Thermodynamics

Definitions Thermodynamics is the study of processes in which energy is transferred as work and heat The system is a set of particles we wish to study The environment is everything else Heat (Q) is the transfer of energy into or out of the system by a temperature difference Work (W) is the transfer of energy into or out of the system by a force Internal energy (U) is the sum of the kinetic and potential energies of all the particles in the system

Diagram This diagram summarizes these concepts: System Heat, QWork, W U Environment System Boundary

Types of Systems An open system allows mass and energy to enter or leave A closed system does not allow mass to enter or leave (but energy can) An isolated system does not allow energy (in any form) to enter or leave

First Law of Thermodynamics Let Q be positive when heat is absorbed by the system Let W be positive when the system does work on the environment The first law of thermodynamics says that for a closed system:  U = Q  W System W UU Q

Understanding the First Law There are only two ways for energy to transfer into or out of a closed system: heat and work The first law is a statement of conservation of energy Note that the sign of Q and W depend on the direction of energy transfer: Signs of Q and W for a System Q > 0Energy added to system as heat Q < 0Energy removed from system as heat Q = 0No transfer of energy as heat W > 0Work done by system (expansion of gas) W < 0Work done on system (compression of gas) W = 0No work done

Example Q: What is the change in the internal energy of a gas that releases 489 J of heat while simul- taneously being compressed by 731 J of work? A:  U = ? Q = -489 J, W = -731 J  U = Q  W = (-489 J)  (-731 J) = 242 J Gas  U = 242 J W = -731 J Q = -489 J

Gases and the First Law The first law allows us to study processes involving gases An ideal gas has the following state variables: Pressure is defined as force per area: P = F/A(SI unit: 1 Pa = 1 N/m 2 ) variablenameunits PpressurePa (= N/m 2 ) Vvolumem3m3 TtemperatureK n# of molesmol Uinternal energyJ

P-V Diagrams A pressure-volume diagram lets us track the state of a gas as it goes through a process pressure (Pa) volume (m 3 ) Initial state final state (P i, V i ) (P f, V f )

Pressure and volume specify the entire state of a gas under the following conditions: – gas is ideal and has the following state equation: PV = nRT[R = J/(mol  K)] – gas does not change phase nor undergo reaction  U = (constant)   T – system is closed so that n = constant A P-V diagram lets us track the state of a gas as energy is transferred as heat and work

Types of Thermodynamic Processes A gas undergoing an isobaric process is at constant pressure  The work done by the gas is W = P  V   U = Q  P  V pressure (Pa) volume (m 3 ) (P,Vi)(P,Vi)(P,Vf)(P,Vf) T1T1 T2T2 T3T3

A gas undergoing an isovolumetric process is at constant volume  W = 0   U = Q pressure (Pa) volume (m 3 ) (P f, V) T1T1 T2T2 T3T3 (P i, V)

A gas undergoing an isothermal process is at constant temperature   U = 0  Q = W pressure (Pa) volume (m 3 ) T1T1 T2T2 T3T3 isotherms

A gas undergoing an adiabatic process does not absorb or release any heat (Q = 0)  Q = 0   U = -W pressure (Pa) volume (m 3 ) T1T1 T2T2 T3T3

Cyclic Processes A cyclic process is one where the system returns to its initial state after going through a series of changes in P, V, T, etc. – In the process of going through this cycle, the system may transfer energy as heat and work – The change in internal energy for one cycle is zero (  U net = 0) There are two classes of cyclic processes: – heat engines (use heat to produce work) – Refrigerators (use work to move heat from a cold reservoir to a hotter one)

Heat Engines The P-V diagram for a heat engine looks like this The process is clockwise The work done by the system is proportional to the area of the “eye” pressure (Pa) volume (m 3 ) T1T1 T2T2 T3T3 Heat in Heat out Heat from a high-temperature source (Q H ) Waste heat transferred to a low-temperature reservoir (Q L )

Since  U net = 0 and Q net = Q H  Q L we have  U net = Q net  W net 0 = Q net  W net 0 = Q H  Q L  W net W net = Q H  Q L This diagram shows the energy flow for a heat engine: Hot Source (T H ) Cold Sink (T L ) QLQL QHQH W net Heat Engine

Efficiency of a Heat Engine The efficiency of a heat engine is a measure of how well the engine operates The efficiency of a heat engine is defined as eff = W net /Q H This can be written as eff =  = 1   QH  QLQH  QL QHQH QLQL QHQH

Example: A steam engine takes in 2.25 × 10 4 kJ from the boiler and gives up 1.92 × 10 4 kJ in exhaust every cycle. a)How much work does the engine do every cycle? W net = Q H  Q L = 2.25 × 10 4 kJ  1.92 × 10 4 kJ = 3.3 × 10 3 kJ b)What is the efficiency of the engine? eff = 1  Q L /Q H = 1  1.92 × 10 4 kJ / 2.25 × 10 4 kJ = 0.15 or 15%

Second Law of Thermodynamics All the king’s horses and all the king’s men Couldn’t put Humpty together again Many processes go only in one direction and cannot be reversed. Why? Even if the first law of thermodynamics is obeyed, certain things are never seen to happen: ONE WAY

Shake- shake – Heat is never observed to flow spontaneously from cold things to hot ones – Broken coffee cups are never seen to spontaneously re- assemble and fly back up on the table – Salt and pepper, once mixed, will never separate back into two layers of salt and pepper by shaking HEAT coldhot

Statements of the Second Law There are many ways to state the second law of thermodynamics, but the general idea is this: In all processes, a system tends to move from order to disorder and, in fact, the total disorder of the universe is always increasing What is the state of maximum disorder for an isolated system? – thermal equilibrium! Isolated gas T1T1 T2T2 More Order T Less Order (Thermal Equilibrium)

A thermodynamic quantity called entropy is a measure of the disorder of a system A more scientific way of stating the second law is: In all processes, the entropy of a system tends to increase with time and, in fact the entropy of the universe is constantly increasing The second law can be understood in terms of probability: disordered states are far more numerous than ordered ones, and thus are far more likely to exist

The Second Law for Heat Engines The second law, when applied to heat engines, puts limits on their efficiency In fact the second law can be stated in terms of heat engines: No heat engine can be 100% efficient. In other words, the efficiency is always less than one, and the “waste heat”, Q L, is never zero In equations: eff < 1 (never equal) Q L > 0 (never equal)