### Calculating the Operating & Fuel Costs of Systems

1. Calculate the Load Requirements of the System

2. Evaluate the Energy Source and Unit Price

3. Explore the Equipment Efficiency

**Heat Transfer**

Conduction: the heat loss/gain depends linearly on:

Exposed surface area

Temperature difference

Wall/roof/window construction and material

q = (Area x ΔT)/ ΣR; ΣR = R1+R2+R3.. [(m² • °C) / W]

If R (resistance) is not available for a specific thickness, use k (conductivity): R = L / k. Or if tables contain C (conductance): C = 1 / R

Convection: occurring on exposed surfaces, depends on the geometry and fluid motion

Overall heat transfer coefficient: U = 1 / ΣR_total

Heat flow equation: q = U • A • ΔT

**Physics****:**

**Physics**

**:**

The simplest possible ways (defined laws) to describe the workings of Nature (behaviours).

The branches of Physics include the Classical:

Mechanics

Thermodynamics

Electromagentism

Waves (Accoustics)

Optics (Light)

Further growing fields include: Particle Physics, Nuclear Physics, Relativity and Quantum Reality.

### Mechanics:

### The way objects move and interact with their environments when subjected to external forces.

**Speed: **the change in an objects position over time.

**Velocity: **speed in a particular direction, a vector quantity having magnitude and direction.

**Acceleration:** the rate of change of the velocity over time.

*Newton's *Laws of Motion (Classical Physics)

**1**^{st}

States that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

**2**^{nd}

Pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

Force = mass * acceleration [ N = kg * (m/s²) ]

**3**^{rd}

For every action, there is an equal and opposite reaction.

**Energy**: an object's or system's capacity to do work: W = F • d [ Joules = Newtons • meter]

Conservation of energy principle: during an interaction, energy can change from one form to another, while the total amount of energy remains the same; energy cannot be created nor destroyed.

Types of Energy we mainly encounter:

**Potential energy**- due to an objects (or molecules) position/arrangement: U = m•g•h

**Kinetic energy**- due to an objects (or molecules) motion/velocity: K = 1/2•m•v²

**Thermal energy**- due to kinetic energy of molecules measured through temperature: Q = m•c•ΔT

**Power: **the rate at which energy is expended [ Joules / second = Watts ]

**Machines:** a device that provides a mechanical advantage (MA), reducing the force needed to do a certain amount of work. Simple machines include levers, incline planes (wedge), wheels & axles, pulleys and the screw.

**Thermodynamics**:

**Thermodynamics**:

Thermodynamics is the study of heat in motion. From the Greek words therme (heat) and dynamis (power).

Heat is the transfer of energy from a hot body to a colder one. This kinetic energy can be transfered in 3 ways (known as **Heat Transfer**): conduction, convection & radiation.

**Conduction:** involves energy moving from hot parts to colder parts of an object through vibration of atoms and molecules as they bump into eachother. This energy transfer is easier in solids as their molecules are closer packed together, but varies which solids are better thermal conductors.

**Convection:** the movement of high energy molecules in liquids and gases (sparser arrangement) allows parts to increase volume and become less dense. This rises above the denser parts replacing the colder parts and creating a convective current.

**Radiation:** is emitted by every object as thermal radiation (light). Radiation can travel through the vacuum of space, as does all the heat reaching us from the sun.

**Heat Capacity **is the amount of heat to be supplied to an object to produce a unit change in its temperature. Ex. the specific heat capacity of water is 4,200 Joules per kg-Kelvin, meaning 4.2 kJ are required to raised the temperature of 1 kg by 1 Kelvin (or 1° Celsius). Metals have a low heat capacity and increase temperature rapidly, while wood has a high heat capacity and increases temperature slowly.

**Lantent Heat **is the energy associated with changes in phase between gas, liquids, and solids. This energy is absorbed by the bonds that tie molecules together, and beyond a threshold the bonds break; such as ice absorbing heat to melt into liquid water and evaporating (or boiling) to water vapour (gas). In reverse the heat energy is released to condense the gas to liquid, and freeze the liquid to solid.

**Sensible Heat **is the kinetic energy (vibration) that would change the temperature of the object with no change in phase. **Temperature** measures the average kinetic energy of atoms or molecules that make up the substance. Molecules stop moving at the lowest conceivable temperature of 0 K (-273.15°C) known as absolute zero.

If a substance is so viscous that its rigid, we call it a **solid**, otherwise we call it a **fluid**. And if a fluid isn't compressible, we call it a **liquid**, otherwise we call it a **gas** or **plasma**.

Any thermodynamic system has the distribution of energy described by two related properties:

**Enthalpy** (denoted by H) is the total energy a system contains. It cannot be measured directly but measuring the change in enthalpy is useful to understanding how the system works.

**Entropy** (denoted by S) is the amount of thermal energy in the system that cannot be used to do work. Often considered the disorder of a system, it cannot be reversed without putting energy in.

A closed system (controlled mass) has a fixed amount of mass, and no mass can cross its boundary, but energy can flow. An open system (controlled volume) allows both mass and energy to cross the boundaries (real and imaginary).

*Laws of Thermodynamics*

**1**^{st}* *

*The net change (increase or decrease) in the total energy of the system (quantity) during a process is equal to the difference between the total energy entering and the total energy leaving the system during that process.*

**2**^{nd}

*States that the total *entropy of an isolated system can never decrease over time. The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium, or is undergoing a (fictive) reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in the thermodynamic sense.

Provides the necessary means to determine the quality as well as the degree of degradation of energy during a process (ex completion of chemical reactions).

*Note: A p**erpetual motion machine- is any device that violates the first or second laws of thermodynamics *

**3**^{rd}* *

*The entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (0 K).*

**0**^{th}

*If two objects are in thermal equilibrium with a third so that no heat flows between them, then they must also be in equilibrium with each other.*

**Waves****:**

**Waves**

**:**

A wave is a repeating disturbance that travels through space and carries energy.

Longitudinal waves: caused by compressions (parallel displacement) creating areas of high and low pressure along the wave path (ie. sound waves).

The human ear can pick up variations at frequencies ranging from 20 to 20,000 Hz. Infrasound is below this, and ultrasound is above this threshold. Sound pressure is is measured in decibels (dB) using a logarithmic scale.

Transverse waves: characterized by displacement at right angles to the wave path.

The 3 common properties of waves are:

**Wavelength: **in transverse waves this is the distance between one peak to the next, and in longitudinal it is the distance between points of greatest compression.

**Frequency: **the rate at which waves are produced, measured in cycles per second, or herts (Hz)

**Amplitude: **the maximum displacement at a peak or trough, or greatest amount of compression

**Velocity:** based on frequency and wavelength: v = f • λ

**Conversions:**

**Conversions:**

**Geometry****:**

**Geometry**

**:**