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Energy
 Energy is an ability possessed by matter to do
 work or exchange heat. That is, the capacity
 to move matter or supply heat.

 Energy exists in different forms which can be
 converted

 The S.I. units are the Joule (J)
Heat
 Heat is the transfer of thermal energy from one object
  to another because they are at different temperatures.
 We usually use the letter q to represent this quantity
 Heat is a method of energy transfer from a hot object
  to a cold one

 Thermal energy is the energy associated with the
 random motion of the atoms and or molecules

 Temperature change is a change in the average kinetic
 energy of an object
Calorie
 The amount of heat required to raise the
 temperature of one gram of pure water by
 one degree Celsius

 one calorie = 4.184 Joules or one Joule = 0.239
  calories

 0ne Joule of energy is about the energy needed for a
 single heartbeat
Potential energy (PE)
 energy an object has as a result of its position or
  composition.
 The energy stored in chemical bonds is called
  chemical potential energy
 Natural gas, coal and other major sources of heat
 have potential (chemical) energy due to their
 composition
Kinetic energy (KE)
 Kinetic energy - energy as object has as
 a result of its motion.

 K.E. = 1/2 mv2
Law of Conservation of Energy
 Energy can be converted from one form to another,
  but the total quantity of energy is assumed to
  remain constant in ordinary processes
Measuring heat transfer
 Specific heat
 Defined as the quantity of heat required to
  raise the temperature of 1.00 gram of the
  substance by 1.00 oC – the book uses the
  symbol C
 for water, C = 4.184 J/goC
Specific Heat Formula
 Changing the temperature of a sample from Ti to Tf
  requires heat (q) = m C ∆T

 ∆T = Tf - Ti
 C = specific heat for a particular substance
 m = mass of the sample of matter


 always have Tf first as the sign of ∆ T is important
 q is + for an endothermic process - Tf > Ti
 q is - for an exothermic process - Tf < Ti
Specific Heat Formula
 Loss of heat for one object = gain in heat of the second

       - q lost = q gained
      - m C ∆T = m C ∆T
**Tip Hot side vs. Cold side**
         Ti – Tf    Tf - Ti
Sample problem
 How much heat is required to raise the temperature of
    100.0 g of Cu from 15.0oC to 35.0oC?
    C for Cu is 0.384 J/goC
   q=      m       C           ∆T
   q = 100.0 g *0.384 J/goC* (35.0 - 15.0)oC
   q = 768 J
   Notice that the value is ( + ) since heat was added to
    the system
Sample problem
 A 4.50 g nugget of pure gold absorbed 276 J of heat.
  What was the final temperature of the gold if the
  initial temperature was 25.0 oC? C for Au is 0.129 J/goC
 q = m C ∆T




 The final temperature is 500. oC
Thermochemistry
 The study of the quantity of heat
  absorbed or given off by chemical
  reactions.
 Or the study of heat change in
  chemical reactions.

 All chemical reactions either give off or
 absorb energy
First Law of Thermodynamics
 The total energy of the universe is a
 constant.

 Energy can be converted from one form
 to another or transferred from a system
 to the surroundings or vice versa.
First Law of Thermodynamics
 Universe = system + surroundings

 System = the specific part of the
 universe that contains the reaction or
 process you wish to study

 Surroundings = everything in the
 universe other than the system
The system is the specific part of the universe that is
of interest in the study.
                     SURROUNDINGS
                             SYSTEM




                  open          closed        isolated

 Exchange:    mass & energy     energy        nothing
                                                          6.2
Exothermic process is any process that
gives off heat or transfers thermal energy
from the system to the surroundings.

 2H2 (g) + O2 (g)      2H2O (l) + energy

        H2O (g)       H2O (l) + energy
Endothermic process is any process in
which heat has to be supplied to the
system from the surroundings.

energy + 2HgO (s)     2Hg (l) + O2 (g)

 energy + H2O (s)      H2O (l)
Enthalpy (H) is used to quantify the heat flow into or out of a
system in a process that occurs at constant pressure.


