Basic Concepts and Definitions

From Uni Study Guides
Jump to: navigation, search

This is a topic from Thermodynamics:
This introduction will introduce and define many key terms which will be used frequently later in the course. It may make reference to as yet undefined concepts, which will be explored in later sections of the UniStudyGuides Thermodynamics notes.

Contents

Introduction

The course is an introduction to thermodynamics, which is essentially the field of science that explores the relationship between work and heat, both of which are methods of energy transfer.

Definitions

Heat - In order for the transfer of energy known as "heat" to occur, there needs to exist a temperature difference or temperature gradient between two regions.
Work - In order for the transfer of energy known as "work" to occur an object must be set in motion against an opposing force and travel a given distance. Recall that W = F.r, meaning work equals net force times distance.
Fluid - The word fluid, in thermodynamics, refers to either a liquid, a vapour or a gas. A fluid cannot sustain a permanent sheer stress.
Pressure - Pressure is the force per unit area. A gas will exert a pressure on the vessel which contains it.

  • P = F / A
  • S.I unit is the Pascall (Pa)
  • 1 bar = 100 kPa
  • 1 atm = 101.325 kPa

Temperature

  • S.I unit is the Kelvin (K)
  • T(K) = T(C) + 273.15 - where C refers to Celsius
  • T(C) = (5/9)[T(F) - 32] - where F refers to Fahrenheit

Summary of the Four Laws of Thermodynamics

0th Law - Temperature/thermal equilibrium
1st Law - Conservation of energy
2nd Law - Increase of entropy in isolated system to a maximum
3rd Law - Absolute entropy

Systems and Surroundings

System - A system is a region of interest defined as distinct from its surroundings, separated by an infinitesimally thin boundary. It is a construct that facilitates thought experiments and calculations in thermodynamics.
Isolated System - The boundary of an isolated system is impervious to any form of energy and matter transfers. It encloses a fixed quantity of mass and energy.
Closed System - The boundary of a closed system is impervious to matter transfers only. It encloses a fixed quantity of mass.
Open System - The boundary of an open system isn't impervious to matter or energy transfers.

Thermodynamic Properties

Property - A quantity is a 'property' if, and only if, its change in value between two states is independent of the process. For example temperature is a property. The same temperature change can be caused by a variety of processes - a change in temperature is independent of the process. Heat on the other hand, is not a property, as it is dependant upon a process.
The following are properties that are pertinent to thermodynamics:

  • T - Temperature . . . . . . . . E - Energy
  • P - Pressure. . . . . . . . . . . . U - Internal energy
  • m - Mass . . . . . . . . . . . . . . H - Enthalpy
  • V - Volume . . . . . . . . . . . . S - Entropy
  • v - Specific volume (v = V / m)
  • u - Specific internal energy (u = U / m)
  • h - Specific enthalpy (h = H / m)
  • s - Specific entropy (s = S / m)

Extensive Properties - These are dependant upon the extent of the system. Consider mass as an example; if you have an object considered to be a system, say a cake, and you divide that system in two, you have divided its mass in two as well.
Intensive Properties - These are independent of the extent of the system. Consider density as an example; if you divide the cake in two the density has not been divided in two, it remains the same. Any property with the word 'specific' in it is an intensive property.
The State Postulate - Two independent intensive properties are required to specify the state of a system. For example, in order to verify that a system contains a gas and not a liquid it is not enough to know that its temperature is above 100°C. One must also know that the pressure is sufficiently low so that condensation has not occurred.
Equilibrium - A system is in equilibrium (or balance) if no changes occur in any of its macroscopic properties.
Thermal Equilibrium - Thermal equilibrium is a state whereby the temperature of a system is constant. Incidentally this implies that the pressure is also constant. If two objects are in thermal equilibrium with one another there is no heat transfer between the two.

Thermodynamic Processes

A thermodynamic process is a energetic development of a thermodynamic system from an initial state to a final state. These processes are often represented on a 'PV diagram' a schematic plot of the changes in pressure against those in volume. There are various named types of thermodynamic process including the following:
Quasi-static process - A process which occurs infinitely slowly such that the system can be considered to be in equilibrium at all times. It is essentially a process considered as a series of instantaneous states. Isobaric process - Constant pressure

  • ΔP = 0
  • V/T = Constant

Isochoric/ Isovolumetric - Constant volume

  • ΔV = 0
  • P/T = Constant

Isothermal - Constant temperature

  • ΔT = 0
  • PV = Constant
  • On a PV diagram the path is hyperbolic. This line of constant temperature is known as an isotherm.

Adiabatic - No heat transfer occurs

  • Q = 0
  • PVk = Constant, where k is the isotropic index

Isentropic - No change in entropy

  • ΔS = 0
  • Q = 0
  • Reversible process

Polytropic - No one property is constant

  • PVn = Constant for some real n

Imgres.jpeg

Point Functions Vs. Path Functions

When performing integrals in thermodynamics it is important to consider whether the integrand is a point function or a path function.

Properties are point functions as they are independent upon how a system gets from its initial state to its final state (from one 'point' on the PV diagram to another). Consider the property temperature as an example.

Screen Shot 2013-03-14 at 4.42.09 PM.png

When integrating a point function the result is a difference between two values - a 'change'.

Heat and work are path functions as they are dependant upon the process by which a system gets from a final state to an initial state (they are dependant upon the 'path' between the two points):

Screen Shot 2013-03-14 at 4.42.13 PM.png

When integrating a path function the result is a single value.

Dimensional Analysis in Thermodynamic Properties

Consider:

  • P = F / A and F = ma, -> P = (kg*ms-2)/m2

Therefore P = kg/ms2

  • EK = mv2/2 = kg*(ms-1)2
  • EP = mgh = kg*ms-2)*m

Therefore, in both cases, E = kgm2s-2

And so whenever a calculation requires division of an energy by a volume, the result is a pressure:

E / V = kgm2s-2 * m-3
= kg/ms2
= P

The 0th Law of Thermodynamics

The 0th law of thermodynamics states that if two objects are independently in thermal equilibrium with each other then they are in thermal equilibrium with each other.

The Ideal Gas Law

The ideal gas law is the relation as follows:

Pv = RT

Where P represents pressure,

v represents specific volume (the reciprocal of density, m3/kg)
R is the specific gas constant
T represents temperature

The ideal gas law may be written in other forms, for example in PHYS1131:

PV = nṜT

Where P represents pressure,

V represents volume
n is the number of moles
Ṝ = 8.314 J/mol
T represents temperature

The Gas Constant The gas constant = The universal gas constant / Molecular mass:

R = Ṝ / M

Where Ṝ = 8.314 J/mol

Molecular mass = kg/mol

Frequently Assessed Derivation

The following derivation combines the conditions for a polytropic process (That PVn = constant) with the ideal gas law, and is frequently examined in the mid-semester exam:

  • From the ideal gas law and from PV = constant respectively:
Screen Shot 2013-03-12 at 6.54.52 PM.png
  • Combining the two gives equation 3:
Screen Shot 2013-03-12 at 7.18.14 PM.png
  • From equation 2, and taking the nth root of both sides:
Screen Shot 2013-03-12 at 7.18.31 PM.png
  • Substituting into equation 3:
Screen Shot 2013-03-12 at 7.18.38 PM.png


(Note this should read P2/P1 but the equation above is an image file and cannot be edited.)

Personal tools
Namespaces

Variants
Actions
Navigation
Toolbox