First Law of Thermodynamics

Physics 102Professor Lee

CarknerLecture 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)

Q2 = mL = (100)(33.5X104) = 3.35X107 J Total = 4.2917X107 J

What is Frosty’s final temperature if Santa removes 45 million joules? Since 45X106 – 42.917X106 = 2.083X106 J, Frosty will be colder

than –5 C Frosty is 9.97 degrees colder than his original –5 C or Tf = -

14.97 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 = mcT Instead of the mass we usually have the number

of moles and so use the molar specific heat (C) Q = nCT

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 (CV) QV = nCVT QV = nCVT = U = (3/2)nRT

Molar specific heat at constant pressure (CP) QP = nCPT QP = nCPT = (3/2)nRT + nRT

CP > CV since some heat goes into work for CP

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=PV U = nCpT-PV

Isobaric Process

Today’s PAL Consider a cylinder with a volume

of 2 m3 filled with 1 mole of an ideal gas at a temperature of 300 K

If the gas is compressed to 1 m3 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(Vf/Vi)

Isotherms

Isochoric

In an isochoric process the volume does not change

W = 0 soU = Q

We can also relate to specific heat at constant volume: Q= nCVT

IsochoricProcess

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 = CP/CV

For any adiabatic process PV = constant TV-1 = constant

Adiabatic Process

Cyclical Process

A cyclical process returns to its initial state

Eint = 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 18.1-18.4 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