Second Law of Thermodynamics q1 q2

Reading Hess Tsonis Bohren & Albrecht Wallace and Hobbs Chapter 3 pp 32 – 37 Tsonis Chapter 5 pp 49 – 70 Bohren & Albrecht Chapter 4 pp 135-180 Wallace and Hobbs pp 93-97

Objectives Be able to state the Second Law of Thermodynamics in its various forms Be able to define heat engine Be able to draw the Carnot cycle and describe the changes in state variables, heat and work throughout the cycle

Objectives Be able to determine whether work is done by or on a system through a Carnot cycle Be able to define ‘cyclic process’ Be able to define the term ‘reversible process’

Objectives Be able to describe and give examples of natural, reversible, and impossible processes Be able to calculate the change of entropy of a system

First Law of Thermodynamics “Energy cannot be created or destroyed. It can only be changed from one form into another.” Rudolf Clausius 1850

First Law of Thermodynamics Conservation of Energy Says Nothing About Direction of Energy Transfer

Second Law of Thermodynamics Preferred (or Natural) Direction of Energy Transfer Spontaneous Process Hot Cold dQ

Second Law of Thermodynamics ‘Un-Natural’ Process Does not occur spontaneously Requires energy to transfer heat in opposite direction Hot dQ Cold

Second Law of Thermodynamics “Heat passes from a warmer to colder body.” Rudolf Clausius 1850

Second Law of Thermodynamics Duh....

Carnot Cycle Nicolas Leonard Sadi Carnot French engineer and physicist A Reflection on the Motive Power of Heat (1824) Cyclic and Reversible Processes

Second Law of Thermodynamics The foundations of the laws of thermodynamics are a result of the steam engine

Thomas Newcomen Steam Engine 1765

Heat Engine Absorb Heat From Source Performs Mechanical Work Discards Some Heat At Lower Temperature

Carnot Cycle The atmosphere is a giant heat engine Hot Cold dQ

Cyclic Process Sequence of Processes That Leaves A Working Substance In The Same State In Which It Started P V

Types of Cycles Otto Cycle Internal Combustion Engine

Types of Cycles Diesel Cycle Internal Combustion Engine

Types of Cycles Rankin Cycle

Types of Cycles Carnot Cycle Basis for All Others P q1 q2 T1 T2 V A B D A B C T1 T2 q1 q2 P V

Carnot Cycle Heat Engine Performs work by transferring heat from warm reservoir to colder reservoir D A B C T1 T2 q1 q2 P V Warm Cold

Types of Cycles Carnot Cycle Heat Absorbed at Same Temperature as Heat Reservoir D A B C T1 T2 q1 q2 P V Warm

Types of Cycles Carnot Cycle Heat Rejected at Same Temperature as Cold Reservoir D A B C T1 T2 q1 q2 P V Warm Cold

Types of Cycles Carnot Cycle Assumes Warm and Cold Reservoirs Are Unaffected by Heat Transfer Large Source & Sink D A B C T1 T2 q1 q2 P V Warm Cold

Carnot Cycle Idealized Heat Engine Operating at maximum efficiency No system works ‘exactly’ like this Gives us a foundation for discovery D A B C T1 T2 q1 q2 P V

Carnot Cycle Isothermal Expansion Heat Added = Work Done Volume Increases Pressure Decreases

Change of Internal Energy Carnot Cycle Adiabatic Expansion = Work Done Volume Increases Pressure Decrease Temperature Cools Change of Internal Energy

Carnot Cycle Isothermal Compression Heat Removed = Work Done Volume Decreases Pressure Increase

Change of Internal Energy Carnot Cycle Adiabatic Compression = Work Done Volume Decreases Pressure Increase Temperature Warms Change of Internal Energy

Carnot Cycle Adiabat P q1 Adiabat q2 A B T1 Isotherm D T2 Isotherm C V

Carnot Cycle Isothermal Expansion Adiabat Q1 Heat Added P q1 Adiabat V Isothermal Expansion

Carnot Cycle Adiabatic Expansion Adiabat cvdT = pdV Cooling P q1 Isotherm D T2 Isotherm C V Adiabatic Expansion

Carnot Cycle Isothermal Compression Adiabat P q1 Adiabat Q2 Heat Removed q2 A B T1 Isotherm D T2 Isotherm C V Isothermal Compression

Carnot Cycle Adiabatic Compression Adiabat cvdT = pdV Warming P q1 Isotherm D T2 Isotherm C V Adiabatic Compression

Carnot Cycle Mechanical energy (work) is done as a result of heat transfer D A B C T1 T2 q1 q2 P V Warm Cold

