)^2 Transformation of Potential & Kinetic Energy V=√(2)(g)(h) Transformation of work & kinetic Energy Fs=(1/2)(m)(v)^2 Power=(w)/(t) *w=work, t=time

*1 watt = 1 J/s *1 Hp = 550 ft-lb/s Torque=(P)/(w) *P=power, w=RAD/S Momentum=(m)(V) Impulse=(F)(∆t) =(P2)-(P1) =(mVfinal)-(mVinitial) Force =(mass)(acceleration)/(time) Coef. Of restitution (e)=1 perfectly elastic (e)=0 completely inelastic (e)=(V2a)-(V2b)/(V1b)-(V1a) *Restoring Force = Accelaration 0 a=-(k)(s)/(m) *k=spring constant, s=displacement, m=mass Period (T)=2(pie)√(m/k) Frequency=(1)/(T) Tortion pendulum=2(pie) )√(1/k) *k=moment of tortion Density=(m)/(V) Weight density=(W)/(V) =(Density)(Gravity) Specific gravity=(Density)/(1000 kg/m^3) Surface Tension = (F)/(L) = (W)/(A) *F=force across the line, L=line, W=work done, A=Area Capillarity (Weight Liquid) (h)=(2)(T)(cosΘ)/(radius)(density)(gravity) Buoyant force=(density)(Vs) =(W) *Vs=volume submerge, W=weight *W(submerge)=W(iceberg) *(density)(V)=(density)(V) Bernoulli’s theorem (P1)/(density)(gravity)+(h1)+(V1)^2/2(gravity) = (P2)/(density)(gravity)+(h2)+(V2)^2/2(gravity) Transverse wave=√(T)/(linear density) *T=tension Law of vibrating string under tension (L)=n(wavelength)/(2) *n=no. of segments Longitudinal wave=√(E)/(density) E=modulus of elasticity Soundwave Speed (fluid/Rod)= √(E)/(density) (Gas) = √(э)(gas constant)(Temp) * э=(Cp)/(Cv), Cv=vacuum. Cp=plenun Frequency observer (fo)=(fs)((v)-(vo))/(v)-(Vs) *v=speed of relative medium, vo=speed of observer, vs=speed of source Luminous flux (F)(lumen)=4(pie)(l) *l=intensity (candela) Illuminance (E)=(F)/(A) =(I)(cosΘ)^2/(r)^2 =(I)/(r)^2 =(E1)/(E2)=(r1/r2)^2 *A=Hemisphere Luminance=I(Θ)/A(cosΘ) Mirror Equation: (1)/(p)+(1)/(q)=(2)/(r)

=(1)/(f) *p=object distance, q=image distance, r=radius curvature, f=focal length Magnification of mirror (m)=(q)/(p) Index of refraction (n)=(c)/(v) *c=speed of light, v=speed *focal length=imaginary+real Snells law: n1(sin Θi)=n2(sin Θr) Image position: (n1)/(p)+(n2)/(q1)=(n2-n1)/(R1) *p is always positive Thin lenses: (1)/ (f) = ((n2/n1)-1) (1)/((R1)+(1)/(R2)) *R(+)=Convex (curved outward), R(-)=Concave (curved inward), f(+)=converging, f(-)=diverging *DIVUS=diverging, upright, smaller *if virtual = negative sign (-) Magnefication of Lenses (m)=(p)/(q)