MECHOPTRONICSTHERMAL PHYSICS

Internal Energy & Kinetic Theory of Gases

Calorimetry, Specific Heat Capacity & Phases of Matter

Points of View

Macroscopic – Consider a system as a whole and see how it interacts with its surroundings

Microscopic – Consider the internal structure of the system and see how its component parts interact with each other.

Thermal Physics: Temperature, Pressure and Volume are

Macroscopic quantities. However, as viewed through a microscopic lens,

we see they are related to the motion of atomic particles.

Analogy – Current : Heat as Electrons : Atoms

Internal Energy

If the temperature of an object changes, then it gained (or lost) energy.

On the molecular scale, this change translates into molecular motion (KE) or stored energy in bonds (PE).

Kinetic Theory of Gases

Molecules are arranged differently depending on the phase of the substance.

Gases will expand to fill a container. T ~ KE P ~ ∑p

Nature of Heat

When Heat Flows, What Is Actually Flowing?

Quantitative Methods Were Developed To Measure The Flow Of Heat But No One Could Describe WHAT Was Flowing: During This Time Benjamin Franklin

Developed The “One-Fluid” Model To Describe The Flow Of Electrical Charges

Perhaps Heat Was Another Of These Invisible Fluids?Historical Perspective: Caloric Fluid (Lavoisier) & Kinetic Motion (Rumford)

Heat

Units of Heat: Calorie (cal) – the amount of heat

needed to raise one gram of water at standard pressure from 14.5ºC to 15.5ºC

(NOTE: The food ‘Calorie’ is a kilocalorie.)

British Thermal Unit [BTU] – the amount of heat needed to raise one pound of water from 63ºF to 64ºF

Heat

Heat was thought to be an invisible substance (Caloric Fluid) that flowed from a hot object to a cold object (Lavoisier). Benjamin Thompson (aka Count Rumford) disproved this theory (Kinetic Motion). James Joule (also responsible for conservation of energy) realized that heat was another form of energy.

Mechanical Equivalent of Heat1 calorie = 4.186 joules

To us, this is just a unit conversion, but at the time, it changed everything!!

Work done on a system can “produce” heat!! A heat engine can convert heat into work! Conservation of energy must include thermal energy!

Example

A 55.0 kg woman cheats on her diet and eats a 540 Calorie jelly doughnut for breakfast.

How many joules of energy are the equivalent of one jelly doughnut?

How many stairs must the woman climb to perform an amount of mechanical energy equivalent to the food energy of the doughnut? Assume the height of a single stair is 15 cm.

Heat Capacity

Without a change in the state, heat transferred to a certain amount of a material is proportional to the change in temperature of the material…Q CΔT

Q = mcΔT

Q – heat (thermal energy transferred) m – mass of substance c – “specific heat” joules of heat needed to raise

1kg 1ºC, or J/kgK (given values!) ΔT – change in temperature (Tf – Ti)

(can be in K or ºC because it’s a change)

Heat Capacity - Example

How many joules of energy are required to raise the temperature of 100g of gold from 20.0ºC to 100ºC?

Phases of Matter

Specific Latent Heat – The amount of energy associated with the phase change. Solid-Liquid…Fusion Liquid-Gas…

Vaporization

QL = L m

Example - #2 Kirk “Blue”

Phase Change Graphical Example

Calorimetry

Calorimetry Is Used To Determine The Specific Heat Capacity (Cp) Of A Substance

QA = -QB

QA is total heat capacity of substance A QB is the total heat capacity of substance B

Note: QA,B = SQ

Molecular Model of an Ideal GasAssumptions for an “ideal” gas: The number of molecules is “large,” and the

average separation between them is large compared to their dimensions.

The molecules obey Newton’s laws of motion, but as a whole, their motion is random.

The molecules’ collisions with each other and the walls of the container are elastic.

The forces between molecules are negligible except during collisions.

All molecules are identical.

Ideal Gases

Most real gases under low pressure and not low temperature are very close to ideal gases.

IDEAL GAS LAW:

PV = nRT P – pressure (in Pa) V – volume (in m³) n - # of moles R – universal gas constant = 8.31 J/mol∙K T – temperature (always in Kelvin)

Ideal Gases

Recall from Chemistry: The number of moles equals the mass of the gas

in grams divided by the molecular mass in g/mol (from the periodic table).

n = m/M

n – number of moles m – mass of gas in grams M – molecular mass

Also remember, number of molecules = nNA, NA = 6.022 x 1023

Example

How many kilograms of N2 are contained in a tank whose volume is 0.75m3 when the pressure is 101atm and the temperature is 27ºC?

Ideal Gases

NOTE: PV/nT = R P1V1 = P2V2

n1T1 n2T2

So, if the amount of gas doesn’t change (n is constant), then PV/T stays constant! P1V1 = P2V2

T1 T2

If n is constant AND the temperature stays constant, then

P1V1 = P2V2

If n is constant AND the pressure stays constant, then V1 = V2

T1 T2

Example

An ideal gas is held in a container at a pressure of 1.07 x 105 Pa and a temperature of 27ºC. If pressure drops to 8 x 104 Pa at a constant volume, what is the new temperature?

Hea

t Cap

acit

y H

/WH

eat C

apac

ity

H/W

5) 1

76�C

7) 1

0.1�

C9)

88.

2W

5) 1

76�C

7) 1

0.1�

C9)

88.

2W

Idea

l Gas

Law

s W

/SId

eal G

as L

aws

W/S

23) a

) 2.

5 x

1019

mol

ecul

esb)

4.1

x 1

0-21

mol

es25

) 560

K27

) 0.0

048k

g

23) a

) 2.

5 x

1019

mol

ecul

esb)

4.1

x 1

0-21

mol

es25

) 560

K27

) 0.0

048k

g