First Law of Thermodynamics Physics 102 Professor Lee Carkner Lecture 6 “of each the work shall become manifest, for the day shall declare it, because in fire it is revealed, and the work of each, what kind it is, the fire shall prove” -- 1 Corinthians 3

PAL #5 Phase Change  Heat needed to melt Frosty (ice at –5 C to water at 20 C)   Q 2 = mL = (100)(33.5X10 4 ) = 3.35X10 7 J   Total = X10 7 J  What is Frosty’s final temperature if Santa removes 45 million joules?  Since 45X10 6 – X10 6 = 2.083X10 6 J, Frosty will be colder than –5 C    Frosty is 9.97 degrees colder than his original –5 C or T f = C

Energy  We know that in mechanics energy is conserved   In what ways can energy be expressed?   Heat can flow in or out  Work can be done on it or by it   The internal energy might change  e.g. by changing the temperature

Work and Internal Energy   No heat can travel in or out  If weight is removed from the piston head, the remaining weight will rise    It must come from the internal energy of the gas

Internal Energy and Work

Work and Heat   The thermal reservoir can add or subtract heat from the system   What happens to the internal energy of the system as heat is applied or work is done?

Heat and Work

Work, Heat and Internal Energy   If we add weight and do 6 J of work we either increase the internal energy by 6 J or produce 6 J of heat or some combination that adds up to 6 

The First Law of Thermodynamics  This conservation of energy is called the First Law of Thermodynamics  U = Q - W   If work is done by the system W is positive, if work is done on the system W is negative    Heat flow in is +, heat flow out is -

PV Diagram  How much work is done if a gas expands and raises a piston?   Depends on:      The relationship between P and  V can be complicated, but  Work equals area under curve in PV diagram

The P-V Curve   If the volume decreases, work is done on the system and the work is negative   If the process is cyclical and returns to the same point by two different paths the area between the paths is equal to the work (and also equal to the heat)

P-V Diagrams

Internal Energy and Temperature   If all energy is in the kinetic energy of the molecules    The total internal energy is the sum of the kinetic energies of the all the molecules   U = (3/2)NkT for N molecules

Ideal Gas Specific Heats   Q = mc  T  Instead of the mass we usually have the number of moles and so use the molar specific heat (C)  Q = nC  T   However, when we add heat to a gas it may cause the gas to expand and the energy to go into work instead of temperature 

Specific Heats  Molar specific heat at constant volume (C V )  Q V = nC V  T   Q V = nC V  T =  U = (3/2)nR  T   Molar specific heat at constant pressure (C P )  Q P = nC P  T   Q P = nC P  T = (3/2)nR  T + nR  T   C P > C V since some heat goes into work for C P

Types of Processes  We want to understand 5 basic types of thermodynamic processes  For each you should know:     

Isobaric  In an isobaric process the pressure does not change   Can use heat capacity at constant pressure:   Since the area under the PV curve is a square:  W=P  V   U = nC p  T-P  V

Isobaric Process

Today’s PAL  Consider a cylinder with a volume of 2 m 3 filled with 1 mole of an ideal gas at a temperature of 300 K  If the gas is compressed to 1 m 3 at constant pressure, what is the magnitude and sign of the work

Isothermal     U = 0 so Q=W   We can use calculus to find the area under the curve  W = nRTln(V f /V i )

Isotherms

Isochoric  In an isochoric process the volume does not change   W = 0 so  U = Q   We can also relate to specific heat at constant volume:  Q= nC V  T

Isochoric Process

Adiabatic  Adiabatic processes are ones in which no heat is transferred   Q=0 so  U = -W  We can also find relationships with the ratio of specific heats  = C P /C V   For any adiabatic process  PV  = constant  TV  -1 = constant

Adiabatic Process

Cyclical Process  A cyclical process returns to its initial state   E int = 0 so Q=W  There are many different ways to produce a cyclical process 

P-V Diagram P V Isobaric (P=const.) Isochoric (V=const) Isothermal (T=const) Adiabatic (Q=0)

Next Time  Read  Homework Ch 18 P 18, 44, 54  Test 1 next Friday  About 10 multiple choice (~25%)  3-4 problems (~75%)  Equation and constant sheet given