IB SL Physics Option B

Engineering Physics: Rotational Dynamics and Thermodynamics

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;

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• 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;