Thermodynamics

Home , Isochoric process

•Temperature •Thermal Expansion •Ideal Gas Law •Kinetic Theory •Heat •Heat Transfer •Phase Changes •Specific Heat •Calorimetry Zeroeth Law

• Two systems individually in thermal equilibrium with a third system (such as a thermometer) are in thermal equilibrium with each other. • That is, there is no flow of heat within a system in thermal equilibrium 1st Law of Thermo • The change of internal energy of a system due to a temperature or phase change is given by: ∆=+E QW int Temperature Change: Q = mc∆T Phase Change: Q = mL

• Q is positive when the system GAINS heat and negative when it LOSES heat. 2nd Law of Thermo

• Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. • Heat flows from hot to cold. • Alternative: Irreversible processes must have an increase in Entropy; Reversible processes have no change in Entropy. • Entropy is a measure of disorder in a system

3rd Law of Thermo

It is not possible to lower the temperature of any system to absolute zero.

TC = T – 273.15 Absolute Temperature Scale, K The absolute temperature scale is based on two fixed points – Adopted by in 1954 by the International Committee on Weights and Measures – One point is absolute zero – The other point is the triple point of water • This is the combination of temperature and pressure where ice, water, and steam can all coexist Phase Change: Triple Point

A temperature and pressure at which all three phases exist in equilibrium.

Lines of equilibrium Freezing-Melting Evaporation -Condensation

Sublimation •Heat Energy is a flow of energy from hotter to colder because of a difference in temperature. Objects do not have heat. [Heat] = Joule

• Internal Energy of a system is a measure of the total Energy due to ALL random molecular motions INTERNAL of the system (Translations KE, Rotational KE, Vibrational KE) and internal POTENTIAL energies due to interactive forces (electromagnetic, strong, weak, gravitational) Objects have energy.

•Mechanical Energy is due to the kinetic and potential energies of the system itself in an external reference frame.

•Mechancial Equivalent of Heat: mechanical energy converted to heat energy by doing work on the system: 1.000 kcal = 4186J •Heat Energy is a flow of energy from hotter to colder because of a difference in temperature. Objects do not have heat. [Heat] = Joule

•Heat Energy entering or leaving a system will cause either a Temperature Change: Q = mc∆T or a Phase Change: Q = mL Specific Heat: Thermal Inertia

The Specific Heat of a substance is the amount of Energy it requires to raise the temperature of 1 kg, 1 degree Celsius. QJ Q= mc ∆ T c = = m∆⋅ T kg0 C

•The higher the specific heat, the more energy it takes and the longer it takes to heat up and to cool off.

•The lower the specific heat, the less energy it takes and the quicker it takes to heat up and cool off.

•Substances with HIGH specific heat STORE heat energy and make good thermal moderators. (Ex: Water, Oceans) Some Specific Heat Values More Specific Heat Values Specific Heat J c = 4186 water kg⋅ 0 C J c = 2410 glycerin kg⋅ 0 C J c = 452 iron kg⋅ 0 C Why does water have such a high specific heat? Heat goes into other modes of energy so that temperature changes slowly. Q= mc ∆ T

How much heat is required to raise the temperature of a 0.750kg aluminum pot containing 2.50kg of water at 30ºC to the boiling point?

Q= mAl c Al ∆+ T mcw w ∆ T

=(mAl c Al +∆ mc w w ) T

  = .75kg (900 J / kg C )+ 2.5 kg (4186 J / kg C ) (70 C ) Q= 7.798 xJ 105 Phase Change Q= mL

•A change from one phase to another •A phase change always occurs with an exchange of energy! •A phase change always occurs at constant temperature! Sample Latent Heat Values Q= mL Phase Change

Energy goes into the system and breaks molecular bonds..

Energy is given up by the system by forming molecular bonds Phase Change: Melting & Freezing Melting: Energy goes into the system and breaks molecular bonds..

Freezing: Energy is given up by the system by forming molecular bon Phase Change: Melting & Freezing Phase Change: Melting & Freezing

•Melting: Solid to Liquid @ the melting temperature •Melting is a cooling process •Freezing: Liquid to Solid @ the melting temperature •Freezing is a warming process.

Why do farmers spray peaches with water to save them from frost?

Freezing is a warming process! If you were in an igloo on a freezing night. You would be warmed more by a) a bucket of ice melting. b) a bucket of water freezing c) the same either way. d) neither - are you nuts?

Phase Change: Evaporation •Takes place at the surface of a liquid due to escaping molecules. •Occurs at all temperatures •Evaporation occurs when water vapor pressure in the liquid exceeds the pressure of water vapor in the surrounding air. •Evaporation is a cooling process.

