Chapter 2 - Thermodynamics and Gases

## Atomic Behavior

The temperature of an object indicates the speed at which the molecules are vibrating

Hot objects = higher speed

Cold objects = slower speed

Temperature is a direct measure of average kinetic energy

In general, hot objects expand and cold objects shrink a little bit

The motion of atoms follows a pattern that is shown in graphs of the number of atoms vs average kinetic energy as a normal curve

Hot temperatures have a lower peak that’s shifted to the right but has the same area under the curve

Cold temperatures have a higher peak that’s shifted to the left but has the same area under the curve

This means that it’s possible for some cold atoms to have greater kinetic energy than hot atoms but on average, hot atoms have more kinetic energy

Thermal energy moves from hot to cold

This is because hot molecules tend to collide with cold molecules which result in a net transfer of kinetic energy to the cold molecule

Remember, this is still on average - exceptions do occur

For objects at the same temperature, there is still an energy exchange between them but the net transfer is 0

We call this

**thermal equilibrium**

## Heat, Temperature, and Power

- a type of energy that can be transferred between objects**Heat (Q)**Measured in Joules

Heat vs. Internal Energy

Heat is transferred not possessed - 10 J of heat was transferred to the second box

Internal energy is possessed - The box has 10 J of internal energy

: The sum of the energies of all molecules in a substance**Internal Energy (U)**

__Temperature (T)__: Related to average kinetic energyMeasured in Kelvins or Degrees Celsius

**Kelvin = Celsius + 273**

Two bodies at the same temperature don’t always have the same internal energy

A bigger object of the same material and temperature will have more internal energy than a smaller object

: Work per time**Power**Measured in Joules per second (same thing as Watts)

## Heat Transfer

There are 3 physical methods of heat transfer

: the transfer of energy from vibrations from atom to atom of an object from the hotter side to the colder side**Conduction**In other words, when 2 objects are touching, the transfer of energy from the hot to the cold object until they’re in thermal equilibrium

Factors that can affect the rate of this heat transfer:

__Thermal conductivity__(k) of the materialMetals are better conductors and have a higher thermal conductivity as compared to something like a piece of wood

The difference in temperatures of the two objects

A greater temperature difference will cause a faster rate of heat transfer

The cross-sectional area of the object the heat is transferred through

A larger cross-sectional area will cause a faster rate of heat transfer

The length of the material the heat is transferred through

A longer object will cause a slower rate of heat transfer

These factors combine to form the equation for the rate of heat transfer:

ΔQ/t = kAΔT/L

ΔQ/t = rate of heat transfer (J/s)

k = thermal conductivity

A = cross-sectional area (m^2)

ΔT = temperature difference (K)

L = length (m)

: the transfer of thermal energy through fluid flow**Convection**Because hotter objects expand, fluids are less dense and naturally rise because their volume is bigger but their mass is the same

: transfer of energy through electromagnetic waves**Radiation**The vibration of charged particles (protons and electrons) creates electromagnetic waves

These waves carry energy away from the object

## Kinetic Theory of Gases

The

assumes for ideal gases:**Kinetic Theory of Gases**Molecules move continuously and randomly

There is a large number of gas molecules in a container

Molecules don’t exert electrical or gravitational forces on each other

All collisions between molecules are elastic

In elastic collisions, kinetic energy is not lost

The Kinetic Theory of Gases derives the following equations:

U = 3/2 nRT = 3/2 NkT

U - internal energy

R - Ideal gas constant - on equation sheet

k - Boltzmann’s constant - given on the equation sheet

T - temperature

Relates the internal energy of a gas to its temperature

v = sqrt((3kT)/(m))

v - velocity of a gas

m - mass

k - Boltzmann’s constant - given on the equation sheet

## Ideal Gas Law

PV = nRT

P - pressure (Pascal - Newton per meter squared)

V - volume of the gas (cubic meters)

n - number of moles of gas

R - ideal gas constant

T - temperature (K)

PV = NkT

N - number of molecules

k - Boltzmann’s constant - given on equation sheet

In times when the number of moles are constant, PV/T is also held constant

Use this formula for calculations

Graphical Analysis

When graphing pressure versus temperature, the temperature at which pressure is 0 is called absolute zero