           H = H (products) – H (reactants)

      H = heat given off or
     absorbed during a reaction at constant pressure
The heat supplied is equal to the change in
another thermodynamic property called enthalpy
(H)
i.e.   H = q
• this relation is only valid at constant pressure



 As most reactions in chemistry take place at
 constant pressure we can say that:
 A change in enthalpy = heat supplied
Therefore
the process
is
              Exothermic
                     Hproducts < Hreactants

                                 H<0

                     Therefore    H is
                                 negative
Therefore
the process
is
              Endothermic

                      Hproducts > Hreactants
                             H>0
                     Therefore    H is
                                 positive
Thermochemical Equations


                             Is H negative or positive?

                                 System gives off heat

                                 Exothermic

                                   H<0


  890.4 kJ are released for every 1 mole of methane
  that is combusted at 25.00C and 1 atm.
CH4 (g) + 2O2 (g)   CO2 (g) + 2H2O (l)   H = -890.4 kJ
Thermochemical Equations


                             Is H negative or positive?

                                System absorbs heat

                                Endothermic

                                 H>0


6.01 kJ are absorbed for every 1 mole of ice that melts
at 00C and 1 atm.

             H2O (s)       H2O (l)       H = 6.01 kJ
Thermochemical Equations
• The stoichiometric coefficients always refer to the
  number of moles of a substance
               H2O (s)       H2O (l)      H = 6.01 kJ
• If you reverse a reaction, the sign of H changes
         H2O (l)                H2O (s)   H = -6.01 kJ
•    If you multiply both sides of the equation by a factor n, then
       H must change by the same factor n.

    2H2O (s)         2H2O (l)       H = 2 x 6.01 = 12.0 kJ
Thermochemical Equations


• The physical states of all reactants and products
  must be specified in thermochemical equations.

   H2O (s)              H2O (l)       H = 6.01 kJ
     H2O (l)             H2O (g)   H = 44.0 kJ
Thermochemical Equations


How much heat is evolved when 266 g of white
phosphorus (P4) burn in air?
    P4 (s) + 5O2 (g)                 P4O10 (s)    H = -3013 kJ

                   1 mol P4
     266 g P4 x                x 3013 kJ    = 6470 kJ
                  123.9 g P4     1 mol P4
Phase Changes
 Melting
 phase change from solid to liquid

 Freezing
 phase change from liquid to solid

 freezing point/melting point
 temperature at which a liquid converts into
 the solid state & vice versa
Melting
 Energy is supplied to a solid to enable
 it to vibrate more enthusiastically
 until molecules can move past each
 other and flow as a liquid

 endothermic process     ( H positive)
Freezing
 Liquid releases energy and allows
 molecules to settle into a lower
 energy state and form a solid

 exothermic process               ( H negative)
 (we remove heat from water when making ice in freezer)
Enthalpy of Fusion
 Enthalpy of fusion (Hfus)
 energy necessary to break enough IMF’s to
 turn a solid into a liquid

 heat absorbed by the substance in changing
 solid into a liquid without raising its
 temperature

 Energy released when turning a liquid into
 a solid = - Hfus
Enthalpy of Fusion Calculations
 Enthalpy of fusion is used in calculating energy
 needed to melt or released when freezing


q = m × H fus
 q = energy
 m = mass of sample or mol depends upon
       information given on the chart
 Hfus = enthalpy of fusion (melting)
 (use (–Hfus ) for freezing)
Sample problem
 Find the enthalpy of fusion of water if it takes 4175 J
    to melt 12.5 g of water.

 m = 12.5 g H2O
 q = 4175 J
                          q = m × H fus
                       4175 J = (12.5 g) × H fus
                         Hfus = 4175 J / 12.5 g
                         Hfus = 334 J/g
Phase Changes
 Vaporization
 phase change from liquid to a gas

 Condensation
 phase change from gas to liquid

 boiling point/condensation point
 temperature at which a liquid converts into
 the gas state & vice versa
Vaporization
 Energy has to be supplied to a liquid
 to enable it to overcome forces that
 hold molecules together

 endothermic process      ( H positive)
Condensation
 Energy has to be released from a gas
 to enable it to hold molecules close
 together

 exothermic process     ( H negative)
Enthalpy of Vaporization
 Enthalpy of vaporization (Hvap)
 The energy necessary to break the rest of
 the IMF’s and turn a liquid into a gas

 The amount of heat required to convert a liquid
 at its boiling point into vapor without an
 increase in temperature

