Download Chemistry/Physical Science - Thermodynamics

1
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
Thermochemistry and Thermodynamics
I. Symbols and Conversion Equations
A. Symbols Used:
1. t
=
Temperature
2. m
=
Mass
3. Cp
=
Specific Heat or Heat Capacity in J/goC
4. Q
=
Heat amount transferred in J or kJ
5. H
=
Enthalpy
6. S
=
Entropy
7. G
=
Gibbs Free Energy
8. W
=
Work
9. U
=
Internal Energy, also symbolized by E
10. M
=
Molar Mass
11. P
=
Pressure
12. V
=
Volume
13. ΔT
=
Change in Temperature (t2 – t1)
B. Temperature Conversions
1. Tc = .556 x (Tf - 32)
2. Tf = (1.8 x Tc) + 32
3. Tk = Tc + 273.16
4. TR = Tf + 460
Celsius / Centigrade
Fahrenheit
Kelvin
Rankine
a. ΔTk = ΔTc
C. Energy Conversions
1. 1 Calorie = 4.185 Joules (J)
2. 1 BTU
= 1.055 x 103 J
a. Energy needed to raise 1 lb H2O 1oF from 63 to 64
b. 1 BTU = 252 cal = 1056 J
c. Convert cal/g to BTU/lb by multiplying cal/g by 1.8
3. 1 Joule
= .2390 calorie
4. 1 kcal
= 1 dietary calorie = 1000 calories (103 cal)
a. Energy needed to raise 1 g H2O 1o C from 14.5 to 15.5
II. Temperature
A. Kinetic Molecular Theory
1. Molecules absorbing energy increases KE, causing more random
movements and collisions, increases level of thermal energy (heat)
B. Temperature – measure of the average KE of the molecules of a substance, a measure
of the intensity of energy in a system
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
2
C. Heat Transference:
1. Conduction – heat transferred from 1 particle to another w/o movement of
matter itself
a. H = K AΔt Δtime
L
where H is amount of heat flowing through a body with length L and cross
section A; K is thermal conductivity; Δt is change in temp; and ΔT is
change in time
b. K is heat in kcal that will pass in 1 sec through a 1m3 with 2 opoosite
sides w/ a 1oC difference in temperature
c. R value
(1) measure of thermal conductivity
(2) Heat flow over time = thermal conductivity x area/length x ΔT
(3) Thermal resistance = length / thermal conductivity
2. Convection – movement of heat via currents
3. Radiation – heat transferred by EM waves and/or particles
a. Stefan-Boltzmann Law
(1) E = kT4
(2) Energy (E) is radiated per second by a body w/ absolute temp
(T) and k is proportionality constant
(3) If E is in kcal radiated per m2/s,
then k = 1.3567 x 10-11 kcal/m2sok4 or 5.67 x 10-8 J/m2sok4
(4)  E = kT4AΔt
4. Other Information:
a. Heat flows / moves in 1 direction until equilibrium acquired
b. Heat always flows towards the cooler area
c. Conductor carries heat / energy; insulators prevent it
D. Specific Heat or Heat Capacity
1. Cp = _Q_
mΔT
a. Measured in J/gCO or J/gK
b. Amount of energy needed to raise the temp of the substance 1oC
c. Ratio between thermal capacity of substance and the thermal capacity
of water
d. Greater the Cp, greater the heat needed to raise its temp
2. Q = CpmΔT; ΔT = Q/Cpm; m = Q/CpΔT; Q = nCpΔT (n is moles)
3. Calorimetry – measuring changes in thermal energy
a. Conservation of thermal energy occurs between two objects
b. EA + EB = Constant with ΔEA + ΔEB = 0
c. mACA(T2 - TA1) + mBCB(T2 - TB1) = 0
 T2 = mACATA1 + mBCBTB1
mACA + mBCB
3
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
d. Heated object into cooler substance, vice versa:
(1) QA = QB;  m(ΔT)(Cp) = m(ΔT)(Cp)
(2) Mass (m) = Volume x Density
4. Thermal Expansion
a. Length
L2 = L1 + α L1 (T2 – T1) or ΔL = αL1ΔT
(1) Where α is linear coefficient of expansion based on material
(2) α = ΔL
L1ΔT
b. Area
ΔA = 2αΔT
A1
c. Volume
ΔV = 3αΔT
V1
 β = 3α
 ΔV = βVΔT
III. Heat of Fusion / Vaporization
A. Heat of Fusion – constants that show the amount of heat to change the state of any specified
mass of material from a solid to liquid state w/o changing its temperature
1. Amount of energy needed to melt 1 kg of a substance (water is 80 cal/g)
2. HF = mLF
where HF is heat needed; m is mass; and LF is heat of fusion
a. Also symbolized as QF
(1)  QF = mHF
b. In J/kg
3. Molar Heat of Fusion – amount of heat needed to melt one mole substance
a. Q = ΔHfus(mass/molar mass) in kJ/mol
(1) Water = 6.02 kJ/mol = 79.7 cal/ml = 334 J/g
B. Heat of Vaporization – amount of heat needed to change any given mass of a material to a
gaseous state (water is 540 cal/g)
1. Amount of energy needed to change 1 kg into a gas from liquid
2. Hv = mLv where LV is heat of vaporization
a. Also symbolized as Qv
(1)  QV = mHv
Molar
Heat
of
Vaporization – to turn I mole into a vapor/liquid in kJ/mol
3.
