Phase Change Diagram

ISNS 3371 - Phenomena of Nature

Phase Change Diagram


Specific Heat Capacity, c: Thermal inertia

Specific Heat Capacity is the quantity of heat required to change the temperature of 1 gram of a substance by 1° C.

Q units of of thermal energy added to 1 gram of a substance produces a temperature change of ∆T,

Q = c x ∆T

Specific heat , c, of a substance is the heat capacity per unit mass.

For m grams of a substance,

Q = cm ∆T or ∆T = Q/cm

Water has high specific heat capacity - used as a cooling fluid.

Specific heat capacity of water is 1 calorie/gram-deg. C


Heat of Fusion Measurement

Add 10 grams of ice (at 0º C) to 100 grams of water.

What is the heat of fusion of water?

Mass of water=M

Mass of ice =m

Hf= heat of fusion of water

To = initial temperature of ice

Tw = initial temperature of water

Tf = final temperature of water

Heat required to melt the ice = mHf

Heat required to raise the temperature of melted ice to final temperature of water = cm ∆T = cm(Tf - To)

Heat absorbed from water = cM ∆T = cM(Tw-Tf)


Heat of Fusion

Heat Absorbed by Ice Heat Transferred from Water

Q1 = cm(Tf - To) +mHf Q2 = cM(Tw - Tf)

Equate heat absorbed by ice to heat transferred from water

cm(Tf - To) + mHf = cM(Tw - Tf)

To = 0 and c = 1, so

mHf = M(Tw - Tf) - m Tf

Hf = M/m((Tw - Tf) - Tf


Heat of Fusion


Q1 = cm(Tf - To) +mHf Q2 = cM(Tw - Tf)


cm(Tf - To) + mHf = cM(Tw - Tf)

To = 0 and c = 1, so

mHf = M(Tw - Tf) - m Tf

Hf = M/m((Tw - Tf) - TfHf = 80 cal/gr


Change of State (Phase Change)

Example:

Add 10 grams of ice at 0º C to 100 grams of water at 30 º C.

What is the final temperature of the water?


Mass of ice =m Mass of water=M

Hf= heat of fusion of water: 80 calories/gram

To = initial temperature of ice

Tw = initial temperature of water

Tf = final temperature of water

Q=cm(Tf - To) +mHf Q=cM(Tw-Tf)




Mass of ice = m = 10 grams Mass of water = M = 100 grams


Q = cm(Tf - To) +mHf Q = cM(Tw - Tf)

Q = 1 x 10(Tf - 0) + 10 x 80 Q = 1 x 100(30 - Tf)


10Tf + 800 = 3000 - 100Tf

110Tf = 3000 - 800

Tf = 2200/110




Mass of ice = m = 10 grams Mass of water = M = 100 grams


Q = cm(Tf - To) +mHf Q = cM(Tw - Tf)

Q = 1 x 10(Tf - 0) + 10 x 80 Q = 1 x 100(30 - Tf)


10Tf + 800 = 3000 - 100Tf

110Tf = 3000 - 800

Tf = 2200/110

Tf = 20º C


Evaporation in a closed container will proceed until there are as many molecules returning to the liquid from the vapor above the liquid as there are escaping - the vapor is then said to be saturated. The pressure of that vapor is called the saturated vapor pressure.

Molecular kinetic energy is greater at higher temperature - more molecules can escape the surface and the saturated vapor pressure is correspondingly higher. If the liquid is open to the air, then the pressure of the air opposes the escape of the molecules. The temperature at which the vapor pressure is equal to the atmospheric pressure is called the boiling point.

Vapor Pressure and Boiling Point


Evaporation vs BoilingBoth start with a liquid and end with a gas. But they are different processes.

Evaporation:Strictly a surface phenomenaOccurs at any temperatureSome hotter (faster)-than-average particles overcome the forces

they feel from their neighbors and escape the liquid, taking their heat energy with them.

Forces only felt from particles beneath them

Boiling:Happens throughout the liquidOccurs at the boiling point/temperature Average motion of particles is fast enough to overcome the forces

holding them close together - all the particles are trying to escape - liquid turns to vapor

Forces felt from particles all around themBoiling point dependent on atmospheric pressure - steam bubbles form

in liquid only when vapor (steam) pressure exceeds atmospheric pressure (plus pressure of water pushing down)


The Boiling Point Depends on the Liquid Temperature and the Atmospheric Pressure

Boiling (evaporation) cools the liquid - when 100º C water is boiling, it is in thermal equilibrium - it is being cooled by the boiling as fast as it is being heated by the heat source - if not the water temperature would continue to rise


Pascal's Law

1) The pressure is the same all over the bottom of a rectangular tank of liquid. More generally, the pressure is the same at all points which are at the same level in one liquid (or gas). Remember:

Pressure is created by atomic and molecular collisions Pressure = force per unit area

Force has direction. Force giving rise to pressure is always perpendicular to the surface.

2) Fluid pressure on any surface is perpendicular to it. (A diver carrying a coin finds the pressure perpendicular to its surface whatever direction it faces.)

3) At any place in a fluid, pressure pushes equally in all directions. (A diver carrying a coin finds the same pressure on the coin whatever direction it faces.)


Pascal's Law, cont.

