Formulas

Question 1

What is the formula for Coefficient of performance (CPR)?

Answer 1

CPR = KW / (ρAt)

CPR: Coefficient of performance; K: Constant; W: Work done; ρ: Density; A: Area; t: Time

Question 2

What is the formula for Voltage difference (ΔV)?

Answer 2

ΔV = (V₂² - V₁²) - (RT / nF) ln([M₁ⁿ⁺] / [M₂ⁿ⁺])

ΔV: Voltage difference; V₁, V₂: Potential; R: Gas constant; T: Temperature; n: Number of electrons; F: Faraday’s constant; M₁ⁿ⁺, M₂ⁿ⁺: Concentrations of ions

Question 3

What is the formula for Rate of reaction (r)?

Answer 3

r = i / nF

r: Rate of reaction; i: Current; n: Number of electrons; F: Faraday’s constant

Question 4

What is the formula for Voltage (V)?

Answer 4

V = IR

V: Voltage; I: Current; R: Resistance

Question 5

What is the formula for Resistivity (ρ)?

Answer 5

ρ = RA / l

ρ: Resistivity; R: Resistance; A: Cross-sectional area; l: Length

Question 6

What is the formula for Conductivity (σ)?

Answer 6

σ = 1 / ρ

σ: Conductivity; ρ: Resistivity

Question 7

What is the formula for Current density (J)?

Answer 7

J = σε

J: Current density; σ: Conductivity; ε: Electric field

Question 8

What is the formula for Electric field (ε)?

Answer 8

ε = V / l

ε: Electric field; V: Voltage; l: Length

Question 9

What is the formula for Conductivity in terms of charge carriers (σ)?

Answer 9

σ = n|e|μₑ + p|e|μₕ

σ: Conductivity; n, p: Charge carrier densities; e: Electron charge; μₑ, μₕ: Mobilities of electrons and holes

Question 10

What is the formula for Total resistivity (ρ_total)?

Answer 10

ρ_total = ρₜ + ρᵢ + ρ_d

ρ_total: Total resistivity; ρₜ: Temperature-dependent resistivity; ρᵢ: Intrinsic resistivity; ρ_d: Defect resistivity

Question 11

What is the formula for Temperature-dependent resistivity (ρₜ)?

Answer 11

ρₜ = ρ₀ + αT

ρₜ: Resistivity; ρ₀: Base resistivity; α: Temperature coefficient; T: Temperature

Question 12

What is the formula for Heat capacity (c)?

Answer 12

c = dQ / dT

c: Heat capacity; dQ: Heat added; dT: Change in temperature

Question 13

What is the formula for Linear expansion (l_f)?

Answer 13

(l_f - l₀) / l₀ = α_l (T_f - T₀)

l_f: Final length; l₀: Initial length; α_l: Linear expansion coefficient; T_f: Final temperature; T₀: Initial temperature

Question 14

What is the formula for Volume change (ΔV)?

Answer 14

ΔV / V₀ = α_v ΔT

ΔV: Volume change; V₀: Initial volume; α_v: Volume expansion coefficient; ΔT: Change in temperature

Question 15

What is the formula for Heat flux (q)?

Answer 15

q = -k (dT / dx)

q: Heat flux; k: Thermal conductivity; dT/dx: Temperature gradient

Question 16

What is the formula for Heat transfer (Q)?

Answer 16

Q = q * A

Q: Heat transfer; q: Heat flux; A: Area

Question 17

What is the formula for Heat transfer in terms of mass (Q)?

Answer 17

Q = mcΔT

Q: Heat transfer; m: Mass; c: Specific heat capacity; ΔT: Temperature change

Question 18

What is the formula for Rate of reaction in terms of concentration change?

Answer 18

rate of reaction = -(1/a)(ΔA/Δt) = (1/b)(ΔB/Δt)

Rate of reaction; a, b: Stoichiometric coefficients; ΔA, ΔB: Change in concentration; Δt: Change in time

Question 19

What is the formula for Reaction rate (Rate)?

Answer 19

Rate = k[A]ᵐ[B]ⁿ

Rate: Reaction rate; k: Rate constant; [A], [B]: Concentrations of reactants; m, n: Reaction orders

Question 20

What is the formula for Rate constant (k)?

Answer 20

k = Ae^(-Ea/RT)

k: Rate constant; A: Pre-exponential factor; Ea: Activation energy; R: Gas constant; T: Temperature

Question 21

What is the formula for Concentration at time t ([A]_t)?

Answer 21

[A]_t = [A]_0 e^(-kt)

[A]_t: Concentration at time t; [A]_0: Initial concentration; k: Rate constant; t: Time

Question 22

What is the formula for Concentration at time t in reciprocal form (1 / [A]_t)?

Answer 22

1 / [A]_t = kt + 1 / [A]_0

[A]_t: Concentration at time t; [A]_0: Initial concentration; k: Rate constant; t: Time