Zero volume of gas will occur at absolute zero if we plot volume as a function of temperature

## First Law of Thermodynamics

__First Law of Thermodynamics__: The internal energy of a system is conservedΔU = Q + W

ΔU - internal energy

Q - heat added to the gas

If heat is added, sign of Q is positive

W - work done on the gas

If the gas is compressed, work is done on the gas and W is positive

If the gas is expanded, work is done by the gas and W is negative

Remember that Work = Force x distance

## PV Diagrams

- graphs of pressure on the y-axis and volume on the x-axis**PV Diagrams**Isothermal lines - a line in which every point that has the same PV value (and therefore the same T)

Work = -PΔV

Moving to the right on a PV graph is negative work and vice versa

Area under the curve of the graph is equal to magnitude of work

To find ΔT, compare the PV path to isothermal lines or see if P or V changed

To find ΔU, find ΔT because ΔU = 3/2 nRΔT

To find Q, use ΔU = Q + W where Q and W are already given or are found from area under the graph and/or ΔT

Cycles on a PV diagram

Cycles: paths on the PV diagram that start and end at the same point

Same PV value at the start and end → ΔT is 0 → ΔU is 0 → Q = -w (remember the first law of thermodynamics)

Work becomes the area contained in the shape created by the cycle

Four Special Processes (Paths)

Constant Pressure -

__Isobaric__Horizontal lines on the PV graph

Constant Volume -

__Isochoric (Isovolumetric)__Vertical lines on PV graph

Constant Temperature -

__Isothermal__Hyperbolic constant lines on the PV graph

Less steep than Adiabatic processes

Q = -W

No Heat Transfer Between System and Environment -

__Adiabatic__Curved path but steeper than Isothermal process

## Entropy

: a measure of disorder**Entropy**: The entropy of a system cannot decrease unless work is done on that system**Second Law of Thermodynamics**Think of a glass: when broken, work must be done to put it back together in a more orderly state

The universe has a tendency towards entropy

When heat flows into a system, entropy increases

# Chapter 2 - Thermodynamics and Gases

## Atomic Behavior

The temperature of an object indicates the speed at which the molecules are vibrating

Hot objects = higher speed

Cold objects = slower speed

Temperature is a direct measure of average kinetic energy

In general, hot objects expand and cold objects shrink a little bit

The motion of atoms follows a pattern that is shown in graphs of the number of atoms vs average kinetic energy as a normal curve

Hot temperatures have a lower peak that’s shifted to the right but has the same area under the curve

Cold temperatures have a higher peak that’s shifted to the left but has the same area under the curve

This means that it’s possible for some cold atoms to have greater kinetic energy than hot atoms but on average, hot atoms have more kinetic energy

Thermal energy moves from hot to cold

This is because hot molecules tend to collide with cold molecules which result in a net transfer of kinetic energy to the cold molecule

Remember, this is still on average - exceptions do occur

For objects at the same temperature, there is still an energy exchange between them but the net transfer is 0

We call this

**thermal equilibrium**

## Heat, Temperature, and Power

- a type of energy that can be transferred between objects**Heat (Q)**Measured in Joules

Heat vs. Internal Energy

Heat is transferred not possessed - 10 J of heat was transferred to the second box

Internal energy is possessed - The box has 10 J of internal energy

: The sum of the energies of all molecules in a substance**Internal Energy (U)**

__Temperature (T)__: Related to average kinetic energyMeasured in Kelvins or Degrees Celsius

**Kelvin = Celsius + 273**

Two bodies at the same temperature don’t always have the same internal energy

A bigger object of the same material and temperature will have more internal energy than a smaller object

: Work per time**Power**Measured in Joules per second (same thing as Watts)

## Heat Transfer

There are 3 physical methods of heat transfer

: the transfer of energy from vibrations from atom to atom of an object from the hotter side to the colder side**Conduction**In other words, when 2 objects are touching, the transfer of energy from the hot to the cold object until they’re in thermal equilibrium

Factors that can affect the rate of this heat transfer:

__Thermal conductivity__(k) of the materialMetals are better conductors and have a higher thermal conductivity as compared to something like a piece of wood

