MECHOPTRONICS THERMAL 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 Heat 1 calorie = 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  C Δ T Q = mc Δ T  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!)  Δ T – change in temperature (T f – T i ) (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 Q L = L m Example - #2 Kirk “Blue”

Phase Change Graphical Example

Calorimetry  Calorimetry Is Used To Determine The Specific Heat Capacity (Cp) Of A Substance Q A = -Q B  Q A is total heat capacity of substance A  Q B is the total heat capacity of substance B  Note: Q A,B =  Q

Molecular Model of an Ideal Gas Assumptions 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 = nN A, N A = x 10 23

Example  How many kilograms of N 2 are contained in a tank whose volume is 0.75m 3 when the pressure is 101atm and the temperature is 27ºC?

Ideal Gases NOTE: PV/nT = R P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2  So, if the amount of gas doesn’t change (n is constant), then PV/T stays constant! P 1 V 1 = P 2 V 2 T 1 T 2  If n is constant AND the temperature stays constant, then P 1 V 1 = P 2 V 2  If n is constant AND the pressure stays constant, then V 1 = V 2 T 1 T 2

Example  An ideal gas is held in a container at a pressure of 1.07 x 10 5 Pa and a temperature of 27ºC. If pressure drops to 8 x 10 4 Pa at a constant volume, what is the new temperature?