Evaporation is a Cooling Process Phase Change: Boiling •Boiling is evaporation under the surface of the liquid. •Liquid boils at the temperature for which its vapor pressure exceeds the external pressure (mostly atmospheric pressure.) •Boiling point depends on temperature AND pressure: •@ 1 atm, bp of water is 100ºC, @ 5atm, bp of water is 374 ºC •Boiling is a cooling process. •At low pressures, liquids are boiled (‘freeze-dried’) into solids. Phase Change: Condensation

•Gas molecules condense to form a liquid. •Condensation is a warming process •Why is a rainy day warmer than a cloudy or clear day in winter? •Why do we feel uncomfortable on a muggy day? Condensation is a Warming Process Phase Change: Humidity

•Vapor is the gas phase of a substance below its boiling temperature. •Air can ‘hold’ only so much water vapor before it becomes saturated and condensation occurs. Humidity is a measure of vapor density. •Warm air can hold more water vapor. More condensation occurs at cooler temperatures because the molecules are moving slower.

Slow moving water molecules coalesce upon collision. Windward: Wet Leeward: Dry

Cools and condenses at Top

Warm Warm Humid Dry Air Air Pushed Falls Up Down Stormy Weather

When warm air rises, it expands and cools. The water vapor in the air soon condenses into water droplets, which form clouds and eventually these droplets fall from the sky as rain.

Phase Change:Sublimation

The conversion of a solid directly to a gas & visa versa Examples: snowflakes, Moth Balls, dry ice Phase Change: Triple Point

A temperature and pressure at which all three phases exist in equilibrium.

Lines of equilibrium Freezing-Melting Evaporation -Condensation

Sublimation Phase Change Q= mL Phase change occurs at a Constant Temperature!

Latent Heats of: Fusion & Evaporation Lf, Lv

L= 334 kJ / kg solid-liquid Water: f ( )

Lv = 2256 kJ / kg ( liquid-gas) Phase Change: Water Q= mL

How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?

•How much energy is needed to raise the ices to 0 °C •How much energy is needed to melt 1kg of ice? •How much energy is given up by the steam? •What happens to the steam that is melting the ice?

Lf = 334 kJ/ kg

Lv = 2256 kJ/ kg 0 cice =2090 J/ kg ⋅ C 0 cwater = 4186 J / kg⋅ C Phase Change: Water Q= mL

How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?

How much energy is needed to raise the ices to 0 °C

00 Q1 =1 kg (2090 J/ kg⋅ C )(30 C ) = 62700J

Lf = 334 kJ/ kg

Lv = 2256 kJ/ kg 0 cice =2090 J/ kg ⋅ C 0 cwater = 4186 J / kg⋅ C Phase Change: Water Q= mL

How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C?

How much energy is needed to melt 1kg of ice?

Q2 = mL =1kg (334 kJ/ kg )

Q2 = 334 kJ

Lf = 334 kJ/ kg

Lv = 2256 kJ/ kg 0 QJ1 = 62700 cice =2090 J/ kg ⋅ C 0 Q2 = 334 kJ cwater = 4186 J / kg⋅ C Phase Change: Water Q= mL

How much steam @ 100 °C does it take to melt 1kg of ice at -30 °C? •How much energy is given up by the steam? •What happens to the steam that is melting the ice?

Lf = 334 kJ/ kg

Lv = 2256 kJ/ kg 0 QJ1 = 62700 cice =2090 J/ kg ⋅ C 0 Q2 = 334 kJ cwater = 4186 J / kg⋅ C Qtotal = 397 kJ •Heat flows from HOT to COLD •Conduction (solids) •Convection (liquids & gases) •Radiation (solids, gases, plasma)

Energy transferred via molecular collisio Heat energy is transferred in solids by collisions between free electrons and vibrating atoms.

•Good Conductors: Most Metals (free electrons!) •Bad Conductors: Organic & Inert Materials •Good Insulators: Air, Water, Wood •Good Conductors are BAD Insulators •& Visa Versa The heat Q conducted during a time t through a material with a thermal conductivity k. dT/dx is the Temperature Gradient. dT P= kA dx Some Thermal Conductivities Temperature Gradient The quantity |dT / dx| is called the temperature gradient

− Q dT dT Thc T ℘= =kA = ∆t dx dx L TT− Conduction Problem ℘=kAhc L

A bar of gold is in thermal contact with a bar of silver of the same length and area as shown. One end of the compound bar is maintained at 80.0°C while the opposite end is at 30.0°C. When the energy transfer reaches steady state, what is the temperature at the junction? Ignore thermal expansion of the metals.

