Mechanics & Molecular Kinetic Theory

Contents Mechanics Molecular Kinetic Theory

Mechanics Linear Motion: speed (m/s) = distance (m) time(s) velocity (m/s) = displacement (m) time (s) acceleration (m/s2) = change in speed (m/s) time taken (s)

Mechanics Distance vs. Time graph:

Mechanics Speed vs. Time graph:

Mechanics Forces and Vectors: Examples: - scalar = speed (1 quantity… no direction) - vector = velocity (2 quantities… speed & direction) Other vector quantities: - displacement - momentum - force Vectors can be added to produce a resultant quantity

Mechanics Adding vectors: And again… + = - =

Mechanics Angular mechanics: Fx = F cos  Fy = F sin  Weight always faces downwards Force on road is perpendicular to motion

Mechanics Projectiles: - an object upon which the only force acting is gravity e.g. bullet - once projected, its motion depends on its inertia Initial velocity vectors: Vx = Vcos  Vy = Vsin  Flight time: t = Viy/g Displacement: X = Vxt Max. height: Y = Viyt + ½gt2

Mechanics Moments: have a direction (clockwise or anti-clockwise) Moment = force × perpendicular distance (Nm) = (N) x (m) clockwise moment = anti-clockwise moment (equilibrium) - this is used to find the centre of gravity Work = Force × distance moved in the direction of the force (Nm or J) = (N) x (m) - When work is done, energy is transferred - Energy comes in many forms; some kinds of energy can be stored, while others cannot - Energy is always conserved

Mechanics Power: rate at which energy is transferred power (W) = energy (J) / time (secs) energy (work done) = force x distance So… power = (force x distance) / time (d/t = speed) power = force x speed P = Fv

Mechanics Energy: the ability to do work. When work is done, energy is transferred - Some kinds of energy can be stored, while others cannot - Energy in a system is always conserved Potential Energy: potential energy = weight × distance moved against gravity (Nm) = (N) x (m) Kinetic Energy: kinetic energy = ½ mass x velocity2 (J) = (kg) x (m/s2)

Heat Capacity Heat capacity (c): quantity of heat required to raise the temperature of a unit mass by 1°K Heat flow = m × c × delta T (J) = (kg) × (Jkg-1K-1) × (K) Q = mc delta  specific latent heat: energy to change the state of a unit mass of liquid without a temperature change - fusion, or melting - vaporisation, or boiling delta Q = ml

Newton’s Laws Newton’s 1st Law: An object continues in its state of rest or uniform motion in a straight line, unless it has an external force acting on it Newton’s 2nd Law: Rate of change of momentum is proportional to the total force acting on a body, and occurs in the direction of the force F = ma Newton’s 3rd Law: If body A exerts a force on body B, body B must exert an equal and opposite force on body A

Collisions Conservation of Momentum: Total momentum before = total momentum after Mu1 + mu2 = Mv1 + mv2 Conservation of Energy: Total energy before = total energy after ½Mu12 + ½mu22 = ½Mv12 + ½mv22 Elastic collisions: zero energy loss Impulse = Force x time (Ns) = (N) x (secs)

Ideal Gases Robert Brown investigated the movement of gas particles – 1820s Air particles (O2 and N2) – too small Observe the motion of smoke grains Microscope Glass box Smoke grain (speck of reflected light) Light

Ideal Gases Pick 1 grain & follow its movement - Jerky, erratic movement due to collisions with (the smaller) air molecules Microscope Glass box Smoke grain (speck of reflected light) Light

Ideal Gases STP = standard temperature and pressure T = 273K, p = 1 atm Average speed of air molecules = 400ms-1 Pressure - in terms of movement of particles Air molecule bounces around inside, colliding with the various surfaces Each collision exerts pressure on the box

If we have a box filled with gas: We can measure: Pressure (Nm-2) Temperature (K) Volume (m3) Mass (kg)

Moles In the periodic table: Oxygen = O Carbon = C Helium = He 8 6 2 16 16 12 12 4 4 Mass number = bottom number = molar mass Mass number = mass (g) of 1 mole of that substance 6.02x1023 particles in 1 mole e.g. 1 mole of He has a mass of 4 grams 1 mole of O2 has a mass of 32 grams Mass (g) = number of moles x molar mass

Boyle’s Law Relates pressure & volume of the gas If the gas is compressed: volume decreases, pressure increases So keeping everything else constant: pV = constant or p α 1/V p p 1/V V

Charles’ Law Relates temperature & volume of the gas If the gas is compressed: volume decreases, temperature decreases So keeping everything else constant: V/T = constant or V α T V -300 -200 -100 0 100 T (C) 100 200 300 400 T (K)

Pressure Law Relates temperature & pressure of the gas If the gas is heated: temperature increases, pressure increases So keeping everything else constant: p/T = constant or p α T p T (K)

which relates the 4 properties mentioned earlier Ideal Gas Equation The 3 gas laws can be written as a single equation which relates the 4 properties mentioned earlier pV = nRT where R = universal gas constant = 8.31Jmol-1K-1 n, number of moles = mass (g) / molar mass (g mol-1) e.g. how many moles are there in 1.6kg of oxygen? molar mass of O2 = 32gmol-1 number of moles, n = 1600g/32gmol-1 = 50 mol

Summary Vectors Projectiles Moments Power, Energy & Work Energy Changes Heat Capacity Newton’s 3 Laws Collisions Molecular Kinetic Theory