thermal content

System definition

whatever part of the universe we choose to study

Surroundings definiton

the parts of the universe we didnt choose to study

Closed definition

no particle exchange between the system and the surrounding

Adiathermal definition

no heat exchange allowed

Adiabatic definition

adiathermal and reversible

Isothermal

constant temperature

Isobaric

constant pressure

Isovolumic

constant volume

Phase

a region within the system that is homogeneous with well defined boundaries

Equilibrium

a state without change

Function of state definition

any physical quantity that has a well defined value for each equilibrium state

Extensive definition

quantities that are proportional to system size

Intensive definition

quantities that are independent of system size

Zero-th law of thermodynamics

Two systems in thermal equilibrium with a third are also in thermal equilibrium with each other

redundancy definition

more functions of state than independent variables

reciprocity theorem

(dx/dy)z(dy/dz)x(dz/dx)y \= -1

why do functions of state always have exact differentials

because they are single valued

First law of thermodynamics

Energy is conserved if heat is taken into account

First law of thermodynamics equation

deltaE \= deltaQ + deltaW

Heat capacity equation

C \= dQ/dT

Isothermal expansion equation

delta Q \= RT ln(V2/V1)

Adiabatic expansion equation

TV^(gamma - 1) \= const

Second law of thermodynamics

entropy always increases

Heat engine

a device that converts thermal energy into mechanical energy

A to B in carnot cycle

isothermal expansion

B to C in carrnot cycle

adiabatic expansion

C to D in carnot cycle

isothermal compression

D to A in carnot cycle

adiabatic compression

How do you find the total work done of a carnot cycle

The area of the p-v graph

what is W in thermodyamics

work done on the system

what is W in heat engines

work done by the system

what is Qh in heat engines

heat absorbed by the system

what is Ql in heat engines

heat released by the system

A to B carnot cycle equation

Qh \= RTh ln(VB/VA)

B to C carnot cycle equation

Th/Tl \= (VC/VB) ^ gamma - 1

C to D carnot cycle equation

Ql \= RTl ln(VC/VD)

D to A carnot cycle equation

Tl/Th \= (VA/VD)^ gamma - 1

What is the efficiency for a heat engine?

the work done divided by the heat

What is the efficiency for a refrigerator?

the heat divided by the work done

Carnots theorem

No real engine operating between two energy reservoirs can be more efficient than a Carnot engine

Thermodynamic temperature scale equation

theta 2 \= theta 1 Q1/Q2

entropy equation

dS \= dQ/T

Work done equation

W \= - integral pdV

What is the heat released by a system when the energy does not depend on the volume?

the work done

where is entropy defined up to?

an arbitrary additive constant

Define entropy in classical thermodynamic terms

dS \= dQrev/T, the entropy is defined up to an arbitrary additive constant, S(B) - S(A) \= integral from A to B dQrev/T

State the law of increase in entropy, sometimes known as the third statement of the second law of thermodynamics

The entropy of an isolated system tends to a maximum

What is the second statement of the second law

heat goes from hot to cold

What is the heat capacity of diatomic air?

Cp \= 7/2 R

Do ideal gases depend on volume?

no

What are some examples of extensive functions of state

Internal energy, volume, magnetisation

What are some examples of intensive functions of state?

Temperature, pressure, magnetic field

Why are microscopic quantities not functions of state?

Because they vary even when in equillibrium

Why is work done of heat transferred not a function of state?

becuase they depend on the process and not just the states involved

How was the first thermometer invented

by trapping air inside a cylinder which was sealed at the top and dipped in liquid in the bottom. As the trapped air cooled or heated liquid was pushed in or sucked out of the cylinder and the temperature could be found

Examples of thermometers based on thermal expansion

bi-metalic strips, thermo-couples, liquid crystal

using the ideal gas law how do we define temperature?

a system has a temperature T if it can maintain thermal equilibrium with an ideal gas at that temperatre

What is the ideal gas equation for one mole (hint- pV\=nRT)

(dV/dT)p \= R/p

what is the adiabatic index

the ratio of the heat capacities: gamma \= Cp/Cv

what is the E for an ideal gas per mole

E \= 3RT/2

what is the heat capacity for an ideal gas with constant volume?

Cv \= 3R/2

What is the heat capacity for an ideal gas with constant pressure

Cp \= 5R/2

what is the adiabatic index (gamma) for an ideal gas?

5/3

For a real diatomic gas that is dilute enough to be ideal what is E

E \= 5RT/2 per mole

For a real diatomic gas what is the heat capacity at a constant volume?

Cv \= 5R/2

For a real diatomic gas what is the heat capacity at a constant pressure?

Cp \= 7R/2

For a real diatomic gas what is the adiabatic index?

1.4

In general for gas with more complex molecules what happens to the values of E and gamma

there are more available energy modes which lead to higher values of E and lower values of gamma

for isothermal expansion what is dE?

dE \= 0 since we have constant internal energy

For isothermal expansion is the work done by the gas on the surroundings or by the surroundings on the gas?

by the gas on the surroundings

what is dQ for adiabatic expansion

dQ \= 0 since no heat is exchanged

What is the equation for the adiabatic index (gamma)

gamma \= 1 + R/Cv

Why are adiabatic lines always steeper than isotherms in p-V plots?

because the adiabatic index (gamma) is greater than 1

What is a reversible processs

A process carried out so slowly that the system goes through an infinite sequence of equilibrium states (which are infinitely close together)

What must there not be for a process to be reversible?

friction, turbulence or acceleration

What does quasistatic mean

if we reverse the process exactly, we would recover the initial state

What are irreversible processes defined by

an asymmetry in time

What is kelvins statement

No process is possible whose sole result is the complete conversion of heat into work

What is Clausius' statement

No process is possible whose sole result is the transfer of heat from a colder body to a hotter body

What does the idea of a sole result require?

the system and surrounding to be returned o their initial state except for the heat and work mentioned

What does a heat engine require?

a working substance which is used cyclically

What is the difference between an adiabatic process and an isothermal process

adiabatic is a thermodynamic change where no heat is supplied, isothermal is a thermodynamic change where the temperature does not change

For a carnot cycle in reverse is the work done by the system on the surroundings or by the surroundings on the system?

the surroundings does work on the system

What is a carnot cycle in reverse?

a system that extracts heat from a lower temperature and delivers in to a higher temperature, like a fridge

what is the equation for efficiency of a carnot engine

fancy n \= (Th-Tl)/Th

what is the equation for efficiency of a carnot refridgerator

fancy n \= Tl/(Th-Tl)

What kind of heat engine does a thermodynamic temperature scale require

one that is reversible

Clausius' inequality equation

closed integral dQ/T

What is T in clausius' inequality?

the temperature of the external heat reservoir from which the heat dQ is supplied

In clausius' inequality what does a negative indicate?

heat leaving the system

equation for entropy change between phases

(S2 - S1) \= L/T where L is the latent heat

What is the energy for equation in differential form

dE \= TdS - pdV

What is the equation for enthalpy in differential form

dH \= TdS + Vdp

What is the equation in differential form for Helmholtz free energy

dF \= -SdT - pdV

What is the equation in differential form for Gibbs free energy

dG \= -SdT + Vdp

What is gibbs free energy minimised for G(T, p)

systems with fixed pressure and temperature

What is enthalpy minimised for? H(S,p)

systems with fixed pressure and heat

What is energy minimised for E(S,V)?

systems with fixed volumes and heat

What is helmholtz free energy minimised for F(T, V)

systems with fixed temperature and volume

Applications of the thermodynamic potential energy (E(S,V)

isolated systems, mechanical equilibrium