physical processes - MCAT

Vectors and scalars, Translational motion, Force and Newton’s laws of motions, Vector analysis and forces acting on an object, Work and energy, Fluids at rest, Fluids in motion, Gas phase, Kinetic molecular theory of gases, Electrostatics, Current and resistance, Capacitors, Magnetism, Electrochemistry, Sound, Light and electromagnetic radiation, IR and UV/Vis Spectroscopy, 1H-NMR, Thin lenses, Spherical mirrors, Reflection and refraction, Atomic nucleus, Electronic structure, Periodic table, Stoichiometry, Balancing chemical equations, Redox reactions

Newton’s laws of motion

First law: Inertia - Resting objects remain at rest & moving objects remain moving at constant speed in straight line, unless acted upon by an unbalanced force

Second law: F = ma

Third law: Every action (force) has equal & opposite reaction

SI units

• provide for: length, mass, time, electric current, temperature, amount of substance, luminous intensity

length — meter (m)

mass — kilogram (kg)

time — second (s)

electric current — ampere (A)

temperature — kelvin (K)

amount of substance — mole (mol)

luminous intensity — candela (cd)

Work

Transfer of energy, force over a distance

W = Fd cos θ

Centripetal force

force required to keep object in circular motion, F_c = mv² / r

• not a “new force”; is produced by existing force (eg. weight, friction, tension, etc.)

Pressure

Force (applied perpendicularly) over an area

P = F/A

SI unit: Pascal, Pa = N/m²

Atmospheric pressure

1 atm

or

101.325 kPa

Density

• Definition

• symbol and formula

• Density of water

How tightly mass is packed into a given space

ρ = m / V

(ρ = rho)

Density of water = 1000 kg/m³

Hydrostatic pressure

• definition

• formula

Pressure exerted by a fluid at rest due to gravity

P = P₀ + ρgh

P₀ = surface/external pressure

ρ = density of fluid

g gravity

h = height of fluid column above measurement point

Continuity equation

Conservation of mass applied to fluids

ρ₁A₁v₁ = ρ₂A₂v₂ // if density doesn’t change you can ignore ρ

A = Area of pipe cross section

v = velocity of fluid

Bernoulli’s equation

Conservation of energy for fluids

P₁ + ρgh₁ + ½ρv₁² = P₂ + ρgh₂ + ½ρv₂²

Derivation:

W₁ + PE₁ + KE₁ = W₂ + PE₂ + KE₂

• W = Fd = Fvt = F/A * Avt = PV = Pm/ρ

P₁m/ρ + mgh₁ + ½mv₁² = P₂m/ρ + mgh₂ + ½mv₂²

P₁ + ρgh₁ + ½ρv₁² = P₂ + ρgh₂ + ½ρv₂²

Poiseuille’s Law / Hagan-Poiseuille equation

• purpose

• equation & variables

models volumetric flow rate of a viscous liquid through a pipe

V/t = ΔPπR⁴ / 8ηL

V/t = Volume / time = Q = volumetric flow rate

ΔP = change in pressure

R = radius of pipe

η = viscosity

L = length of pipe

Venturi effect

• define

• explain why it happens

If u got a liquid flowing through a pipe, if pipe is constricted then fluid moves faster and pressure (on pipe walls) decreases

• true because conservation of mass / energy — same amount of fluid must pass through a smaller space at the same rate, so must move faster

Ideal Gas Law

• equation

• 5 assumptions

PV = nRT

P = Pressure, V = Volume, n = number of moles, R = Ideal gas constant (8.314 J/Kmol or 0.08206 Latm/Kmol), T = Temperature (K)

Assumptions:

• Negligible volume of particles

• Negligible intermolecular forces

• Constant, random, linear motion until collision

• Collisions are perfectly elastic

• Average Kinetic energy of gas molecules is proportional to absolute temperature only (so all molecular motion ceases if temperature drops to absolute zero, 0 K)

Gases behave more ideally at ____ temperature and ____ pressure (low or high)

high temperature and low pressure

Boyle’s Law, Charles’ Law, Avogadro’s Law

P₁V₁ = P₂V₂

V₁/T₁ = V₂/T₂

V₁/n₁ = V₂/n₂

Standard Temperature and Pressure (STP)