 Energy released when turning a gas into a
 liquid = - Hvap
Enthalpy of Vaporization
               Calculations
 Enthlapy of vaporization is used in calculating
 energy needed to boil or released when condensing


q = m × H vap
 q = energy
 m = mass of sample or mol depends upon
      information given on the chart
 Hvap = enthalpy of vaporization (boiling)
 (use –Hvap for condensing)
Sample Problem
 How much energy is required to vaporize 10.0 g of
    water at its boiling point?
 m = 10.0 g H2O
 Hvap = 2260 J/g
                          q = m      x Hvap
                          q = 10.0 g x 2260 J / g
                          q = 22600 J

Heating Curve for H2O
                        Each step along the line
                        requires a certain
                        amount of energy
                         Step 1  q1 = m C ∆T

                         Step 2  q2 = m H fus
                         Step 3  q3 = m C ∆T

                         Step 4  q4 = m H vap
                         Step 5  q5 = m C ∆T



Total energy  qtot= q1+q2+q3+q4+q5
Sample Problem
 See packet
Phase Changes
 Sublimation
 conversion of a solid directly to a gas


 Deposition
 conversion of a gas directly to a solid


 ΔHsublimation = -ΔHdeposition
Standard Enthalpies of Formation
 The standard enthalpy of formation of a substance,
 denoted Hfo, is the enthalpy change for the
 formation of one mole of a substance in its
 standard state from its component elements in
 their standard state.

  – Note that the standard enthalpy of formation for
    a pure element in its standard state is zero.
 Standard conditions = 25 0 C and 1.0 atm
Examples
Standard Enthalpies of Formation
 The law of summation of heats of formation states
 that the enthalpy of a reaction is equal to the total
 formation energy of the products minus that of the
 reactants.
     o             o                      o
 H           n   H f (products )    m   H f (reactants )
         is the mathematical symbol meaning “the
         sum of”, and m and n are the coefficients of
         the substances in the chemical equation.
A Problem to Consider
 You record the values of Hfo under the formulas in
 the equation, multiplying them by the coefficients in
 the equation.

4NH 3 (g ) 5O 2 (g )        4NO(g ) 6H 2O(g )
4( 45.9)      5(0)        4(90.3)    6( 241.8)
  - You can calculate Ho by subtracting the values
    for the reactants from the values for the
    products.
Calorimetry
 Process of measuring the heat of reaction of a physical
 or chemical change
Coffee cup calorimetry
•A chemical reaction is spontaneous if it is accompanied by an increase in the
total entropy of the system and the surroundings




• Spontaneous exothermic reactions are common (e.g. hot metal block
spontaneously cooling) because they release heat that increases the entropy
of the surroundings.


•Endothermic reactions are spontaneous only when the entropy of the system
increases enough to overcome the decrease in entropy of the surroundings
A spontaneous change is a change that has a
 tendency to occur without been driven by an
 external influence
 e.g. the cooling of a hot metal block to the
 temperature of its surroundings



A non-spontaneous change is a change that occurs
only when driven
e.g. forcing electric current through a metal block
to heat it
Total entropy               entropy change of             entropy change of
change                =     system                +       surroundings



                           Dissolving




          disorder of solution           disorder of
                                         surroundings




  • must be an overall increase in disorder for dissolving to occur
Second Law of Thermodynamics:
  the disorder (or entropy) of a system tends to
increase

                       ENTROPY (S)


       •Entropy is a measure of disorder
       • Low entropy (S) = low disorder
       •High entropy (S) = greater disorder




• hot metal block tends to cool
• gas spreads out as much as possible
•A change in internal energy can be identified with the heat supplied at constant
volume




                 ENTHALPY (H)

(comes from Greek for “heat inside”)



  • the change in internal energy is not equal to the heat supplied when the
  system is free to change its volume
  • some of the energy can return to the surroundings as expansion work

         U < q
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10
&cts=1331740615595&sqi=2&ved=0CGkQFjAJ&url=http%3A%2F%2Ffunn
yscience.co.uk%2Fsciweb%2Ftriple%2F21stCentury7s%2Fenergetics%25
20revision%2520lesson%2Fteacherledpowerpoint.ppt&ei=B7pgT-
bBOKHo0QGzwdGLBw&usg=AFQjCNHUVlz2eea3crXO6PNmgc2v8gP
6tQ&sig2=a3DxAba4X0zgrxQOZ0VdWg