70. The inside of a hollow cylinder is maintained at a temperature Ta while the outside is at a lower temperature, Tb (Fig. P20.70). The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy conduction from the inner to the outer surface in the radial direction is

dQ  T − T  = 2πLk a b  dt  ln(b/ a)

(Suggestions: The temperature gradient is dT/dr. Note that a radial energy current passes through a concentric cylinder of area 2πrL.)

In the same room, at the same temperature, the tile floor feels cooler than wood floor. How can they be the same temperature? Hot Air rises, expands and cools, and then sinks back down causing convection currents that transport heat energy. Hot air rises because fast moving molecules tend to migrate toward regions of least obstruction - UP - into regions of lesser density! Rising air cools because a decrease in density reduces number of collisions & speeds decrease. As the air cools, it becomes denser, sinking down, producing a convection current. Uneven heating on the earth and over water cause convection currents in the atmosphere, resulting in WINDS.

Global wind patterns (Trade Winds, Jet Streams) are due to convection current from warmer regions (equator) to cooler regions (poles) plus rotation of Earth.

Convection Currents in the Ocean (Gulf Stream) transport energy throughout the oceans.

Air & Ocean Convection causes the WEATHER. Convection between water and land causes the Winds. Sea Breeze High Pressure Dry Warm Weather

Low Pressure Stormy Weather

Electromagnetic Radiation is emitted and absorbed via atomic excitations. All objects absorb and emit EM waves. Electromagnetic Radiation is emitted and absorbed via atomic excitations. All objects absorb and emit EM waves. Frequency ~ Temperature When an object it heated it will glow first in the infrared, then the visible. Most solid materials break down before they emit UV and higher frequency EM waves. Long

Short Stefan’s Law

• P = σAeT 4 – P is the rate of energy transfer, in Watts – σ = 5.6696 x 10-8 W/m2 . K4 – A is the surface area of the object – e is a constant called the emissivity • e varies from 0 to 1 • The emissivity is also equal to the absorptivity – T is the temperature in Kelvins A good absorber reflects little and appears Black A good absorber is also a good emitter. P= eTAσ 4

Radiant heat makes it impossible to stand close to a hot lava flow. Calculate the rate of heat loss by radiation from 1.00 m2 of 1200C fresh lava into 30.0C surroundings, assuming lava’s emissivity is 1.

44 The net heat transfer by radiation is:P = eσ AT()21 − T 44 P= eσ AT()21 − T =1(5.67x 10−8 J / smK 42 )1 m ((303.15 K )4− (1473.15K )4 ) P= −266 kW How do fur coats keep you warm? Fur is filled with air. Convection currents are slow because the convection loops are so small. Any two systems placed in thermal contact will have an exchange of heat energy until they reach the same temperature.

If the systems are in thermal equilibrium then no net changes take place. Today’s Quiz: Was ist das? During which process does the temperature increase? Decrease? Remain the same?

Fig. 20-9, p. 569 QuickCheck 17.13

A gas in a container expands rapidly, pushing the piston out. The temperature of the gas

A. Rises. B. Is unchanged. C. Falls. D. Can’t say without knowing more.

Slide 17-89 QuickCheck 17.13

A gas in a container expands rapidly, pushing the piston out. The temperature of the gas

A. Rises. B. Is unchanged. C. Falls. D. Can’t say without knowing more.

Slide 17-90 QuickCheck 17.14

A gas in a container expands rapidly, pushing the piston out. The temperature of the gas falls. This is because

A. The gas pressure falls. B. The gas density falls. C. Heat energy is removed. D. Work is done. E. Both C and D.

Slide 17-95 QuickCheck 17.14

A gas in a container expands rapidly, pushing the piston out. The temperature of the gas falls. This is because

A. The gas pressure falls. B. The gas density falls. C. Heat energy is removed. D. Work is done. E. Both C and D.

Slide 17-96 The First Law of Thermodynamics

∆=+Eint QW

• The First Law of Thermodynamics is a special case of the Law of Conservation of Energy – It takes into account changes in internal energy and energy transfers by heat and work • Although Q and W each are dependent on the path, Q + W is independent of the path Temperature Change and Specific Heat

. The amount of energy that raises the temperature of 1 kg of a substance by 1 K is called the specific heat c of that substance. . If W = 0, so no work is done by or on the system, then the heat needed to bring about a temperature change ∆T is:

The molar specific heat C is the amount of energy that raises the temperature of 1 mol of a substance by 1 K.