• temperature, pressure, how much volume occupied by 1 mol of gas

Temperature = 0^oC = 273.15 K

Pressure = 1 atm = 101.325 kPa

At STP, 1 mol of gas occupies volume of 22.4 L

Van Der Waals equation

• purpose

• modifications/variables

A modification of the ideal gas law that accounts for non-negligible particle volume and intermolecular forces:

(P + a(n/V)²)(V - bn) = nRT 

a(n/V)² = intermolecular forces decrease pressure 

bn = volume occupied by gas particles (so V - bn = free volume for particles to move in)

a (molecular attraction) and b (molecular volume) are constants with different values for different gases 

Boltzmann’s Constant, k_B

• formula/value

• usage

Boltzmann’s Constant is equal to the ideal gas constant / avogadro’s number

k_B = R / N_A = 1.38 * 10^-23 

Relates temperature and energy: 3/2 k_BT = KE_avg for 1 particle, 3/2 RT = KE_avg for 1 mol

Heat capacity, C

• definition

• formula

• formulas for heat capacity at constant pressure and constant volume

Amount of heat required to change temperature of substance by 1^oC:

C = Q/ΔT heat capacity = heat added / change in temperature

molar heat capacity: C = Q/nΔT

Heat capacity at constant Pressure C_P = 5/2 Nk_B = 5/2 nR (molar heat capacity = 5/2 R) for a monoatomic ideal gas

Heat capacity at constant Volume C_V = 3/2 Nk_B = 3/2 nR (molar heat capacity = 3/2 R) for a monoatomic ideal gas (N = number of atoms or molecules of gas, equal to n * N_A)

Derivations: https://www.khanacademy.org/test-prep/mcat/physical-processes/kinetic-molecular-theory-of-gas/v/heat-capacity-at-constant-volume-and-pressure

Provide definitions and formulae for:

• Electric force

• Electric field

• Electric potential energy

• Electric potential, aka Voltage

Force that 2 charges exert on one another, F_E = kq₁q₂/r²

Measure of force that would be exerted per unit of charge at a certain point, E = kq/r²

Energy associated with separating 2 charges a distance apart, U = kq₁q₂/r

Measure of potential energy per unit charge, V = U/q = kq/r

• k = coulomb’s constant, a proportionality factor (turns result into standard force units)

Relate Current, Resistance and Voltage in a circuit

V = IR

V = Voltage, I = Current, R = Resistance

Equivalent resistance in series vs. in parallel

• provide formulas and briefly justify

Resistors in series: R_eq = R₁ + R₂ + R₃ + …

• Overall voltage must equal sum of voltage drops across each resistor: V_T = V₁ + V₂ + V₃

• Current must be same for all resistors in series, so V/I = V₁/I + V₂/I + V₃/I, therefore R_eq = R₁ + R₂ + R₃

Resistors in parallel: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + …

• Voltage must be same across all resistors in parallel (because they share the same 2 points in the circuit or smth)

• Overall current must equal sum of currents through each resistor

• this means overall conductance equals sum of conductances: G_eq = G₁ + G₂ + G₃

• Conductance is inverse of resistance, so 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

Resistivity and Conductivity

• formula for resistance & relationship between the two

R = ρL/A

ρ = “rho”sistivity, L = Length, A = Area (of cross section)

Conductivity = inverse of resistivity (σ = 1/ρ)

How to determine electrolytic conductivity

Electrolytic conductivity is solution’s ability to conduct current

R = ρL/A

• Measure Resistance of circuit in solution of known resistivity so you can determine value of L/A, which will be constant independent of solution

• Then when you measure Resistance of unknown solution you have L/A value and can calculate ρ

Voltmeters and Ammeters

• Hook up to circuit in series or parallel?

• Should have low or high resistance?

Voltmeters should have high resistance (ideally infinite) and be hooked up in parallel

Ammeters should have low resistance (ideally 0) and be hooked up in series