Carnot Cycle What if the cycle is reversed? Heat Taken From Colder Temperature and Deposited at Warmer Temperature D A B C T1 T2 q1 q2 P V Warm Cold

Carnot Cycle Refrigerator Heat Taken From Colder Temperature and Deposited at Warmer Temperature

Carnot Cycle Refrigerator Work is required to transferring heat from cold reservoir to warm reservoir D A B C T1 T2 q1 q2 P V Warm Cold

Carnot Cycle Alternate Form of Second Law “Heat cannot of itself pass from a cold to a warm body.” D A B C T1 T2 q1 q2 P V Warm Cold

Carnot Cycle Reversible Process each state of the system is in equilibrium process occurs slow enough state variables reach equilibrium D A B C T1 T2 q1 q2 P V

Carnot Cycle Reversible Process reversal in direction returns substance & environment to original states D A B C T1 T2 q1 q2 P V

Carnot Cycle Cyclic Process A process in which the Initial State is also the Final State D A B C T1 T2 q1 q2 P V

Carnot Cycle Cyclic Process Internal Energy (U) is unchanged P q1 q2 B C T1 T2 q1 q2 P V

Carnot Cycle Cyclic Process An exact differential Intergral around a closed path is zero D A B C T1 T2 q1 q2 P V

Carnot Cycle Cyclic Process Work done is not an exact differential Path dependent D A B C T1 T2 q1 q2 P V

Carnot Cycle W1 Work done by system during expansion D A B C T1 T2 q1 V W1 Work done by system during expansion

Carnot Cycle W2 Work done on system during compression P q1 q2 A B T1 V Work done on system during compression

Carnot Cycle P V q1 q2 A B DW T1 D T2 C Net work done by system

Carnot Cycle Cyclic Process Net work done by system is the net heat absorbed D A B C T1 T2 q1 q2 P V

Carnot Cycle Net work done by system DW = DQ = Q1 - Q2 q1 P q2 Q1 A B V D A B C T1 T2 q1 q2 Q1 Q2 DW = DQ = Q1 - Q2

Carnot Cycle Efficiency of a System Cannot Convert All Heat Available Into Work P V D A B C T1 T2 q1 q2 Q1 Q2

Carnot Cycle Problems Net work done q1 P Path dependent q2 A Not mathematically “elegant” Difficult to make quick calcualtions P V D A B C T1 T2 q1 q2 QNet

Carnot Cycle Is there a way to describe the heat change of a system without having to deal with “work done”? YES!!!! …but it will take some work!

For an adiabatic process Carnot Cycle Before we begin... It can be shown from the First Law & the Ideal Gas Law Poisson’s Equation For an adiabatic process where g = cp/cv

Carnot Cycle Lets examine each “leg” of the cycle q1 P q2 Q1 A B T1 D V D A B C T1 T2 q1 q2 Q1 Q2

Carnot Cycle From A to B PAVA = PBVB isothermal expansion temperature is constant (T1) so.. P V q1 q2 Q1 A B T1 T2 PAVA = PBVB

Carnot Cycle From A to B isothermal expansion work done (W1) is heat added (Q1) P V q1 q2 Q1 A B T1 T2

Carnot Cycle From A to B heat added (Q1) for 1 mole q1 P q2 Q1 A B T1 V q1 q2 Q1 A B T1 T2 Ideal Gas Law So...

Carnot Cycle From A to B heat added (Q1) for 1 mole q1 P q2 Q1 A B T1 V q1 q2 Q1 A B T1 T2

Carnot Cycle From B to C PCVgC = PBVgB adiabatic expansion (q2) q1 P

Carnot Cycle From C to D isothermal compression work done (W2) is heat removed (Q2) q1 P q2 T1 D Q2 C T2 V

Carnot Cycle From C to D heat removed (Q2) for 1 mole q1 P q2 T1 D Q2 Ideal Gas Law So...

Carnot Cycle From C to D heat added (Q1) for 1 mole q1 P q2 T1 D Q2 T2 V

Carnot Cycle From D to A PDVgD = PAVgA adiabatic compression (q2) q1 P

Carnot Cycle For the adiabatic processes q1 P q2 A B T1 D T2 C V q1 q2 A B T1 D C T2 Take the ratio Remember this!! or

Carnot Cycle For the isothermal processes q1 P q2 Q1 A B T1 D Q2 T2 C V q1 q2 A Q1 B T1 D Q2 C T2 Take the ratio

Carnot Cycle For the isothermal processes q1 P q2 Q1 A B T1 But .... D V q1 q2 A Q1 B T1 But .... D Q2 C T2

Carnot Cycle For the cyclic process A lot of work just to say ... q1 P V q1 q2 A Q1 B T1 D Q2 C T2 A lot of work just to say ...

