Thermodynamics Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work.

Zeroth law of thermodynamics If two thermodynamic systems are each in thermal equilibrium with a third, then all three are in thermal equilibrium with each other.

First Law of Thermodynamics The first law of thermodynamics is the generalization of the law of conservation of energy that includes heat transfer. Heat (Q), internal energy (U), and work (W) are the quantities involved in thermodynamics processes.

First law of thermodynamics: Conservation of energy Whenever heat is added to a system, it transforms to an equal amount of some other form of energy. The added energy does one (or both) of two things: 1) It increases the internal energy of the system if it remains in the system. 2) It does work on things external to the system if it leaves the system.

First law of thermodynamics U = Q + W Sign convention: +Q means that heat is added to the system +W means that work is done on the system (for example, when gas is compressed) -Q means that heat is removed from the system -W means that work is done by the system (for example, the work done by an expanding gas)

U, Q, and W Any given system in a particular state will have a certain amount of internal energy U. A system does not have certain amount of heat or work. These are what change the state of the system, and generally change the internal energy.

U, Q, and W When heat is added to or removed from a system, or work is done on or by a system, thermodynamics processes occur that can change the system from one state to another, each having a particular internal energy U. The internal energy depends only on the state of the system, and not what brought it there.

First law of thermodynamics The first law can be applied to several processes for a closed system on an ideal gas in which one of the thermodynamic variables is kept constant. These processes have names beginning with iso- (from the Greek isos, meaning “equal”)

Thermodynamics Processes Isothermal – constant temperature T = 0; U = 0; Q = -W Isobaric – constant pressure P = 0; W = -PV = -(area under the curve) U = Q + (-PV) Isochoric (or isovolumetric) – constant volume V = 0; W = 0; U = Q Adiabatic – no gain or loss of heat to the system (isolated) which means that heat flow is zero. Q = 0; U = W

Work on the gas W = Fd Since F = PA, W = PAd where V = -Ad. Therefore, W = -PV On a PV diagram, work can be calculated by taking the area under the curve. Remember: When the gas expands work on the gas is negative (or work is done by the gas). When the gas is compressed, work is positive (or work is done on the gas).

Work done in cyclic process Cyclic process is a process where a system starts from and returns to the same thermodynamic state. In cyclic process, network is equal to the area enclosed by the graph in the PzV diagram. For a clockwise cycle, net work is done by the gas (W  0). For counterclockwise cycle, network is done on the gas (W  0).

PV diagrams

Second law of thermodynamics “Heat will not flow spontaneously from a colder body to a warmer body AND heat energy cannot be transformed completely into mechanical work.” The bottom line: Heat always spontaneously flows from a hot body to a cold body. Nothing is 100% efficient.

Heat Engine Any device that changes internal energy into mechanical work. Heat engine works by: 1. absorbing internal energy from a reservoir of higher temperature; 2. converting some of this energy into mechanical work; and, 3. expelling the remaining energy to some lower-temperature reservoir.

Heat engine a

Engine efficiency In order to determine the thermal efficiency of an engine you have to look at how much ENERGY you get OUT based on how much you energy you take IN. In other words:

Rates of energy usage Sometimes it is useful to express the energy usage of an engine as a RATE. For example: The RATE at which heat is absorbed! The RATE at which heat is expelled. The RATE at which WORK is DONE

Efficiency in terms of rates

Carnot Engine The most efficient heat engine cycle is the Carnot cycle, consisting of two isothermal processes and two adiabatic processes. The Carnot cycle can be thought of as the most efficient heat engine cycle allowed by physical laws. In order to approach the Carnot efficiency, the processes involved in the heat engine cycle must be reversible and involve no change in entropy. This means that the Carnot cycle is an idealization, since no real engine processes are reversible and all real physical processes involve some increase in entropy.

Carnot Cycle A Carnot engine -- or a Carnot cycle -- is a combination of isothermal expansions and compressions and adiabatic expansions and compressions.

Carnot engine efficiency It can be shown that the ratio of the heat expended to the heat absorbed, Qc/Qh, is also equal to the ratio of the cold temperature to the hot temperature, Tc/Th. Then the efficiency of a Carnot engine can also be written as 𝑒=1 − 𝑇 𝐶 𝑇 𝐻

Heat pump (refrigerator) A machine or device that moves heat from the ‘heat source' at a lower temperature to the 'sink' or 'heat sink' at a higher temperature.  May be thought of as a "heater" if the objective is to warm the heat sink (as when warming the inside of a home on a cold day), or a "refrigerator" if the objective is to cool the heat source (as in the normal operation of a freezer).

Entropy and disorder Entropy is the measure of “disorder” or "multiplicity" associated with the state of the objects. The entropy of the Universe increases in all natural processes; this is as alternative statement of the second law.

Entropy and disorder A disorderly arrangement is much more probable than an orderly one if the laws of nature are allowed to act without an interference.

Example Imagine that you have a bag of 100 marbles, 50 red and 50 green. You are allowed to draw four marbles from the bag according to the following rules. Draw one marble, record its color, return it to the bag, and draw again. Continue this process until four marbles have been drawn. End Result Possible Draws Total number of same results All R RRRR 1 1G, 3R RRRG,RRGR,RGRR,GRRR 4 2G, 2R RRGG,RGRG,GRRG,GRGR,GGRR 6 3G, 1R GGGR,GGRG,GRGG,RGGG All G GGGG

Third law of thermodynamics The entropy of a system approaches a constant value as the temperature approaches absolute zero.

Third law of thermodynamics Water in gas form has molecules that can move around very freely. Water vapor has very high entropy (randomness). As the gas cools, it becomes liquid. The liquid water molecules can still move around, but not as freely. They have lost some entropy. When the water cools further, it becomes solid ice. The solid water molecules can no longer move freely, but can only vibrate within the ice crystals. The entropy is now very low. As the water is cooled more, closer and closer to absolute zero, the vibration of the molecules diminishes. If the solid water reached absolute zero, all molecular motion would stop completely. At this point, the water would have no entropy (randomness) at all.