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5
&cts=1331741024820&ved=0CEwQFjAE&url=http%3A%2F%2Fwww.che
mistry.mtu.edu%2Fpages%2Fcourses%2Ffiles%2Fch1120-
sgreen%2Fchap19_lec_sg.ppt&ei=JsBgT7SDGYPt0gH5iI3OBw&usg=AF
QjCNGWPbwiYC8QiQFgkRpRcnBAfCYC5w&sig2=_J_vMHh6iTyOAQd
ZPU2FlA
links
 http://www.google.com/url?sa=t&rct=j&q=&esrc=s&so
 urce=web&cd=1&cts=1331745413332&sqi=2&ved=0CDA
 QFjAA&url=http%3A%2F%2Fandromeda.rutgers.edu
 %2F~jimms%2Fsummerpp_6.ppt&ei=itFgT6q7NsPtsg
 bW1-
 WQBg&usg=AFQjCNE2Q7902UdFJWATVzJdE60I8M
 VhSQ&sig2=wUUb2pJcqXOjJpaqMCv01g

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Energy ch 16

  • 1. Energy  Energy is an ability possessed by matter to do work or exchange heat. That is, the capacity to move matter or supply heat.  Energy exists in different forms which can be converted  The S.I. units are the Joule (J)
  • 2. Heat  Heat is the transfer of thermal energy from one object to another because they are at different temperatures.  We usually use the letter q to represent this quantity  Heat is a method of energy transfer from a hot object to a cold one  Thermal energy is the energy associated with the random motion of the atoms and or molecules  Temperature change is a change in the average kinetic energy of an object
  • 3. Calorie  The amount of heat required to raise the temperature of one gram of pure water by one degree Celsius  one calorie = 4.184 Joules or one Joule = 0.239 calories  0ne Joule of energy is about the energy needed for a single heartbeat
  • 4. Potential energy (PE)  energy an object has as a result of its position or composition.  The energy stored in chemical bonds is called chemical potential energy  Natural gas, coal and other major sources of heat have potential (chemical) energy due to their composition
  • 5. Kinetic energy (KE)  Kinetic energy - energy as object has as a result of its motion.  K.E. = 1/2 mv2
  • 6. Law of Conservation of Energy  Energy can be converted from one form to another, but the total quantity of energy is assumed to remain constant in ordinary processes
  • 7. Measuring heat transfer  Specific heat  Defined as the quantity of heat required to raise the temperature of 1.00 gram of the substance by 1.00 oC – the book uses the symbol C  for water, C = 4.184 J/goC
  • 8. Specific Heat Formula  Changing the temperature of a sample from Ti to Tf requires heat (q) = m C ∆T  ∆T = Tf - Ti  C = specific heat for a particular substance  m = mass of the sample of matter  always have Tf first as the sign of ∆ T is important  q is + for an endothermic process - Tf > Ti  q is - for an exothermic process - Tf < Ti
  • 9. Specific Heat Formula  Loss of heat for one object = gain in heat of the second  - q lost = q gained  - m C ∆T = m C ∆T **Tip Hot side vs. Cold side**  Ti – Tf Tf - Ti
  • 10. Sample problem  How much heat is required to raise the temperature of 100.0 g of Cu from 15.0oC to 35.0oC? C for Cu is 0.384 J/goC  q= m C ∆T  q = 100.0 g *0.384 J/goC* (35.0 - 15.0)oC  q = 768 J  Notice that the value is ( + ) since heat was added to the system
  • 11. Sample problem  A 4.50 g nugget of pure gold absorbed 276 J of heat. What was the final temperature of the gold if the initial temperature was 25.0 oC? C for Au is 0.129 J/goC  q = m C ∆T  The final temperature is 500. oC
  • 12. Thermochemistry  The study of the quantity of heat absorbed or given off by chemical reactions.  Or the study of heat change in chemical reactions.  All chemical reactions either give off or absorb energy
  • 13. First Law of Thermodynamics  The total energy of the universe is a constant.  Energy can be converted from one form to another or transferred from a system to the surroundings or vice versa.
  • 14. First Law of Thermodynamics  Universe = system + surroundings  System = the specific part of the universe that contains the reaction or process you wish to study  Surroundings = everything in the universe other than the system
  • 15. The system is the specific part of the universe that is of interest in the study. SURROUNDINGS SYSTEM open closed isolated Exchange: mass & energy energy nothing 6.2