a. Q = ΔHvap(mass/molar mass) in kJ/mol
(1) Water = 40.7 kJ/mol = 539 cal/ml = 2260 J/g
IV. Thermodynamics / Thermochemistry
A. 1st Law - the mechanical equivalent of heat, and in any process – the total amount of energy
remains constant (Basically the Law of Conservation of Energy)
1. Thermal energy can be increased by adding heat or work to a system
a. Total increase in themal energy of a system is the Σ W and added heat
2. W = mechanical equivalent of heat
Q
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
4
B. 2nd Law – natural processes go in a direction that maintains/increases the total entropy of the
universe (i.e. from hot to cold); every spontaneous change is accompanied by an increase in
entropy (S and at STP is So)
1. Entropy (S) is the measure of randomness/disorder in a system; increases as heat
increases
a. Law of Disorder – spontaneous processes always proceed in such a way that
entropy of the universe increases
b. Predicting changes in entropy
(1) ΔSsystem = Sproducts - Sreactants
(a) Sproducts > Sreactants and ΔS is +
(b) Sproducts < Sreactants and ΔS is –
c. Change of Entropy Situations:
(1) Can predict changes in entropy associated w/ changes in phases
(2) Entropy increases w/ increase in KE
(3) Dissolving gas in a solvent results in decrease in S
(4) Increase in T causes an increase in S
(5) If no change in phase, S of system increases when number of
gaseous product particles is greater than the number of gaseous reactant
particles
(6) Heat cannot be converted completely into useful work
(7) Every isolated system becomes disordered over time
4. Gibbs Free Energy (G)
a. A combination of entropy and enthalpy
(1) Tells how far rxn is from a state of equilibrium
b. G of the system, or free energy, is the energy available to do work
c. ΔGsystem is difference between ΔHsystem and the product of ΔoK temp and
ΔSsystem
(1)  ΔGsystem = ΔHsystem - T ΔSsystem at STP
(2) if change of G is neg, rxn is spontaneous
C. 3rd Law – As temperature approaches absolute zero, the entropy of the system approaches a
constant minimum
D. Zeroth Law – if 2 thermodynamic systems are in equilibrium with a third, then they are in
thermal equilibrium with each other
E. Enthalpy (H) – the heat content of a system at constant pressure
1. ΔH or ΔHrxn is the change in heat of a reaction (endo/exothermic)
a. ΔHrxn = Hfinal - Hinitial or ΔHrxn = Hproducts - Hreactants
b. Exothermic rxn have negative enthalpy
2. H = E + PV
or
H = U + PV
where E is internal energy,
P is pressure and V is volume
F. Thermochemical Equations
1. A balanced equation with all physical states of units included an the change of energy
indicated (ΔH)
a. ΔHo is standard enthalpy change at STP (1 atm and 25oC / 298K)
b. Example: C6H12O6(s) + 6O2(g)  6CO2(g) + 6H2O(l) ΔHcomb = -2808kJ
5
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
2. Molar Enthalpy of:
a. Fusion (ΔHofus) is heat required to melt one mole of a solid
(1) Water = 6.01 kJ
b. Vaporization (ΔHovap) is heat needed vaporize one mole of a liquid
(1) Water = 40.7 kJ
3. Calculating Enthalpy Change
a. Uses a calorimeter to measure heat evolved / absorbed by reaction
(1) For short time rxns
b. Hess’s Law – Allows for total enthalpy of a rxn by breaking it down into a
series of separate reactive steps
(1) If can add 2+ thermochemical equations to produce a final equation
for a rxn, then the sum of enthalpy changes for individual rxns is the
enthalpy change for the final rxn
4. Reaction Spontaneity
a. Spontaneous process is a physical/chemical change w/ no outside intervention
(1) Exothermic are spontaneous; endothermic are not
5. Kapp’s Rule – method used to determine heat capacities for compound molecules in a
liquid or solid phase at or near 293K
a. Cp of l or s = to sum of Cp of the individual species in the cmpd multiplied by
a constant determined by how many atoms of that element are in the compound
b. Cp = Σ(aici) where a is individual components of compound and c its heat
capacity
6. Newton’s Law of Cooling – the hotter an object is, the faster it cools
a. Rate of cooling is proportional to the temp difference between an object and
its surroundings
b. T(t) = TA + (TH - TA)e –kt where TA is ambient temp, TH is initial
temp of object, -k is constant and t is time
c. H = A(THot - TCold)
where A is area, H is heat loss, R is
R
insulating value
d. H = AU(THot - TCold)
where U is conductance
V. General Information
A. Water Data
Cp
ΔH
(s) 2.108 J/goC
Fusion
(l) 4.187 J/goC
Vaporization
(g) 1.996 J/goC
6.02 kJ/mol
40.7 kJ/mol
B. Example Using Water:
Q = mCpΔT
Q = mCpΔT
Q = mLF

Q = mCpΔT
Q = mLV

______________________________________________________________
- xoC
0 oC
100oC
+xoC
Solid
Liquid
Vapor / Gas
 Σ Q = Q1 + Q2 + Q3 + Q4 + Q5
6
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
Specific heats and molar heat capacities for various substances at 20 C
c in cal/gm K or Molar C
Btu/lb F
J/mol K
Substance
c in J/gm K
Aluminum
0.900
0.215
24.3
Bismuth
0.123
0.0294
25.7
Copper
0.386
0.0923
24.5
Brass
0.380
0.092
...
