IB SL Physics Option B

Engineering Physics: Rotational Dynamics and Thermodynamics

Conservation of energy

Conservation of energy

Energy can not be created or destroyed, it just changes form

Angular displacement

a change in angle

Angular velocity

Alt 1: rate of change of angular displacement

Alt 2: change in angular displacement per unit time

Angular acceleration

Alt 1: rate of change of angular velocity

Alt 2: change in angular velocity per unit time

Angular momentum

product of moment of inertia and angular velocity

Conservation of angular momentum

Alt 1: if the net external force acting on a system is zero, the momentum of the system remains constant

Alt 2: for a closed system, the momentum remains constant

Centre of gravity

• point where weight/gravitational force of object

• may be considered / appears to act

Moment of inertia

Alt 1: an object’s ability to resist a change in rotational motion

Alt 2: equivalent of mass in rotational equations

Inertia

the ability of an object to resist linear acceleration

Rotational equilibrium

sum of the torques/moments of the forces is zero

Equilibrium

• sum of forces acting on the object is zero

• sum of torques on the object is zero

Stress

equal to force per unit area

Strain

extension of an object from its original length

Torque (Moment)

• ability of a force to produce rotation

• equal to the product of the magnitude of a force and the perpendicular distance to the axis of rotation

Torque of a couple

• a couple is pair of equal parallel forces that act in opposite directions

• torque of a couple is equal to product of magnitude of a force and perpendicular distance between forces;

Work (for rotational dynamics)

equal to the product of torque and angular displacement parallel to/in the direction of the force

Newton’s first law (for rotational dynamics)

A body remains at rest or at a constant angular velocity unless acted on by a net external torque

Newton’s second law (for rotational dynamics)

• net torque is equal to the product of moment of inertia and angular acceleration

• the rate of change of angular momentum of a body is equal to the net torque acting on the body

Newton’s third law

when two bodies A and B interact, the force that A exerts on B is equal and opposite to the force that B exerts on A

Ideal gas

1: a gas that obeys the universal gas law/ideal gas law at all pressures, volumes and temperatures

Ideal gas assumptions

• large number of identical particles

• particles move in random motion at high speeds

• no intermolecular forces

• all collisions are elastic

• duration of collisions much less than time between collisions

• volume of molecules is negligible to volume of container

Internal energy

sum of random kinetic energy and intermolecular potential energy in the particles of a substance

Temperature

Alt 1: proportional to a measure of the average kinetic energy of the particles of a substance

Alt 2: macroscopic measure of average kinetic energy of particles of a substance

Thermal energy

the non-mechanical transfer of energy between two different bodies as a result of a temperature difference between them

Thermal equilibrium

rate of energy absorption is equal to the rate of energy emission

System

complete set of objects that are under consideration

Surronding

everything that is not part of a system

Open system

a system in which mass can enter and leave

Closed system

a system in which mass cannot enter and leave

Isolated system

a system in which energy cannot enter or leave

Monatomic gas

a gas that consists of particles that have single atoms

State

a system is at a particular state if all the parameters defining the system are given (temperature, pressure, volume)

Thermodynamic process

any process that changes the state of the system

Adiabatic process

• a change in the pressure, volume and temperature of the system

• in which no thermal energy transferred between the system and the surroundings

Isobaric process

a process that takes place at constant pressure

Isochoric (isovolumetric) process

a process that takes place at constant volume

Isothermal process

a process in which temperature remains constant

First law of thermodynamics

• the energy transferred between a system and its surroundings

• is equal to the work done on the system plus the change in internal energy of the system

Second law of thermodynamics

Alt 1: the total entropy of an isolated system never decreases

Alt 2: the total entropy of the universe is always increasing

Alt 3 (Clausius): work is required to be supplied in order for thermal energy to flow from a cold to a hot object

Alt 4 (Kelvin): In a cyclic process, it is impossible to completely convert heat into mechanical energy

Cyclic process

a process in which the initial and final state are the same

Entropy

the measure of disorder in a system

Heat engine

a device that converts thermal energy into mechanical work

Carnot engine

• consists of two isothermal and two adiabatic thermodynamic processes

• no engine can be more efficient than a Carnot engine operating between the same temperatures

Outline how an approximate adiabatic change can be achieved.

• adiabatic means no transfer of heat in or out of the system;

• should be fast;

• can be slow if the system is insulated;

State a reason why a Carnot cycle is of little use for a practical heat engine.

the isothermal processes would have to be conducted very slowly

Some nuclear reactors have a heat exchanger that uses a gas that is kept at constant volume.

Describe how the first and second laws of thermodynamics apply in the operation of the heat exchanger

• no change in volume therefore W = 0;

• When heat is transferred from reactor to gas, internal energy of gas increases;

• When heat is transferred from gas to surroundings, internal energy of gas decreases;

• entropy of the gas increases as energy is transferred from the reactor;

• entropy of the surroundings increases as energy is transferred from the gas;

• entropy of gas decreases on cooling;

• overall the entropy of the total system increases;

State, by reference to energy exchanges, the difference between a heat pump and a heat engine.

• heat pump uses work to transfer thermal energy from a cold to a hot reservoir;

• heat engine transfers thermal energy into work;

When a chicken develops inside an egg, the entropy of the egg and its contents decreases. Explain how this observation is consistent with the second law of thermodynamics.

• the process gives off thermal energy;

• therefore entropy of surroundings increases by a greater factor;

State what happens to the entropy of water as it freezes. Outline how this change in entropy is consistent with the second law of thermodynamics.

• the entropy of water decreases;

• when water freezes it releases energy;

• therefore KE of surrounding air molecules increases;

• therefore, the surroundings are in a more disordered state;

• and entropy of the universe increases;