The difference in temperatures of the two objects

A greater temperature difference will cause a faster rate of heat transfer

The cross-sectional area of the object the heat is transferred through

A larger cross-sectional area will cause a faster rate of heat transfer

The length of the material the heat is transferred through

A longer object will cause a slower rate of heat transfer

These factors combine to form the equation for the rate of heat transfer:

ΔQ/t = kAΔT/L

ΔQ/t = rate of heat transfer (J/s)

k = thermal conductivity

A = cross-sectional area (m^2)

ΔT = temperature difference (K)

L = length (m)

: the transfer of thermal energy through fluid flow**Convection**Because hotter objects expand, fluids are less dense and naturally rise because their volume is bigger but their mass is the same

: transfer of energy through electromagnetic waves**Radiation**The vibration of charged particles (protons and electrons) creates electromagnetic waves

These waves carry energy away from the object

## Kinetic Theory of Gases

The

assumes for ideal gases:**Kinetic Theory of Gases**Molecules move continuously and randomly

There is a large number of gas molecules in a container

Molecules don’t exert electrical or gravitational forces on each other

All collisions between molecules are elastic

In elastic collisions, kinetic energy is not lost

The Kinetic Theory of Gases derives the following equations:

U = 3/2 nRT = 3/2 NkT

U - internal energy

R - Ideal gas constant - on equation sheet

k - Boltzmann’s constant - given on the equation sheet

T - temperature

Relates the internal energy of a gas to its temperature

v = sqrt((3kT)/(m))

v - velocity of a gas

m - mass

k - Boltzmann’s constant - given on the equation sheet

## Ideal Gas Law

PV = nRT

P - pressure (Pascal - Newton per meter squared)

V - volume of the gas (cubic meters)

n - number of moles of gas

R - ideal gas constant

T - temperature (K)

PV = NkT

N - number of molecules

k - Boltzmann’s constant - given on equation sheet

In times when the number of moles are constant, PV/T is also held constant

Use this formula for calculations

Graphical Analysis

When graphing pressure versus temperature, the temperature at which pressure is 0 is called absolute zero

Zero volume of gas will occur at absolute zero if we plot volume as a function of temperature

## First Law of Thermodynamics

__First Law of Thermodynamics__: The internal energy of a system is conservedΔU = Q + W

ΔU - internal energy

Q - heat added to the gas

If heat is added, sign of Q is positive

W - work done on the gas

If the gas is compressed, work is done on the gas and W is positive

If the gas is expanded, work is done by the gas and W is negative

Remember that Work = Force x distance

## PV Diagrams

- graphs of pressure on the y-axis and volume on the x-axis**PV Diagrams**Isothermal lines - a line in which every point that has the same PV value (and therefore the same T)

Work = -PΔV

Moving to the right on a PV graph is negative work and vice versa

Area under the curve of the graph is equal to magnitude of work

To find ΔT, compare the PV path to isothermal lines or see if P or V changed

To find ΔU, find ΔT because ΔU = 3/2 nRΔT

To find Q, use ΔU = Q + W where Q and W are already given or are found from area under the graph and/or ΔT

Cycles on a PV diagram

Cycles: paths on the PV diagram that start and end at the same point

Same PV value at the start and end → ΔT is 0 → ΔU is 0 → Q = -w (remember the first law of thermodynamics)

Work becomes the area contained in the shape created by the cycle

Four Special Processes (Paths)

Constant Pressure -

__Isobaric__Horizontal lines on the PV graph

Constant Volume -

__Isochoric (Isovolumetric)__Vertical lines on PV graph

Constant Temperature -

__Isothermal__Hyperbolic constant lines on the PV graph

Less steep than Adiabatic processes

Q = -W

No Heat Transfer Between System and Environment -

__Adiabatic__Curved path but steeper than Isothermal process

## Entropy

: a measure of disorder**Entropy**: The entropy of a system cannot decrease unless work is done on that system**Second Law of Thermodynamics**Think of a glass: when broken, work must be done to put it back together in a more orderly state

The universe has a tendency towards entropy

When heat flows into a system, entropy increases