© 2013 Pearson Education, Inc. Slide 17-60 Work in Thermodynamics • Work can be done on a deformable system, such as a gas • Consider a cylinder with a moveable piston • A force is applied to slowly compress the gas – The compression is slow enough for all the system to remain essentially in thermal equilibrium – This is said to occur quasi-statically dW=⋅Fr d =−⋅=−=− Fˆˆ j dy j Fdy PA dy =− PdV dW= − PdV Work in Ideal-Gas Processes

. On a pV diagram, the work done on a gas W has a nice geometric interpretation. . W = the negative of the area under the pV curve between Vi and Vf.

V W= −∫ f P dV V i

V W= −∫ f P dV V i Isochoric

In an isochoric process, when the volume does not change, no work is done.

In an isobaric process, when pressure is a constant and the volume changes by ∆V = Vf − Vi, the work done during the process is:

In an isothermal process, when temperature is a constant, the work done during the process is:

The work done on the gas in this process is

A. 8000 J. B. 4000 J. C. 0 J. D. –4000 J. E. –8000 J.

The work done on the gas in this process is

A. 8000 J. B. 4000 J. C. 0 J. D. –4000 J. E. –8000 J. W = –(area under pV curve)

If the work done is NEGATIVE then how did the Temperature go up?

A gas is taken through the cyclic process as shown. Find the work done from AB, BC and CA. What is the net work done?

In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PV diagram Cyclic Processes

∆Eint = 0

• A cyclic process is one that starts and ends in the same state – On a PV diagram, a cyclic process appears as a closed curve

• If ∆Eint = 0, Q = -W • In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PV diagram

Cyclic Processes

∆Eint =+= QW 0 A gas is taken through the cyclic process as shown. (a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversed—that is, the process follows the path ACBA—what is the net energy input per cycle by heat? Find the net work done. V Work Done By Various Paths W= −∫ f P dV V i

Not necessarily an isotherm!

=−− W= − P() V dV W=−− PVif() V i W PVff() V i ∫

The work done depends on the path taken! QuickCheck 17.7

Three possible processes A, B, and C take a gas from state i to state f. For which process is the heat transfer the largest?

A. Process A. B. Process B. C. Process C. D. The heat is the same for all three.

Three possible processes A, B, and C take a gas from state i to state f. For which process is the heat transfer the largest?

A. Process A. B. Process B. C. Process C. D. The heat is the same for all three. Same for all three

∆Eth = W + Q

Most negative for A ...... so Q must be most positive.

. Processes A and B have the same ∆T and the same ∆Eth, but they require different amounts of heat. . The reason is that work is done in process B but not in process A. . The total change in thermal energy for any process, due to work and heat, is:

Slide 17-78 The Specific Heats of Gases . It is useful to define two different versions of the specific heat of gases, one for constant-volume processes and one for constant-pressure processes. . We will define these as molar specific heats because we usually do gas calculations using moles instead of mass. . The quantity of heat needed to change the temperature of n moles of gas by ∆T is:

where CV is the molar specific heat at constant volume and CP is the molar specific heat at constant pressure. Slide 17-79 Molar Specific Heats Isobaric requires MORE HEAT than Isochoric for the same change in Temperature!!!! C and C P V Note that for all ideal gases:

where R = 8.31 J/mol K is the universal gas constant.

Slide 17-80 Example 17.7 Heating and Cooling a Gas

Slide 17-83 AdiabaticAdiabatic Processes Processes: Q=0 . An adiabatic process is one for which:

where:

. Adiabats are steeper than hyperbolic isotherms because only work is being done to change the Temperature. The temperature falls during an adiabatic expansion, and rises during an adiabatic compression. Slide 17-88 A 4.00-L sample of a nitrogen gas confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Find the number of moles of the gas. (c) Find the volumes and temperatures at the end of each process (d) Find the Work and heat for each process. (e) What was the net work done on the gas for this cycle? C and C P V Note that for all ideal gases:

where R = 8.31 J/mol K is the universal gas constant.

Slide 17-80 ∆=+E QW Thermo Processes int • Adiabatic – No heat exchanged

– Q = 0 and ∆Eint = W • Isobaric – Constant pressure

– W = P (Vf – Vi) and ∆Eint = Q + W • Isochoric – Constant Volume

– W = 0 and ∆Eint = Q • Isothermal – Constant temperature V W= nRT ln i ∆Eint = 0 and Q = -W  Vf

Why is winter cold and summer hot?