Gold
0.126
0.0301
25.6
Lead
0.128
0.0305
26.4
Silver
0.233
0.0558
24.9
Tungsten
0.134
0.0321
24.8
Zinc
0.387
0.0925
25.2
Mercury
0.140
0.033
28.3
2.4
0.58
111
Water
4.186
1.00
75.2
Ice (-10 C)
2.05
0.49
36.9
Granite
.790
0.19
...
Glass
.84
0.20
...
Alcohol(ethyl)
Specific Heat Capacities Table
J/kg/oC
or J/kg/K
cal/g/oC
or cal/g/K
Methyl Alcohol
2549
0.609
Steam (100 oC)
2009
0.480
Benzene
1750
0.418
Wood (typical)
1674
0.400
Soil (typical)
1046
0.250
Air (50 C)
1046
0.250
Marble
858
0.205
Glass (typical)
837
0.200
Iron/Steel
452
0.108
Substance
o
7
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
Melting Points and Heat of Fusion
Substance
Helium
Melting point Melting point Heat of fusion
K
°C
(103 J/kg)
3.5
-269.65
5.23
Hydrogen
13.84
-259.31
58.6
Nitrogen
63.18
-209.97
25.5
Oxygen
54.36
-218.79
13.8
Ethyl alcohol
159
-114
104.2
Mercury
234
-39
11.8
Water
273.15
0.00
334
Sulfur
392
119
38.1
Lead
600.5
327.3
24.5
Antimony
903.65
630.50
165
Silver
1233.95
960.80
88.3
Gold
1336.15
1063.00
64.5
1356
1083
134
Copper
*From Young, Hugh D., University Physics, 7th Ed. Table 15-4.
Boiling
point
K
Boiling
point
°C
Heat of
vaporization
(103 J/kg)
Helium
4.216
-268.93
20.9
Hydrogen
20.26
-252.89
452
Nitrogen
77.34
-195.81
201
Oxygen
90.18
-182.97
213
Ethyl alcohol
351
78
854
Mercury
630
357
272
Water
373.15
100.00
2256
Sulfur
717.75
444.60
326
Lead
2023
1750
871
Antimony
1713
1440
561
Silver
2466
2193
2336
Gold
2933
2660
1578
Copper
2840
2567
5069
Boiling Points and Heat of
Vaporization
Substance
*From Young, Hugh D., University Physics, 7th Ed. Table 15-4.
8
Chemistry and Physics
Thermal Energy / Heat Study Guide
Dr. Hazlett
State
Temperature
K
Hydrogen
Triple point
13.81
Hydrogen
Boiling point
20.28
Neon
Boiling point
27.102
Oxygen
Boiling point
54.361
Argon
Triple point
83.798
Oxygen
Boiling point
90.188
Water
Triple point
273.16
Water
Boiling point
373.125
Tin
Melting point
505.074
Zinc
Melting point
692.664
Silver
Melting point
1235.08
Gold
Melting point
1337.58
Temperature Standard Points
Substance
Primary fixed points in the international temperature scale.
From Halliday and Resnick
Triple Point Data
Substance
Temperature Pressure
K
105Pa
Helium-4 (-point)
2.17
0.0507
Hydrogen
13.84
0.0704
Deuterium
18.63
0.171
Neon
24.57
0.432
Oxygen
54.36
0.00152
Nitrogen
63.18
0.125
Ammonia
195.40
0.0607
Sulfur dioxide
197.68
0.00167
Carbon dioxide
216.55
5.17
Water
273.16
0.00610
From Young, University Physics, 8th Ed., Table 16-3