Thermodynamics Flashcards
random things I may need to know
difference between heat and temperature?
heat: refers to energy transfer caused by dif temps.
temperature: form of measurement. associated with the sense of touch and related to kinetic energies of the molecules in the material.
0th law of thermodynamics
if C is initially at eqlbm w both A & B, then A & B are both at eqlbm with each other
Actual temperature vs temperature interval
actual temp: written as __°C (blank degrees Celsius)
temp interval: __ C° ( blank Celsius degrees); its a difference/ change in temp
when volume is constant, pressure is directly proportional to…
Kelvin temperature so T1/T2 = P1/P2
ratio of two temps in Kelvin equals the ratio of corresponding pressures
To find the temp of T at the triple point of water…
Use the temp-pressure ratio.
T/T_triple = P/P_triple
T_triple = 273.16K
Linear Thermal Expansion eqn
ΔL = αL_oΔT
ΔL = change in length
α = coefficient of linear expansion
L_o = original length
ΔT = temp change
what is α and what are the units?
α is the coefficient of linear expansion, it is constant and is based on material.
units are K^-1 or C°^-1
Volume Thermal Expansion Eqn
ΔV = ßV_oΔT
ΔV= Change in Volume
ß = coefficient of volume expansion
V_o = Original volume
ΔT= change in temp
same units as linear expansion
When do you use volume expansion versus linear expansion
Volume expansion = liquids
linear = rods, change in length, solids
How to find ß when given the α of a material?
ß = 3α
Young’s modulus eqn - this involves tension
Y = (F/A)/(ΔL/L_o)
= (FL_o)/(AΔL)
to calculate thermal strain…
ΔL/L_o = αΔT
To solve thermal stress F/A…
F/A = -YαΔT
F = force needed to keep length of rod
A = cross sectional area of material
Y= young’s modulus
α = coefficient of linear expansion
ΔT= change in temp
what is young’s modulus and the units?
Young’s modulus is a measure of stiffness of a material
it is Tensile Stress/ Tensile Strain
Low Y =more flexible
High Y = more stiff
Units are Pa or N/m^2
what is tensile stress eqn
stress is force applied per area (F/A)
what is tensile strain eqn
deformity / change in shape due to force (ΔL/L_o)
What’s Hooke’s Law?
the greater the deforming forces, the greater the resulting deformation
tensile stress vs compressive stress
tensile stress is when force stretches/ elongates material
compressive stress is when force compresses/ shrinks the material
in general tensile is stretching
when temperature goes down, what force /stress is needed to maintain length?
contraction would happen when ΔT is negative so tensile force and stress is needed to pull the material to keep the length
when temp goes up, what force/stress is needed to maintain length?
material expands when ΔT is positive so required force and stress is compressive in order to maintain length
elastic modulus
property of material of which object is made
the ratio is stress/ strain
what is elasticity? elastic v plastic?
it depends on the type of material and not size
elastic: return to OG state after stress is removed
plastic: remains deformed after stress is removed
what is Bulk strain
ΔV/V_o
change in volume per unit volume
pressure in a fluid eqn
P=F/A
P = pressure in a fluid
F = force
A = area over which force is exerted
what is the bulk modulus for compression?
bulk stress/ bulk strain = -ΔP/(ΔV/V_o)
ΔP= additional pressure on object
ΔV = change in volume
V_o= OG volume
*minus sign is bc inc in pressure always leads to dec in volume
pressure is inversely proportional to…
volume
stress is proportional to…
strain
heat flow/ heat transfer
energy transferred only by ΔT
equation for heat required to change temp
Q=mcΔT
m = mass of material
c = specific heat of material
ΔT = change in temperature
high v low specific heat
high specific heat needs more heat to change temp
low specific heat heats up and slows down quicker
heat required to change temp of a certain number of moles
Q =nCΔT
n = # of moles
C = molar mass times specific heat capacity
ΔT = change in temp
heat of fusion/ latent heat of fusion (solid to liquid) Q needed
Q = +/- mL_f
m = mass of material
L_f = latent heat
what is heat of vaporization
the heat per unit mass to change liquid to gas
heat current in conduction/ rate of heat flow eqn
H = kA(Th-Tc)/L
H= heat current
k= thermal conductivity of rod material
A= cross-sectional area of rod
Th-Tc = temp of hot and cold rod
thermal resistance of slab in correlation to H is
H = A(Th-Tc)/R
R= thermal resistance
A = cross-sectional area
thermal resistance is given by
L/k
L= thickness of rod
k = thermal conductivity
materials with low k…
are good insulators
materials with a large k…
are good conductors of heat
when doubling thickness what happens to R
R doubles
what is emissivity?
e is a measurement of how efficiently a surface emits thermal radiation compared to a perfect black body at the same temperature
what is a black body?
