start Flashcards
what is an operational definition of temperature
The temperature of a substance is a measure of the mean
translational kinetic energy associated with the disordered microscopic motion of its constituent atoms or molecules.
direction of heat flow
Heat flows from a region of higher temperature toward a region of lower temperature.
things needed to make a theromometer
a system with a suitable thermometric property,
an easily duplicated method of construction
what does a useful thermometer have
reproducible readings, small heat capacity(so it doesnt change the properties of the system), a wide operating range
thermometric property
is any physical property that changes measurably with temperature
Good Thermometric Property
independent of the properties and sample-dependence of specific substance
pressure temp law
The pressure p of a fixed mass of gas at low density in a constant volume is proportional to the absolute temperature, T
Constant-Volume Gas Thermometer operation
Allow gas and system to reach thermal
equilibrium, Adjust height of mercury reservoir to
bring meniscus to the constant volume
reference mark, Measure the height h and hence determine the pressure p, Use T = ap, where a is a constant for the thermometer to determine the temperature T
Constant-Volume Gas Thermometer used to compare temp of systems
T1=ap1 T2=ap2 therfore T1/T2=p1/p2
Kelvin scale
Based on properties of an ideal gas and the 2nd Law of
Thermodynamics, Requires only a single fixed point defined as T triple point= 273.16K, The value for
T triple point is defined so that (T melting point)–(Tboiling point)= 100K
Celcius temperature scale
Uses pure water at 101 kPa to determine two fixed points, which are defined as being 100 degrees apart (hence
centigrade)
thermodynamic temperature scale
one that does not depend on the properties of the substances that are used to measure temperature
why is kelvin thermodynamic
because it is based on: Equation of state of an ideal gas, Properties of a reversible heat engine
Calibration of the CV Gas Thermometer
The triple-point of pure water gives a very reproducible temperature reference, Error bounds of +0.0μK/ –150μK are achievable. This allows determination of the calibration constant a for a CV gas
thermometer. For low pressures results become independent of the gas used.
how are thermodynamic properties of a system determined
by its thermodynamic state
how is the thermodynamic state of a system specified
by values of a suitable set of parameters known as
state variables
State variables
density ρ, enthalpy H, entropy S, internal energy
U, mass M, number of moles n, chemical potential μ,pressure p, temperature T, volume V
Equation of State definition
a mathematical relationship between state variables
An equation of state properties
exists for every thermodynamic system, cannot be determined using thermodynamics, can be determined from experiments or a molecular theory, for a closed system, relates T to two other variables
The equation of state of an ideal gas
pV=nRT, useful approximation for real gases at low
p or high T
Path-Independence of State
Independent of the path (sequence) of state-variable values used to make the change
The P-V-T Surface
The state variables p, V, T, n are the coordinates in a 4-space, The equation of state defines surfaces in this space
Isotherms
p vs V at constant temperature
Isobars
V vs T at constant pressure
Isochors
p vs T at constant volume
critical temperature
above this the gas cant be liqified by preassure alone
Van der Waals Equation of State
(p+an^2/V^2)(V-nb)=nRT
a and b are empirical constants that differ for each gas
info about Van der Waals Equation of State
takes into account : molecular volume which is nbso the volume available for the molecules to move in is (V–nb),Intermolecular attraction is represented by an^2/V^2.This decreases the pressure at high densities
Virial Equation of State
pV/nRT=1+……Bn(n/v)^n
Bn are the virial coefficients. These are specific to each gas and are functions of T
Virial Equation of State info
uses a power-series expansion, reduces to the ideal gas equation of state at low densities, can be derived using
statistical mechanics, is valid for any isotropic substance if enough terms are used.
Equation of State for a Simple Solid
V =V0[1+β(T−T0)−kT(p−p0)]
kT=−ΔV/V0Δp is the isothermal compressibility
β=ΔV/V0ΔT is the isobaric volumetric expansivity
Heat is
measure of the energy transferred between two systems as a result of a temperature difference,
specific heat capacity equation
ΔQ=cMΔT
Specific heat capacity holding preassure constant
c=1/M(δQ/dT)
Specific heat capacity holding volume constant
c=1/M(δQ/dT)
three mechanisms that transfer heat between systems
Conduction, Convection, Radiation
importance of heat transfer mechanisms depends on
nature of the systems, geometry of the systems, temperature regime involved
Conduction is
the transfer of heat through a medium that is stationary on a macroscopic scale
thermal resistance equation
R=L/κA k=thermal conductivity L=legnth A=cross sectional area
charge thermal equivalent
heat
current thermal equivalent
heat flux
capacitance thermal equivalent
heat capacity
pd thermal equivalent
temp
reistance thermal equivalent
thermal resistance
Convection
the transfer of heat via the movement of a medium on a macroscopic scale important in fluids
Convection forced
externally driven flow
Convection free
thermally induced density gradients drive the flow
Radiation is
the transfer of heat via electromagnetic waves, No medium is required,
Stefan-Boltzmann law
P=εσAT^4 for p net T^4-Tenv^4
Kinetic Theory of Gases assumptions
A container with volume V contains a very large number N of identical spherical molecules, each with mass m
The molecular radius is small compared with the average distance between molecules and the size of the container
The molecules are in constant rapid random motion and obey Newton’s laws
There is no force acting between molecules except during
collisions.
The molecules collide with each other and with the
walls of the container. All collisions are perfectly elastic
The container walls are perfectly rigid and infinitely massive
The gas is in equilibrium
Collision Frequency of molecules with wall
(N/2V)A∣v_x∣dt
The gas is isotropic so
v^2x=v^2y=v^2z=(1/3)v^2total
force exerted by gas
Fx=momentum change x arrival rate =2mv (N/2V)A∣v_x∣
pressure equation
force/area = 1/3Nmv^2
Microscopic Interpretation of Temperature
mean translational kinetic energy
per molecule
Internal Energy of the Ideal Gas assumptions
No intermolecular forces
No rotational kinetic energy
No vibrational kinetic energy
Internal Energy of the Ideal Gas equations
3/2NkT=3/2NnRT
The heat capacity of n moles of ideal gas
3/2nRT
velocity density
function
f(v)=Aexp(−Bv^2) v=sqrt(ln(v)/2) at half height
A=sqrt(B/pi)
speeds of molecules
v most probable < v average < v rms
Ideal gas model does not describe
thermal conductivity electrical resistivity viscosity diffusion because these depend on the frequency of collisions between molecules
collision rate of one molecule with other stationary molecules
(N/V)4πr^2⟨v⟩
collision rate of one molecule with other moving molecules
(N/V)4√2πr2⟨v⟩
mean free path proportionalities
λ∝T. λ∝1/p
viscosity
momentum transfer
thermal conductivity
energy transfer
coefficient of diffusion
mass transfer
Thermal Conductivity proportionalities
independent of density κ∝(1/r^2)sqrt(T/m)
