Mechanics & Molecular Kinetic Theory

Contents Mechanics Mechanics Molecular Kinetic Theory Molecular Kinetic Theory

Mechanics Linear Motion: Linear Motion: speed (m/s) = distance (m) speed (m/s) = distance (m) time(s) time(s) velocity (m/s) = displacement (m) time (s) acceleration (m/s 2 ) = change in speed (m/s) time taken (s)

Mechanics Distance vs. Time graph: Distance vs. Time graph:

Mechanics Speed vs. Time graph: Speed vs. Time graph:

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

Mechanics Adding vectors: Adding vectors: And again… And again… + = -=

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

Mechanics Projectiles: 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:  V y = Vsin  V x = Vcos  V y = Vsin  Flight time: t = V iy /g Displacement: X = V x t Max. height: Y = V iy t + ½gt 2

Mechanics Moments: have a direction (clockwise or anti-clockwise) Moments: have a direction (clockwise or anti-clockwise) Moment = force × perpendicular distance (Nm) = (N) x(m) (Nm) = (N) x(m) clockwise moment = anti-clockwise moment (equilibrium) 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 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: 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 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: potential energy = weight × distance moved against gravity (Nm) = (N) x(m) Kinetic Energy: Kinetic Energy: kinetic energy = ½ mass x velocity 2 (J) = (kg) x (m/s 2 )

Heat Capacity Heat capacity (c): quantity of heat required to raise the temperature of a unit mass by 1°K 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 -1 K -1 )× (K) Q = mc delta  specific latent heat: energy to change the state of a unit mass of liquid without a temperature change 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 1 st 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 1 st 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 2 nd Law: Rate of change of momentum is proportional to the total force acting on a body, and occurs in the direction of the force Newton’s 2 nd 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 3 rd Law: If body A exerts a force on body B, body B must exert an equal and opposite force on body A Newton’s 3 rd 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 Conservation of Momentum: Total momentum before = total momentum after Mu 1 + mu 2 = Mv 1 + mv 2 Conservation of Energy: Total energy before = total energy after Conservation of Energy: Total energy before = total energy after ½Mu ½mu 2 2 = ½Mv ½mv 2 2 Elastic collisions: zero energy loss Elastic collisions: zero energy loss Impulse = Force x time (Ns) = (N) x (secs) (Ns) = (N) x (secs)

Ideal Gases Robert Brown investigated the movement of gas particles – 1820s Air particles (O 2 and N 2 ) – too small Observe the motion of smoke grains Smoke grain (speck of reflected light) Light Microscope Glass box

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

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 ) Pressure (Nm -2 ) Temperature (K) Temperature (K) Volume (m 3 ) Volume (m 3 ) Mass (kg) Mass (kg)

Moles In the periodic table: Oxygen = OCarbon = CHelium = He Mass number = bottom number = molar mass Mass number = mass (g) of 1 mole of that substance 6.02x10 23 particles in 1 mole e.g. 1 mole of He has a mass of 4 grams 1 mole of O 2 has a mass of 32 grams Mass (g) = number of moles x molar mass

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

Charles’ Law Relates temperature & volume of the gas Relates temperature & volume of the gas If the gas is compressed: volume decreases, temperature decreases So keeping everything else constant: V/T = constant orV α T V T (C) T (K)

Pressure Law Relates temperature & pressure of the gas Relates temperature & pressure of the gas If the gas is heated: temperature increases, pressure increases So keeping everything else constant: p/T = constant orp α T p T (K) 0

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 -1 K -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 O 2 = 32gmol -1 number of moles, n= 1600g/32gmol -1 = 50 mol

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