Heat, work and first law of thermodynamics

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Heat, work and first law of thermodynamics

• Phys 2101
• Gabriela González

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Temperature, Heat and heat capacity

• Temperature is a property of systems in thermal
  equilibrium.
• Heat is energy transferred between systems at
  different temperatures.
• When talking about heat, we usually use the
  symbol Q. The SI unit for heat is the Joule.
  However, more common units are Btu (British
  thermal unit) and calories
• 1 Btu 1055 J
• 1 cal 4.186 J (1 Cal 1kcal 1,000 cal)
• The heat capacity C of an object is the
  proportionality constant between heat absorbed
  and resulting change in temperature
• Q C ?T C (Tf-Ti)
• SI units for C are J/k, but common units are
  cal/oC.

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Heat capacity, heat of transformation

• Heat capacity, like volume or mass, is a
  property that depends on the amount of material
  we are considering. A property that only depends
  on the substance (like density) is specific heat
  c
  cC/m ? Q c m ?T
• The specific heat of water is
• c 1 cal/(goC) 1 Btu/(lboF)
  4190 J/kg K
• When a material undergoes a phase transformation
  (it is melting, or boiling), the temperature will
  not change, but heat is absorbed (or emitted) in
  the transformation. The energy per unit of mass
  is called the heat of transformation L
• Q
  L m
• The heat of transformation for water is 333 kJ/kg
  (fusion), 2256 kJ/kg (vaporization)

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Example

• What is the amount of energy required to melt
  100g of silver at room temperature?
• First, we need to get the silver to the
• melting temperature, 1235K from room
  temperature, 293K
• Q1 cAgm?T 236 (J/kgK) x 0.1 kg x
  (1235K-293K)22,231 J
• Then, we need to melt the silver
• Q2 Lm 105 kJ/kg x 0.1kg 10,500 J
• Total energy required
• Q Q1Q2 32,731 J 31 Btu 7.8 Cal

A--Granulating ladles. B--Wind furnace.
C--Another wind furnace made of potter's clay, on
a tripod. D--Crucible in which the silver is
melted. E--Crucible used as ladle. F--Copper
basin for drying the granules. G--An iron grate
on which to heat the silver. H--The man who
granulates. K--The man holding the broom.
Treatise on the foremost mineralogy and
metallurgy (1598)
http//oldsite.library.upenn.edu/etext/collections
/smith/ercker/
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Heat and Work

• A force acting on a system can heat it up (or
  cool it down), by working on it.
• A change in temperature produced in a system can
  be used to produce mechanical work.

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p-V diagrams
Changing the systems pressure and volume from an
initial to a final state can be done using
different amounts of work (and heat transferred)
Going back to the original state does not mean
that no work was done!
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First law of Thermodynamics

• The work W done by the system during a
  transformation from an initial state to a final
  state depends on the path taken.
• The heat Q absorbed by the system during a
  transformation from an initial state to a final
  state depends on the path taken.
• However, the difference Q W does not depend on
  the path taken! We define this quantity as the
  change in internal energy
• ?Eint Q W
• The internal energy of a system increases if
  energy is added as heat, and decreases if energy
  is lost as work done by the system.

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Example

• The figure shows four possible paths to take a
  system from an initial state to a final state.
  Rank the paths according to
• the change in internal energy
• the work done by the system
• the magnitude of energy transferred as heat

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1st Law special cases

• First Law of thermodynamics ?Eint Q
  W
• Special processes
• Adiabatic Q0 ? ?Eint W
• thermally insulated system, or
• very quick process
• Constant Volume W0 ? ?Eint Q
• Cyclical ?Eint 0 ? Q W
• Free expansion Q W 0 ? ?Eint 0
• happens in isolated systems

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Example

• Figure (a) shows a cylinder containing gas and
  closed by a movable piston. The cylinder is kept
  submerged in an ice water mixture. The piston is
  quickly pushed down from position 1 to position 2
  and then held at position 2 until the gas is
  again at the temperature of the ice water
  mixture it then is slowly raised back to
  position 1. Figure (b) is a p-V diagram for the
  process. If 140 g of ice is melted during the
  cycle, how much work has been done on the gas?