**Thermal Energy**

Temperature and Heat

-Heat Transfer

-Thermal Expansion

**Ideal Gases**

Equal to Boltzmann's Constant times Avogadro's number

Boltzmann's Constant=1.38x10^23 J/K

Avogadro's number=the number of basic particles per mole of a substance NA=6.0221415 × 1023

Atomic Model of Gas

PV Diagrams

Represents ideal gas processes

Each point represents a single unique state of gas

Constant Volume, Vf=Vi

Represented as a vertical line

Isobaric Processes= constant pressure, Pf=Pi

Represented as a horizontal line

Isothermal Processes= constant temperature, Tf=Ti

Represented as a hyperbola due to the inverse relationship between pressure and volume

Adiabatic=an instant change in pressure with no time to change heat

Laws of Thermodynamics

First Law and Second Law

Entropy

The Carnot Cycle

**Amanda Hymer, Katie Darrah, and Samantha Caramico.**

Processes

**Ideal gas- gas where all collisions between atoms and molecules are perfectly elastic**

Ideal gas law- PV=nRT

P=pressure

V=volume

n=number of moles

R=ideal gas constant (8.314 J·K−1·mol−1)

T= temperature in kelvins

Ideal gas law- PV=nRT

P=pressure

V=volume

n=number of moles

R=ideal gas constant (8.314 J·K−1·mol−1)

T= temperature in kelvins

Ideal Gas Constant

Thermal Energy is equal to the total kinetic energy of the moving atoms in gas

Temperature is a measure of average kinetic energy

measured in kelvins

T(K)=T(C)+273

Kavg=(3/2)KBT

KB=Boltzmann's Constant 1.38x10^23 J/K

Thermal energy of an ideal gas with N atoms is equal to the sum of kinetic energy

Eth=NKavg=(3/2)NKBT

Thermal Energy id directly proportional to temperature

Energy of Ideal Gas

Kinetic Theory= a theory that describes physical properties in terms of motion in atoms and molecules, such as pressure and volume

Molecules in a sample have different speeds

The average speed is called root mean square (rms)

Vrms=√(3Kb/T)

Ideal Gas Processes

Properties:

Quantity is fixed

Defined initial state of pressure, volume and temperature

Defined final state of pressure, volume and temperature

Number of moles and molecules does not change in a sealed container

(PiVi)/Tf=(PfVf)/Tf

First Law: when only the thermal energy changes

Eth= W + Q

Eth= thermal energy; W= work (J); Q= heat (J)

Second Law: the entropy of an isolated system always increases until equilibrium is reached

heat energy spontaneously flows only from hot to cold

the energy transformation is irreversible

no heat engine can be 100% efficient

-Mechanical Equivalent of Heat.

-Methods of Heat Transfer

-occurs when energy is transferred into or out of something, caused by differences in temperature.

A measure of the degree of disorder in a system, and this always increases because no system is perfect

Isovolumetric: a gas process with an unchanging volume. So W=0 and V=0

Eth=Q

Isobaric: a gas process that occurs with an unchanging pressure. So p=0 and W= -p V

Eth= Q + (-p V)

Isothermal: a gas process that occurs with an unchanging temperature. So T=0 and Eth=0

Q=-W

Adiabatic: a gas process that occurs when heat is not transferred. So Q=0 in this case.

Eth= W

-the amount of heat energy depends on three quantities

-change in temperature: T

-mass: m

-heat capacity: c

Q=cm T

H=

Q

L

___

kA(T -T )

_________

2

1

L

=

=

kA T

_______

L

-the rate at which heat conducts depends on:

-temperature difference: T

-cross section area heat is flowing through: A

-thermal conductivity: k

-distance: L

-energy passes from heat to cold

-Conduction: substances in direct contact with one another

*more conduction= more rapid heat transferred

*substance heated, particles gain more energy

-Convection: warmer areas of a liquid or gas rise to cooler areas

*continuous circular pattern

-Radiation: does not rely upon contact between the heat source and the heated object

*infrared radiation: heat transmitted through an empty space by thermal radiation

-electromagnetic radiation

-no mass exchanged

-most substances change in size once applied to a change in temperature

*increase in temperature= expansion

*decrease in temperature= contracts

-temperature is the measure of how much internal energy a substance contains.

-Example: With an increase in heat, the metal plate will increase. The hole in the center will expand instead of getting smaller.

Heat Engine

takes thermal energy and converts it to other forms

efficiency is described as how much useful work is output for a given amount of heat energy input

emax=1- (Tc/Th)

The Carnot Cycle is the most efficient engine possible

Formula: J=W/Q

-Amount of work required to raise the temperature of a substance of unit mass by one degree Kelvin.

-Constant through nature

Example:

An iron ball is dropped onto the pavement from a height of 100 m. If half of the heat generated goes into warming the ball, find the temperature increase of the ball. (The specific heat capacity of iron is 450J/((kg)(degrees Celsius))

Q=

mgh

2

_____

; Q=cm T

_____

mgh

2

=cm T

T

=

gh

___

2c

=

______________

(9.81m/s )(100m)

2

2(450J/((kg)(C )

.

=1.10 C

.

The Physics Hedgehog