4) Pressure is transmitted without loss from one place to another throughout a fluid. (push a piston in at one place in a hydraulic system and the pressure you exert is carried to every wall and any other pistons in the system.)

5) The difference in pressure between any two places in a single fluid is given by h x d where h is the vertical difference of level and d is the density of fluid.


The Gas Laws


The Gas Laws


Properties of gases

• Very compressible.• Acquires shape of its container,• Completely fills any closed container.• Very low density compared with a liquid or a solid.• Exhibits a pressure on the walls of its container.• Pressure = force per unit area

P = F/A

Force has direction. Force giving rise to pressure is always perpendicular to the surface.

ISNS 3371 - Phenomena of Nature Gas LawsP = pressure of gasV = volume of gasT = absolute (kelvin) temperature of gas

– Boyle's Law: PV = constant, if T is constant

– Charles’ Law: V/T= constant, if P is constant

– Guy Lussac’s law P/T = constant, if V is constant

– General or ideal gas law PV/T = constant

PV = n RT

• R = general gas constant = 8.314 joules/degree-mole • n = number of moles of gas - a mole is 22.4 liters of a gas

Ideal gas - one in which we can ignore interactions between the gas molecules. Most gases behave in the same universal way as long as the temperature is kept far from the liquefaction temperature.


Remember third law of thermodynamics:No system can reach absolute zero.

How do you determine absolute zero?

Consider Guy Lussac’s law:

P/T = constant, if V is constant

This is for an ideal gas

Temperature must get smaller as pressure gets smaller

Theoretically, as pressure goes to zero, temperature must go to some smallest value

This value is absolute zero and can be determined by measuring the pressure and temperature of a gas at several values and extrapolating to zero pressure

Guy Lussac’s Law and Absolute Zero


Boyle’s Law

PV = constant, if T is constant

Boyle’s Law animation


Any gas will cool that is allowed to expand freely from a higher pressure to a lower pressure without the transfer of external energy to the gas. Similarly, a gas will heat if compressed from a lower to a higher pressure in the absence of a transfer of energy from the gas.

Consider gas in a bicycle pump: Push the pump in quickly - the gas heats up – you are doing work on the gas. Pull the pump out quickly - gas will cool down - the gas is doing work for you.

On a molecular scale.

The gas particles are moving with a speed that is determined by the temperature of the gas:

Push the pump in - the particles speed up - when they collide with the oncoming piston, they rebound more quickly - they heat up. Pull the pump out - the particles slow down - when they collide with the outgoing piston, they rebound more slowly - they cool down.

The Law of Adiabatic Expansion (or Compression))

ISNS 3371 - Phenomena of NatureThe same reasoning works for a gas that is expanding freely. Rather than bouncing off a container, the particles bounce off each other. But they are all moving outwards. So any collisions at the edges of the gas will have the effect of taking some of the speed off the expanding molecules. Explains why fog formed in chamber when pressure suddenly reduced:

All air contains water vapor of varying quantities. A state of saturation exists when the air is holding the maximum amount of water vapor possible at the existing temperature and pressure.

Dew point - the temperature to which the air would have to cool in order to reach saturation - indicates the amount of moisture in the air. Condensation of water vapor begins when the temperature of air is lowered to its dew point and beyond - results in the formation of tiny water droplets that leads to the development of fog, frost, clouds, or even precipitation.

When the air in the chamber suddenly expands, the temperature of the air is suddenly reduced to below the dew point and the water vapor condenses to form fog in the chamber.

Why is your breath colder when blown out through pursed lips?


Bernoulli Effect

For horizontal fluid flow, an increase in the velocity of flow will result in a decrease in the static pressure.


The Airfoil (Wing) and the Bernoulli Effect

The air across the top of the airfoil experiences increased air speed relative to the wing - it must go farther to reach the back edge of the airfoil. This causes a decreases in pressure and provides a lift force.

Increasing the angle of attack gives a larger lift from the upward component of pressure on the bottom of the wing. The lift force can be considered to be a Newton's 3rd law reaction force to the force exerted downward on the air by the wing.

At too high an angle of attack, turbulent flow increases the drag dramatically and will stall the aircraft.


If the greater curvature on top of the wing and the Bernoulli effect are evoked to explain lift, how is this possible? An increase in airstream velocity over the top of the wing can be achieved with airfoil surface in the upright or inverted position - requires adjustment of the angle of attack. Typical asymmetric shape of airfoil increases efficiency of lift production but not essential for producing lift.

How Does an Airplane Fly Upside Down?


The Curve Ball and the Bernoulli Effect

A non-spinning baseball or a stationary baseball in an airstream exhibits symmetric flow.

A baseball which is thrown with spin will curve because the air flows faster on one side of the ball than the other side because of friction. So one side of the ball will experience a reduced pressure.

The roughness of the ball's surface and the laces on the ball are important! With a perfectly smooth ball you would not get enough interaction with the air.


A ball balances on a stream of air because of the Bernoulli effect.

If the ball is displaced from the center of the air stream, it will feel a force pulling it back into the center. The air on the right side of the ball in not moving so pressure is lower on the left side of the ball and the ball feels a force toward the center of the air stream.

No matter which direction the ball is deflected, it is attracted to the center of the air stream, and stays balanced.

Balancing Ball and the Bernoulli Effect

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Phase Change Diagram