Engineering Physics Option

B.2 Thermodynamics

Laws

First Law of Thermodynamics

Energy can neither be created nor destroyed, but can be changed from one form to another

If a quantity of energy Q is supplied to a gas, it can either gain internal energy or do work
Q=change in U+W

Second Law of Thermodynamics

Thermal energy always flows spontaneously from a hot to a cold body

Planck

In an irreversible process, the total entropy of an isolated system increases, and in a reversible process, the total entropy of an isolated system remains unchanged

Any process which appears to locally decrease the entropy of a system (a fridge makes air cool) is always accompanied by an increase in entropy elsewhere (the fridge’s coolant pump gets hot)

Clausius

Thermal energy cannot be spontaneously transferred from a cold body to a hot body

Kelvin

In a cyclic system, it is impossible to completely convert heat to work

A consequence of this is that the entire universe will eventually be filled with degraded (useless) heat

Work Done

W = F * d cos(theta)

In a gas cylinder, W = pressure*A * displacement (x)

W = P * change in V

Sign Conventions

Types of Processes

Isothermal

Temperature (and internal energy) remain constant (ΔU = 0)
System must be in contact with a large reservoir (something outside the system that either provides or absorbs heat) and the process must be slow

Isobaric

Pressure remains constant

Isovolumetric

Volume remains constant, no work is done by or on the gas (W = 0)

Adiabatic

No thermal energy is transferred between the gas and its surroundings (Q = 0)
Process must be rapid and the gas must be well-insulated

Entropy

Measure of the “amount of disorder” present in a thermal system

Change in entropy is defined as the change in heat of a system divided by its temperature (when temperature is constant)

Change in S = change in Q/T

Entropy increases when heat is added and decreases when heat is removed

Thermodynamic Cycles

Carnot Cycles

The efficiency of a cycle is equal to the ratio between the useful work done and the energy put into the cycle

ncarnot = 1 - Tcold/Thot

No heat engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same reservoirs

Isothermal expansion, Adaiabtic expansion, Isothermal compression, adiabatic compression

A sequence of processes which change the pressure, volume, and temperature of a gas, but eventually returns it to its initial state

The work done by a thermodynamic cycle is equal to the area enclosed by the shape formed by the cycle on a pV graph

Internal Energy

Internal energy is the sum of the random kinetic energy of the molecules and their total potential energy. Since there are no IMFs in a gas under the kinetic molecular theory, there is no potential energy. Internal energy is equal to total KE of molecules summed.

B.1 Rigid bodies and
rotational dynamics

Moment of inertia

Ability to resist changes to its rotational motion

Sum of the mass of all the particles in an object multiplied by their distance to the axis squared

Rotational analog of mass

Rotational and translational equilibrium

Translational equilibrium when resultant force is 0
Rotational equilibrium when the resultant torque on an object is 0

Conservation of angular momentum

Angular momentum is conserved unless acted upon by an external torque.

The area under a torque-time graph is equal to the change in angular momentum

Equations

Rolling without slipping

Potential energy turns into translational kinetic energy and rotational kinetic energy
Mgh = 1/2Iw^2 + 1/2mv^2

Torque

Rotational force, the component that is perpendicular from the line of action through the point

T=Frsin(theta)

r is distance from force applied to the centre of rotation (point)

Torque is zero if it goes through the axis of rotation

This can be considered any point, meaning torque will be at equilibrium when considering at any point

Clockwise torque opposes counterclockwise rotation
Clockwise can be considered positive
Counterclockwise can be considered negative

Torque from couples (opposite direction, same magniute) cause twice the felt torque, meaning it can be multiplied by two.