Thermodynamics - QMplus

Thermodynamics

• Work and Energy in Chemical Systems

• Enthalpy and Heat

• Entropy and Disorder

• Free Energy and Equilibrium

Thermodynamics – From last lecture

• We can define Energy, Work and Heat• Define system, surroundings, universe• Types of systems• Zeroth law of thermodynamics• First law of thermodynamics• Enthalpy • Use thermochemical data to calculate standard

enthalpies at any temperature

Thermodynamics

• Work and Energy in Chemical Systems

• Enthalpy and Heat

• Entropy and Disorder

• Free Energy and Equilibrium

Second law of thermodynamics – the concept of Entropy

• The second law is of central importance in the whole of science, and

hence in our rational understanding of the universe, because it

provides a foundation for understanding why any change occurs.

• Thus, not only is it a basis for understanding why engines run and

chemical reactions occur, but it is also a foundation for understanding

those consequences of chemical reactions.


The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time.


•What is Entropy?

Measure of a system’s thermal energy per unit of

temperature that is unavailable for doing useful

work.


The concept of entropy developed in

response to the observation that a certain

amount of functional energy released

from combustion reactions is always lost

to dissipation or friction and is thus not transformed into useful work.


The second law of thermodynamics states that the total thermal energy per unit of temperature unavailable for doing useful

work of an isolated system can never decrease over time.


• It concerns a fundamental asymmetry in the universe. • This asymmetry manifests itself in many different ways, and there

are, therefore, many ways of expressing the second law.• Kelvin statement. No process is possible in which the sole effect is

the absorption of heat from a reservoir and its complete conversion into work (i.e. a perfect engine is impossible).

• Clausius statement. No process is possible in which the sole effect is the transfer of heat from a colder reservoir to a hotter reservoir (i.e. a perfect fridge is impossible)


• The second law has been expressed in many ways.

• In 1824 Sadi Carnot showed in his Fundamental Principles of Equilibrium and Movement, that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity (or useful work done).

• First statement of the second law of thermodynamics.

Steam engine

Carnot (1796–1832) analysing the constraints on the efficiency of a steamengine found that heat was a kind of imponderable fluid that, as it flowedfrom hot to cold, was able to do work, just as water flowing down a gradientcan turn a water mill, that the efficiency of a perfect steam engine isindependent of the working substance and depends only on the temperaturesat which heat is supplied from the hot source and discarded into the cold sink.

Energy

pis

ton

Efficiency(ε) = 1 − Tsink/Tsource


• Rudolf Clausius in 1854 described that,although energy has a tendency to migrate asheat from hot to cold, the reverse migration isnot spontaneous. He formulated into what isnow known as the Clausius’ statement of thesecond law of thermodynamics: heat does notpass from a body at low temperature to one athigh temperature without an accompanyingchange elsewhere.

• We observe that heat always flows spontaneously from a warmer object to a cooler one. This direction of heat flow is one of the ways of expressing the second law of thermodynamics:

• When objects of different temperatures are brought into thermal contact, the spontaneous flow of heat that results is always from the high temperature object to the low temperature object. Spontaneous heat flow never proceeds in the reverse direction.


Heat engines• Convert heat into work. They are the technological foundation of

our society (power stations, transportations…)

• In a heat engine: - Internal energy of a gas is increased

by heat and work,- Some of that added internal

energy is used to do work,- The rest is thrown away.

Heat Engines and the Carnot Cycle

A heat engine is a device that converts heat into work. A classic example is the steam engine.

• Fuel heats the water;

• the vapor expands and does work against the piston;

• the vapor condenses back into water again and the cycle repeats


All heat engines have:

• a high-temperature reservoir (Th)

• a low-temperature reservoir (Tc)

• a cyclical engine

Carnot Cycle• Reversible isothermal expansion of the gas at the "hot"

temperature, TH (isothermal heat addition or absorption). the gas is allowed to

expand and it does work on the surroundings. The temperature of the gas does not

change during the process, and thus the expansion is isothermic. The gas expansion is propelled by absorption of heat energy Q1 from the high temperature reservoir.

• Reversible Adiabatic expansion of the gas. the piston and cylinder are assumed to

be thermally insulated, thus they neither gain nor lose heat. The gas continues to

expand, doing work on the surroundings, and losing an equivalent amount of internal

energy. The gas expansion causes it to cool to the "cold" temperature, TC. The

entropy remains unchanged.

• Reversible isothermal compression of the gas at the "cold" temperature, TC. The gas

is exposed to the cold temperature reservoir while the surroundings do work on the gas by

compressing it (such as through the return compression of a piston), while causing an

amount of heat energy Q2 to flow out of the gas to the low temperature reservoir. This work

is less than the work performed on the surroundings in step 1 because it occurs at a lower

pressure given the removal of heat to the cold reservoir as the compression occurs.

• Isentropic compression of the gas. The piston and cylinder are assumed to be thermally

insulated and the cold temperature reservoir is removed. The surroundings continue to do work

to further compress the gas and both the temperature and pressure rise now that the heat sink

has been removed. This additional work increases the internal energy of the gas, compressing

it and causing the temperature to rise to TH. The entropy remains unchanged. At this point the gas is in the same state as at the start of step 1.

• (1) Place the working substance in thermal contact with the hot reservoir (at TH) and allow it to undergo a frictionless, quasi-static expansion. Heat QH enters the working substance from the reservoir.

