Thermodynamics

AP Phys B Test Review Thermodynamics 4/30/2008

Overview  Thermodynamics

• Heat, Temperature, Energy • Thermal Expansion • Ideal Gas Law • PV Diagrams • Laws of Thermodynamics

Internal Energy and Heat  Internal

Energy: consists of the kinetic and potential energy of the molecular components of a system (i.e. molecular translation, rotation, vibration and bonds).  Heat: The transfer of energy between systems as a result of a temperature difference.

Temperature  Macroscopic:

How “how” or “cold”

something is

• Microscopic: related to the motion of the atoms of a system

 Measured

in Celsius (relative) or Kelvin (absolute) scales.

• Absolute zero.

Thermal Expansion of Solids 

When a “linear” object’s temperature increases, it’s physical dimensions will typically increase.

∆ L = αL 0 ∆ T • 

Coefficient of linear expansion

For a truly 3-d object, there is a volume expansion with increasing temperature

∆V = βV 0∆T

Ideal Gas Law  PV=nRT

(wimpy chemistry version)  PV=Nk T (buff physics version) B

• K : Boltsmann constant B

 ‘nuff

said.

Kinetic Theory of Gases 

 

The number of molecules is large, and the average separation between gas molecules is large The molecules obey Newton’s Laws of Motion The molecules undergo completely elastic collisions with each other and with the walls

•

 

No other interactions

All the gas molecules are identical Note: this allows us to interpret the ideal gas law in terms of microscopic objects!

Kinetic Theory of gases 



Pressure is proportional to the number of molecules per unit volume and their average translational kinetic energy Temperature of a gas is a direct measure of the average kinetic energy of the molecules of the gas.

•

For a monatomic gas, the internal energy is:

3 U = NkBT 2

Specific Heat 

The specific heat of a substance is the amount of heat energy it takes to cause in increase or decrease in temperature.

Q = m c∆T • •

c = specific heat, different for every substance Calorimetry: measuring specific heat by using heat transfer.

Latent Heat 

Latent Heat is defined as the amount of energy it takes to induce a phase change in a substance.

Q = m L •

L = latent heat, varies with phase and substance.

Latent Heat and Specific Heat

Temperature Conduction  Thermal

conduction

• Contact • Radiative • Convection

Zeroth Law of Thermodynamics  If

objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with one another.

• Two objects in thermal equilibrium with each other are at the same temperature.

First Law of Thermodynamics 

The change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its environment

∆U = Q − W • •

If work is done on the system, W is negative. A piston is a good example of this.

Thermodynamic Processes 

Isothermal: Constant temperature

•



Isobaric: constant pressure

•



P = constant

Isovolumetric: constant volume

•



PV = constant

V = constant

Adiabatic: No heat flows into or out of the system

•

Q=0

Thermodynamic Processes  Isothermal

Process

Isobaric and Isovolumetric Processes

Adiabatic Processes

Thermodynamic Processes 

Work done is given by the following:

W = P∆V • • • •

Isothermal, ∆U=0, and Q=-W Isobaric: W=P∆V, Q= ∆U+ P∆V Isovolumetric, W=0 and ∆U=Q Adiabatic, Q=0 so ∆U=W

Second Law of Thermodynamics 

In any closed system, the total entropy must be increasing.

Q ∆S = T



Heat can flow spontaneously from a hot object to a cold object, but not vice versa

Heat Engines  Mechanical

Energy obtained from thermal energy when heat is allowed to flow from a hot reservoir to a cold reservoir.

• First law is critically important here.

Heat Engines 

Efficiency of a heat engine is defined as

Q H − Q L Q L W e = = = 1 − Q H Q H Q H



For the Carnot cycle (see next slide)

TH − TL TL e = = 1 − TH TH

Carnot Cycle  The

most efficient process theoretically possible (not realistic). No device will have an efficiency equal to or greater than a Carnot engine.

Third Law of Thermodynamics  It

is impossible to achieve absolute zero in a real physical system.