Carnot Cycle For a cyclic process V D A B C T1 T2 q1 q2 Q1 Q2 The ratio of the heat absorbed to heat rejected depends only on the initial and final temperature

Carnot Cycle That’s great for steam engines, but what about the atmosphere?

Carnot Cycle Patience, grasshopper!

Carnot Cycle Isothermal Process Heat absorbed or released Amount of heat depends on temperature P V D A B C T1 T2 q1 q2 Q1 Q2

Carnot Cycle But ... P V D A B C T1 T2 q1 q2 Q1 Q2 or The ratio Q/T is the same regardless of the isotherm chosen

Carnot Cycle The ratio P V D A B C T1 T2 q1 q2 Q1 Q2 is a measure of the difference between the two adiabats. It is the same for any two adiabats in a cyclic process

For a reversible process Entropy Difference in entropy between adiabats P V q1 q2 Q1 A B T1 D Q2 C T2 For a reversible process

Entropy The path dependent integral no longer depends on path q1 P q2 V q1 q2 T1 dQ T2

Entropy An integrating factor (T) makes the differential exact P Q1 T1 V

Entropy For the cyclic & reversible process P Q1 T1 Q2 T2 1st Law V Ideal Gas Law

Entropy Substitute for a Integrate

Entropy Over the closed path P V T1 T2 Q1 Q2 So ....

Entropy Function of state T, P Not path dependent P V T1 T2 Q1 Q2

Entropy For adiabatic processes P V T1 T2 q1 q2 But ... So ...

Entropy For adiabatic processes No change in entropy Isentropic q1 P V T1 T2 q1 q2

Entropy Potential temperature (q) is conserved for adiabatic processes! How is potential temperature related to entropy?

Entropy Logarithmically Differentiate

Entropy Wait a second ... This looks like ... Let’s combine them!

Entropy Combining equations Integrate

Entropy Meteorologically speaking ... Entropy depends only on potential temperature! Dry adiabatic processes are isentropic!

Review Second Law of Thermodynamics It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work, with the system ending in the same state in which it began.

Review Second Law of Thermodynamics It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body.

Second Law of Thermodynamics No process is possible in which the total entropy decreases, when all systems taking part in the process are included.

Types of Processes Natural (or Irreversible) Impossible Reversible

Natural (or Irreversible) Process Processes That Proceed Spontaneously in One Direction But Not The Other Non-Equilibrium Process Equilibrium Only At End of Process

Natural (or Irreversible) Process Examples Conversion of Work to Heat Through Friction Free Expansion of Gas

Natural (or Irreversible) Process Most Natural Processes Are Irreversible Analogy – Water Wheel Water Flows from Higher Elevation to Lower Elevation Work is Done

Natural (or Irreversible) Process Analogy – Water Wheel Water Ends Up At A Lower Height Unable to Perform More Work

Natural (or Irreversible) Process Analogy – Water Wheel Irreversible Water Does Not Flow Back Up By Itself

Natural (or Irreversible) Process Similarly, some of the heat is not available to due work T1 T2 q1 q2 P V Warm Cold

Impossible Process Violate Second Law Cannot Occur

Impossible Process Examples Free Compression of Air Conduction in which Cold Object Gets Colder and Warm Object Gets Warmer

Reversible Process System & Surroundings Already Close to Thermodynamic Equilibrium Changes of State Can Be Reversed Through Infinitesimal Changes

Reversible Process System Always in Equilibrium Idealized Concept Changes Would Never Take Place Initially Small Changes

Entropy Carnot Cycle Idealize Engine Reversible Process Maximum Efficiency P q1 dQ1 q2 T1 dQ2 T2 V

Dry Adiabatic Process Isentropic Reversible No Change in Entropy Potential Temperature is Constant Reversible Substance and Environment return to original condition

Entropy Real World Dry Adiabatic Process Approximation to real world conditions Not what really happens Mixing

Entropy A Quantitative Measure of Randomness or Disorder

Entropy Example Conversion of Mechanical Energy Into Heat Increase in Disorder Random Molecular Motion

Entropy In The Atmosphere Processes Are Not Exactly Dry Adiabatic Process

Entropy Most Natural Processes Are Irreversible

Entropy Would Require More Energy to Return System and Environment to Equilibrium

Entropy This implies an increase in entropy

Entropy The entropy of the universe is ever increasing Conversion from more useful to less useful states