25 cardsECAT Pakistan
ECAT Engineering Formulas
Calculus rules, conic properties, mechanics equations, thermodynamics constants and chemical principles for UET ECAT.
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Product Rule of Differentiation
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Terms in this deck (25)
1
Product Rule of Differentiation
*d/dx [u v] = u dv/dx + v du/dx**.
2
Quotient Rule of Differentiation
*d/dx [u / v] = (v du/dx - u dv/dx) / v^2*.
3
Integration by Parts Formula
*integral (u dv) = u v - integral (v du)**.
4
Point-to-Line Perpendicular Distance
*d = |Ax0 + By0 + C| / sqrt(A^2 + B^2)*.
5
Ellipse Eccentricity Formula
e = c / a = sqrt(a^2 - b^2) / a (with 0 < e < 1).
6
Sum of Infinite Geometric Progression
S_inf = a / (1 - r) for common ratio |r| < 1.
7
Standard Parabola Focus and Directrix
For y^2 = 4ax: focus at (a, 0), directrix line x = -a.
8
Vector Cross Product Magnitude
*|a x b| = |a| |b| sin(theta)*; represents area of spanned parallelogram.
9
Fluid Continuity Equation
*A1 v1 = A2 v2* for steady incompressible fluid flow.
10
Bernoulli's Equation
*P + (1/2) rho v^2 + rho g h = constant* along a streamline.
11
Torque and Angular Momentum Relation
*tau = I alpha = dL / dt**, rotational analogue of Newton's second law.
12
Adiabatic Process PV Relation
*P V^gamma = constant and T V^(gamma - 1) = constant* (gamma = C_p / C_v).
13
Carnot Refrigerator Coefficient of Performance
COP = T_C / (T_H - T_C), with temperatures in Kelvin.
14
Motional EMF Formula
*E = B v L sin(theta)** for a conductor moving across magnetic flux.
15
LC Circuit Resonant Frequency
*f_0 = 1 / (2 pi sqrt(L C))**.
16
Brewster's Law for Polarizing Angle
tan(theta_B) = n2 / n1; reflected light is completely linearly polarized.
17
Energy Stored in a Capacitor
*U = (1/2) C V^2 = (1/2) Q V = Q^2 / (2C)*.
18
Van der Waals Real Gas Equation
*[P + a (n/V)^2] [V - nb] = n R T**.
19
Root-Mean-Square Molecular Speed
*v_rms = sqrt(3 R T / M)*.
20
Nernst Equation at 298 K
*E = E° - (0.0592 / n) log10(Q)** for an n-electron transfer reaction.
21
Henderson-Hasselbalch Equation
pH = pKa + log10([conjugate base] / [weak acid]).
22
Faraday's Law of Electrolysis
*m = (M I t) / (z F)**, where F = 96,500 C/mol.
23
Solubility Product for AxBy Salt
*K_sp = [A^(y+)]^x [B^(x-)]^y = x^x y^y s^(x+y)**.
24
Monomers of Nylon 6,6
Adipic acid (hexanedioic acid) and hexamethylenediamine (1,6-diaminohexane).
25
Friedel-Crafts Acylation Electrophile
Acylium ion (R-C#O+), generated by treating RCOCl with anhydrous AlCl3.