A black body is an idealized object that absorbs all incident radiation and emits the maximum possible radiation at a given temperature
heat current of radiation equation aka Stefan-Boltzmann Law
H = AeσT^4
H = rate of heat flow
A = surface area of emitting surface
e = emissivity of surface
σ = Stephan Boltzmann constant = 5.67037442 * 10^-8 W/(m^2*K^4)
T = absolute temp of surface
Net Heat current in radiation
H_net = H-emitted - H-absorbed
= AeσT^4 - AeσT_s^4
H_net = Aeσ(T^4 - T_s^4)
T = temperature of the radiating surface
T_s = temperature of the surroundings or the object with which the surface is radiating to
Wien’s Law
λ_max = (2.9Kmm)/T
λ_max = peak wavelength
what is the fraction of power in a certain range of wavelength?
the fraction of area under the graph in that range
when two objects are at equilibrium…
H_in = H_out
H_in = rate at which sunlight/ source of heat is absorbed
H_out = rate at which heat is absorbed
what is albedo
albedo is the overall average reflection coefficient for solar radiation incident on an object
What is H_in due to sunlight
H_in = I_scpir_e^2 (1-a_e)
I_sc = solar constant
r_e = radius of earth
a_e = albedo
what is solar constant
the intensity of sunlight, I_sc
What is the temperature equilibrium equation for radiation?
T_e = [(1-a_e)I_sc/(4e_eσ)]^1/4
T_e = temperature eqlbm
a_e = albedo
I_sc = solar constant
e_e = emissivity
σ = stephan boltzmann constant
what is intensity formula
power/area
what is total power in terms of intensity
power = intensity * area
H_in for earth
H _in = H_sun (r_e^2)/(4R_s-e^2)(1-a_e)
r_e = radius of earth
R_s-e = distance from sun to earth
a_e= albedo of earth
if surface moves towards particle…
surface does work on particle during collision
if surface is stationary…
work is done on the surface by the particle
in a PV- diagram, if the volume expands….
work is positive - work is also the area under the curve
in a PV - diagram, if the volume decrease…
work is negative
in a PV- diagram, if work is done at constant pressure…
work is positive and is equal to p=(V_2-V_1)
path
a series of intermediate states that get passed thru when a thermodynamic system changes from an initial state to a final state
is work path dependent
yes it is
- depends not only on the final and initial state but also the intermediate states
- Q is also path dependent
First Law of Thermodynamics
ΔU = Q - W
is ΔU path dependent
no it is independent from the path; only depends on initial and final state
Adiabatic
no heat transfer into or out of system;
Q = 0 therefore:
ΔU = -W
when system expands adiabatically, work…
is done on its surroundings
work is pos = -ΔU
when system compresses adiabatically, work…
is done on the system by surroundings
W is neg = + ΔU
Isochoric
constant volume process
W = 0 therefore
ΔU = Q
For isochoric processes, work is….
not done on surroundings, it doesn’t exist.
Isobaric
constant - pressure process
W = p(V2-V1)
none of the qualities are zero
Isothermal
constant temp
ΔU = 0 therefore:
W = Q
For an ideal gas Cp =
Cp = Cv + R
Cp = molar heat capacity at constant pressure
Cv= molar heat capacity at constant volume
R = gas constant (8.314 J/(mol*K))
Ratio of heat capacities
γ = Cp/Cv
at constant pressure for an ideal gas ΔU…
ΔU = nCpΔT
at constant volume for an ideal gas ΔU…
ΔU = nCvΔT
thermal efficiency of an engine
e = W/Q_H = 1 - |Qc/Q_H|
e = thermal efficiency
W = work done by engine
Qc= heat rejected by engine
Q_H = heat absorbed by engine
Steps in an Otto Cycle
cyclic process (starts and ends at the same place)
1.compressed adiabatically
2. heated at constant volume
3. expands adiabatically
4. cooled at constant volume
thermal efficiency in otto cycle
e = 1- 1/(r(γ -1))
r= compression ratio
γ = ratio of heat capacities
Steps in a Diesel Cycle
- compressed adiabatically
- heated at constant pressure
- expanded adiabatically
- cooled at constant pressure
work for an engine
W = Q_H + Qc
W = |Q_H| - |Qc|
work for refrigerator
|W| = |Q_H| - Qc
what is the equation for CoP?
K = |Qc|/|W|
= |Qc| / [ |Q_H| - |Qc| ]
K = coefficient of performance of a refrigerator
W = work input of refrigerator
Q_H = Heat rejected from refrigerator
Qc = heat removed from inside of refrigerator
Irreversible Processes
proceeds spontaneously in one direction but not the other
Second Law of Thermodynamics - Kelvin Plank Statement “Engine” Statement
heat cannot completely be converted into mechanical work and be a cyclic process
Second Law of Thermodynamics - “refrigerator” statement
heat does not go from cold to hot naturally without assistance
entropy
the randomness of molecules; the more entropy, the more energy there is
total entropy change during a reversible isothermal process
ΔS = Q/T
total entropy for a Carnot engine
zero
is entropy path dependent
no; only needs initial and final state
Second Law of Thermodynamics
no process is possible in which total entropy decreases
Carnot Engine
maximum possible efficiency of an engine
on a temp v entropy graph its a square
Steps of the Carnot Engine
- expands isothermally -> absorbs heat Q_H
- expands adiabatically -> Tc drops
- compresses isothermally -> rejects |Qc|
- expands adiabatically to OG state