• (2) Thermally insulate the working substance and allow it to undergo a further frictionless, quasi-static expansion (this part of the cycle is adiabatic).

• (3) Place the working substance in thermal contact with the cold reservoir (at TC), and allow it to undergo a frictionless, quasi-static compression. Heat Qc leaves the working substance and goes into the reservoir.

• (4) Thermally insulate the working substance and allow it to undergo a further frictionless, quasi-static compression (adiabatic).

Carnot Cycle


An amount of heat Qh is supplied from the hot reservoir to the engine during each cycle. Of that heat, some appears as work, and the rest, Qc, is given off as waste heat to the cold reservoir.

The efficiency is the fraction of the heat supplied to the engine that appears as work.

• After 1 cycle, the working substance has returned to its original state (but the reservoirs have not). The 1st law the net work done by the working substance is

• W could be negative, if the net work is done on the substance. In this case we would be running the engine in reverse, as a fridge.


The efficiency can also be written:

In order for the engine to run, there must be a temperature difference; otherwise heat will not be transferred.


If the efficiency depends only on the two temperatures, the ratio of the temperatures must be the same as the ratio of the transferred heats. Therefore, the maximum efficiency of a heat engine can be written:


The maximum work a heat engine can do is then:

If the two reservoirs are at the same temperature, the efficiency is zero; the smaller the ratio of the cold temperature to the hot temperature, the closer the efficiency will be to 1.


• The maximum-efficiency heat engine is described in Carnot’s theorem:

• If an engine operating between two constant-temperature reservoirs is to have maximum efficiency, it must be an engine in which all processes are reversible. In addition, all reversible engines operating between the same two temperatures, Tc

and Th, have the same efficiency.

• This is an idealisation; no real engine can be perfectly reversible.


The concept of entropy is the foundation of the operation of heat engines,

heat pumps, and refrigerators.

A refrigerator is a device for removing heat from an object and

transferring that heat to the surroundings. This process does not occur

spontaneously because it corresponds to a reduction in total entropy.

Thus, when a given quantity of heat is removed from a cool body, there is

a large decrease in entropy. When that heat is released into warmer

surroundings, there is an increase in entropy, but the increase is smaller

than the original decrease because the temperature is higher. Therefore,

overall there is a net decrease in entropy.

Refrigerators don’t work unless you turn them on.

Refrigerators, Air Conditioners, and Heat Pumps

While heat will flow spontaneously only from a higher temperature to a lower one, it can be made to flow the other way if work is done on the system. Refrigerators, air conditioners, and heat pumps all use work to transfer heat from a cold object to a hot object.


If we compare the heat engine and the refrigerator, we see that the refrigerator is basically a heat engine running backwards – it uses work to extract heat from the cold reservoir (the inside of the refrigerator) and exhausts to the kitchen.

Note that

- more heat is exhausted to the kitchen than is removed from the refrigerator.


An ideal refrigerator would remove the most heat from the interior while requiring the smallest amount of work. This ratio is called the coefficient of performance, COP:

Typical refrigerators have COP values between 2 and 6.


An air conditioner is essentially identical to a refrigerator; the cold reservoir is the interior of the house or other space being cooled, and the hot reservoir is outdoors. Exhausting an air conditioner within the house will result in the house becoming warmer, just as keeping the refrigerator door open will result in the kitchen becoming warmer.


Finally, a heat pump is the same as an air conditioner, except with the reservoirs reversed. Heat is removed from the cold reservoir outside, and exhausted into the house, keeping it warm. Note that the work the pump does actually contributes to the desired result (a warmer house) in this case.


In an ideal heat pump with two operating temperatures (cold and hot), the Carnot relationship holds; the work needed to add heat Qh to a room is:

The COP for a heat pump:

EntropyA reversible engine has the following relation between the heat transferred and the reservoir temperatures:

Rewriting,

This quantity, Q/T, is the same for both reservoirs, and is defined as the change in entropy.


Entropy (S) change in entropy of a system as the result

of dividing the energy transferred as heat by

the temperature at which the transfer took

place:

∆𝑆 =𝑄

∆𝑇

∆𝑆 = 𝑒𝑛𝑡𝑟𝑜𝑝𝑦 𝑐ℎ𝑎𝑛𝑔𝑒

𝑄 = 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 ℎ𝑒𝑎𝑡 𝑓𝑟𝑜𝑚 𝑇1 𝑡𝑜 𝑇2

Units: J /K

For this definition to be valid, the heat transfer must be reversible.

Entropy

Entropy

A real engine will operate at a lower efficiency than a reversible engine; this means that less heat is converted to work. Therefore,

Any irreversible process results in an increase of entropy.

∆𝑆 > 0

Entropy

• The total entropy of the universe increases whenever an irreversible process occurs.

• The total entropy of the universe is unchanged whenever a reversible process occurs.

• Since all real processes are irreversible, the entropy of the universe continually increases. If entropy decreases in a system due to work being done on it, a greater increase in entropy occurs outside the system.

Order, Disorder, and Entropy

Entropy can be thought of as the increase in disorder in the universe. In this diagram, the end state is less ordered than the initial state – the separation between low and high temperature areas has been lost.

This is all for today. Tomorrow we will study the concept of free energy, third law of thermodynamics and do some

thermodynamic exercises.Thanks!

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Thermodynamics - QMplus