  • 16. Exothermic process is any process that gives off heat or transfers thermal energy from the system to the surroundings. 2H2 (g) + O2 (g) 2H2O (l) + energy H2O (g) H2O (l) + energy
  • 17. Endothermic process is any process in which heat has to be supplied to the system from the surroundings. energy + 2HgO (s) 2Hg (l) + O2 (g) energy + H2O (s) H2O (l)
  • 18. Enthalpy (H) is used to quantify the heat flow into or out of a system in a process that occurs at constant pressure. H = H (products) – H (reactants) H = heat given off or absorbed during a reaction at constant pressure
  • 19. The heat supplied is equal to the change in another thermodynamic property called enthalpy (H) i.e. H = q • this relation is only valid at constant pressure As most reactions in chemistry take place at constant pressure we can say that: A change in enthalpy = heat supplied
  • 20. Therefore the process is Exothermic Hproducts < Hreactants H<0 Therefore H is negative
  • 21. Therefore the process is Endothermic Hproducts > Hreactants H>0 Therefore H is positive
  • 22. Thermochemical Equations Is H negative or positive? System gives off heat Exothermic H<0 890.4 kJ are released for every 1 mole of methane that is combusted at 25.00C and 1 atm. CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) H = -890.4 kJ
  • 23. Thermochemical Equations Is H negative or positive? System absorbs heat Endothermic H>0 6.01 kJ are absorbed for every 1 mole of ice that melts at 00C and 1 atm. H2O (s) H2O (l) H = 6.01 kJ
  • 24. Thermochemical Equations • The stoichiometric coefficients always refer to the number of moles of a substance H2O (s) H2O (l) H = 6.01 kJ • If you reverse a reaction, the sign of H changes H2O (l) H2O (s) H = -6.01 kJ • If you multiply both sides of the equation by a factor n, then H must change by the same factor n. 2H2O (s) 2H2O (l) H = 2 x 6.01 = 12.0 kJ
  • 25. Thermochemical Equations • The physical states of all reactants and products must be specified in thermochemical equations. H2O (s) H2O (l) H = 6.01 kJ H2O (l) H2O (g) H = 44.0 kJ
  • 26. Thermochemical Equations How much heat is evolved when 266 g of white phosphorus (P4) burn in air? P4 (s) + 5O2 (g) P4O10 (s) H = -3013 kJ 1 mol P4 266 g P4 x x 3013 kJ = 6470 kJ 123.9 g P4 1 mol P4
  • 27. Phase Changes  Melting  phase change from solid to liquid  Freezing  phase change from liquid to solid  freezing point/melting point  temperature at which a liquid converts into  the solid state & vice versa
  • 28. Melting  Energy is supplied to a solid to enable it to vibrate more enthusiastically until molecules can move past each other and flow as a liquid  endothermic process ( H positive)
  • 29. Freezing  Liquid releases energy and allows molecules to settle into a lower energy state and form a solid  exothermic process ( H negative)  (we remove heat from water when making ice in freezer)
  • 30. Enthalpy of Fusion  Enthalpy of fusion (Hfus)  energy necessary to break enough IMF’s to turn a solid into a liquid  heat absorbed by the substance in changing solid into a liquid without raising its temperature  Energy released when turning a liquid into a solid = - Hfus
  • 31. Enthalpy of Fusion Calculations  Enthalpy of fusion is used in calculating energy needed to melt or released when freezing q = m × H fus  q = energy  m = mass of sample or mol depends upon information given on the chart  Hfus = enthalpy of fusion (melting)  (use (–Hfus ) for freezing)
  • 32. Sample problem  Find the enthalpy of fusion of water if it takes 4175 J to melt 12.5 g of water.  m = 12.5 g H2O  q = 4175 J  q = m × H fus  4175 J = (12.5 g) × H fus  Hfus = 4175 J / 12.5 g  Hfus = 334 J/g
  • 33. Phase Changes  Vaporization  phase change from liquid to a gas  Condensation  phase change from gas to liquid  boiling point/condensation point  temperature at which a liquid converts into  the gas state & vice versa
  • 34. Vaporization  Energy has to be supplied to a liquid to enable it to overcome forces that hold molecules together  endothermic process ( H positive)
  • 35. Condensation  Energy has to be released from a gas to enable it to hold molecules close together  exothermic process ( H negative)