Intensity: The Radiation Power, P, passing through an area, A. P W I = 4mπ r 22 Assume that the sun is a sphere of radius 6.96 x 108 m and that its surface temperature is 5.8 x 103 K. a) If the sun is a perfect emitter, at what rate is energy emitted from the surface of the sun? b) What is the rate per square meter at the sun's surface - that is, the Intensity? c)What is the Intensity at which energy is received on Earth in one hour? Ignore effects of absorption due to the atmosphere. The average distance from the Earth to the sun is 1.50 x 1011 m. P = 4 I 2 = σ 4π r P eTA The Solar Constant Solar Cycle: 11 year Cycle

http://www.nasa.gov/mission_pages/sunearth/news/solarcycl e-primer_prt.htm

Tambora in 1815, together with an eruption from an unknown volcano in 1809, produced the “Year Without a Summer” (1816)

Alan Robock Department of Environmental Sciences Tambora, 1815, produced the “Year Without a Summer” (1816)

“Darkness” I had a dream, which was not all a dream. by Byron The bright sun was extinguish'd, and the stars Did wander darkling in the eternal space, Rayless, and pathless, and the icy earth Swung blind and blackening in the moonless air; Morn came and went—and came, and brought no day, And men forgot their passions in the dread Of this their desolation; and all hearts Were chill'd into a selfish prayer for light: And they did live by watchfires—and the thrones, The palaces of crowned kings—the huts, The habitations of all things which dwell, Were burnt for beacons; cities were consumed, And men were gather'd round their blazing homes To look once more into each other's face; . . .

Alan Robock Department of Environmental Sciences Tambora, 1815, produced the “Year Without a Summer” (1816)

Percy Bysshe Shelley Mary Shelley John Polidori

Alan Robock Department of Environmental Sciences

During periods of high activity, the Sun has more sunspots than usual. Sunspots are cooler than the rest of the luminous layer of the Sun’s atmosphere (the photosphere). Paradoxically, the total power output of the active Sun is not lower than average but is the same or slightly higher than average. Work out the details of the following crude model of this phenomenon. Consider a patch of the photosphere with an area of 5.10 × 1014 m2. Its emissivity is 0.965. (a) Find the power it radiates if its temperature is uniformly 5 800 K, corresponding to the quiet Sun. (b) To represent a sunspot, assume that 10.0% of the area is at 4 800 K and the other 90.0% is at 5 890 K. That is, a section with the surface area of the Earth is 1 000 K cooler than before and a section nine times as large is 90 K warmer. Find the average temperature of the patch. (c) Find the power output of the patch. Compare it with the answer to part (a). Why are cloudy nights warmer than cold nights? The heating effect of a medium such as glass or the Earth’s atmosphere that is transparent to short wavelengths but opaque to longer wavelengths: Short get in, longer are trapped!

CO2 & Temperature Change Impacts of a Warming Arctic

The Arctic Climate Impact Assessment, a study commissioned by the United States and the seven other countries with Arctic territory, projects that rising global concentrations of heat-trapping emissions will drive up temperatures particularly quickly at high latitudes. RISING SEAS One of the most important consequences of Arctic warming will be increased flows of meltwater and icebergs from glaciers and ice sheets, and thus an accelerated rise in sea levels. Forrest vs Tundra

Caught between rising seas on one side and expanding shrub-filled zones to the south, tundra ecosystems around the Arctic will likely shrink to their smallest extent in at least 100 years, the scientists concluded. This could reduce breeding areas for many tundra-dwelling bird species and grazing lands for caribou and other mammals.

1 Meter Rise In Florida ZEPO:A Melting Glacier in Tibet

"Thirty years ago, there was no river here. If you come back here in another 30 years, one thing is for sure: There will definitely be no more ice here." -Dr. Yao Tandong, Institute of Tibetan Plateau Research

Global Glacial Ice Melting

On Kilimanjaro in Kenya, an 11,700-year-old ice cap that measured 4.3 square miles in 1912 had shrunk to 0.94 square miles in 2000, and is projected to disappear altogether in about 15 years. Melting of glaciers in Patagonia has doubled in recent years.

Ice Caps Melting in Peru

In Peru, the Quelccaya ice cap retreated a rate of more than 600 feet a year from 2000 to 2002 - up from just 15 feet a year in the 1960's and 70's - leaving a vast 80-foot-deep lake where none had existed when his studies began. “It is much too late for sustainable development; what we need is a sustainable retreat.” -James Lovelock, The Revenge of Gaia The Gaia Theory

“The organic and inorganic components of Planet Earth have evolved together as a single living, self-regulating system Life maintains conditions suitable for its own survival.” - James Lovelock Our Spaceship Earth

One island in one ocean...from space “...we’re all astronauts aboard a little spaceship called Earth” - Bucky Fuller 67,000 miles/hr 500,000 miles/hr "We are on a spaceship; a beautiful one. It took billions of years to develop. We're not going to get another.” - Bucky Fuller, Operating Manual for Spaceship Earth