  • 36. Enthalpy of Vaporization  Enthalpy of vaporization (Hvap) The energy necessary to break the rest of the IMF’s and turn a liquid into a gas  The amount of heat required to convert a liquid at its boiling point into vapor without an increase in temperature  Energy released when turning a gas into a liquid = - Hvap
  • 37. Enthalpy of Vaporization Calculations  Enthlapy of vaporization is used in calculating energy needed to boil or released when condensing q = m × H vap  q = energy  m = mass of sample or mol depends upon information given on the chart  Hvap = enthalpy of vaporization (boiling)  (use –Hvap for condensing)
  • 38. Sample Problem  How much energy is required to vaporize 10.0 g of water at its boiling point?  m = 10.0 g H2O  Hvap = 2260 J/g  q = m x Hvap  q = 10.0 g x 2260 J / g  q = 22600 J 
  • 39. Heating Curve for H2O Each step along the line requires a certain amount of energy Step 1  q1 = m C ∆T Step 2  q2 = m H fus Step 3  q3 = m C ∆T Step 4  q4 = m H vap Step 5  q5 = m C ∆T Total energy  qtot= q1+q2+q3+q4+q5
  • 41. Phase Changes  Sublimation  conversion of a solid directly to a gas  Deposition  conversion of a gas directly to a solid  ΔHsublimation = -ΔHdeposition
  • 42. Standard Enthalpies of Formation  The standard enthalpy of formation of a substance, denoted Hfo, is the enthalpy change for the formation of one mole of a substance in its standard state from its component elements in their standard state. – Note that the standard enthalpy of formation for a pure element in its standard state is zero.  Standard conditions = 25 0 C and 1.0 atm
  • 43.
  • 45. Standard Enthalpies of Formation  The law of summation of heats of formation states that the enthalpy of a reaction is equal to the total formation energy of the products minus that of the reactants. o o o H n H f (products ) m H f (reactants ) is the mathematical symbol meaning “the sum of”, and m and n are the coefficients of the substances in the chemical equation.
  • 46. A Problem to Consider  You record the values of Hfo under the formulas in the equation, multiplying them by the coefficients in the equation. 4NH 3 (g ) 5O 2 (g ) 4NO(g ) 6H 2O(g ) 4( 45.9) 5(0) 4(90.3) 6( 241.8) - You can calculate Ho by subtracting the values for the reactants from the values for the products.
  • 47.
  • 48. Calorimetry  Process of measuring the heat of reaction of a physical or chemical change
  • 50. •A chemical reaction is spontaneous if it is accompanied by an increase in the total entropy of the system and the surroundings • Spontaneous exothermic reactions are common (e.g. hot metal block spontaneously cooling) because they release heat that increases the entropy of the surroundings. •Endothermic reactions are spontaneous only when the entropy of the system increases enough to overcome the decrease in entropy of the surroundings
  • 51. A spontaneous change is a change that has a tendency to occur without been driven by an external influence e.g. the cooling of a hot metal block to the temperature of its surroundings A non-spontaneous change is a change that occurs only when driven e.g. forcing electric current through a metal block to heat it
  • 52. Total entropy entropy change of entropy change of change = system + surroundings Dissolving disorder of solution disorder of surroundings • must be an overall increase in disorder for dissolving to occur
  • 53. Second Law of Thermodynamics: the disorder (or entropy) of a system tends to increase ENTROPY (S) •Entropy is a measure of disorder • Low entropy (S) = low disorder •High entropy (S) = greater disorder • hot metal block tends to cool • gas spreads out as much as possible
  • 54. •A change in internal energy can be identified with the heat supplied at constant volume ENTHALPY (H) (comes from Greek for “heat inside”) • the change in internal energy is not equal to the heat supplied when the system is free to change its volume • some of the energy can return to the surroundings as expansion work U < q
  • 56. links  http://www.google.com/url?sa=t&rct=j&q=&esrc=s&so urce=web&cd=1&cts=1331745413332&sqi=2&ved=0CDA QFjAA&url=http%3A%2F%2Fandromeda.rutgers.edu %2F~jimms%2Fsummerpp_6.ppt&ei=itFgT6q7NsPtsg bW1- WQBg&usg=AFQjCNE2Q7902UdFJWATVzJdE60I8M VhSQ&sig2=wUUb2pJcqXOjJpaqMCv01g