First law of thermodynamics

1. First law of thermodynamics • first law of thermodynamics: • heat added to a system goes into the internal energy of the system and/or into doing work • heat in = work + change in internal energy: Q = W + U • is different formulation of energy conservation • for isolated system: • no heat flow  if work done, must reduce internal energy • historical note: • 1st law quoted as a law in its own right because it took a long time to realize that heat is a form of energy. Until around 1800, heat was considered a fluid called “caloric” that is contained in materials, can be soaked up by materials,.. • It took about 50 years to replace this with the new paradigm that heat is a form of energy, and that total energy, including thermal energy, is conserved. • Milestones on path to first law: Experiments and observations by Benjamin Thompson, James Prescott Joule, Julius Robert Mayer,.. and conjectures by Mayer, Hermann Helmholtz, Rudolf Clausius,..

2. HEAT ENGINES • heat engine: • is a device that converts heat into work • principle: heat input, some of it used to do work, some of it discarded • operate in cyclical process, i.e. at end of an “engine cycle”, engine must be in same state as before; • for a cyclical process: Unet = 0,  Q = W, i.e. work done = net heat input = (heat in) - (heat out) • heat engine operates between two “reservoirs”; • reservoir = system from which heat may be readily extracted and into which heat can be deposited at given temperature; • heat engine takes heat from high temperature reservoir, converts some of it into work, and ejects rest of heat into low temperature reservoir; • example: car engine: • hot reservoir = cylinder in which air-fuel mixture is exploded; • cold reservoir = environment to which waste heat is expelled; • thermal efficiency of a heat engine = ratio of work output to heat input: •  = W/Qin = W/ Qh = 1 - (Qc /Qh )

3. heat engines and refrigerators • engine • refrigerator

4. CARNOT ENGINE • Nicolas Léonard Sadi Carnot (1796 -1832) (“Réflexions sur la puissance motive de la chaleur”, 1824) • constructed idealized method for extracting work with greatest possible efficiency from an engine with heat-flow from one substance at higher temperature to another substance at lower temperature, - the “Carnot cycle” • Carnot cycle is reversible process - can run in either direction; • Carnot engine: • container with piston • can be brought into thermal equilibrium with two heat reservoirs, one at high temperature Th, one at low temperature Tc; • or can be isolated from outside world (i.e. no heat-flow to or from container); • isothermal process: temperature constant; • adiabatic process: isolated  no heat exchange; • efficiency of Carnot engine:  = 1 - (Tc /Th) (note temperature here is measured in Kelvin) • Carnot engine is the most efficient engine possible (2nd law of thermodynamics).

5. Second law of thermodynamics • several different formulations of 2nd law; • all can be shown to be equivalent: • law of heat flow: “Heat (thermal energy) flows spontaneously (i.e. without external help) from region of higher temperature to region of lower temperature. By itself, heat will not flow from cold to hot body. • Kelvin formulation: No process is possible whose sole result is the removal of heat from a source and its complete transformation into work. • Clausius formulation: No process is possible whose sole result is the transfer of thermal energy from a body at low temperature to a body at high temperature. • heat engine formulation: No heat engine can be more efficient than the Carnot engine. • consequence of 2nd law: • the quality of thermal energy (its ability to do work) depends on the temperature; • thermal energy at low temperature less useful than thermal energy at high temperature; • “using energy” does not mean destroying it (cannot be destroyed); it means converting it into work and thermal energy at lower temperature than before  ”degradation of energy”

6. ENTROPY • Entropy: • when heat Q at temperature T enters a system, the system's entropy S changes by S = Q/T • for the Carnot cycle: Qh taken from reservoir at temperature Th , Qc given to reservoir at temperature TcS = Qh/Th - Qc/Tc = 0, i.e. for the Carnot cycle, the change in entropy is = 0. • for other cyclical processes: 2nd law of thermodynamics  efficiency smaller than that of Carnot process • entropy formulation of 2nd law of thermodynamics: • For any process, the total entropy of all the participants either increases or stays the same; it cannot decrease. • entropy related to the degree of disorder, to the probability of a state; • order is less probable than disorder (there are many more ways of having disorder than there are of having order); • some systems (e.g. living things and beings) decrease their entropy, but at the cost of increasing the entropy of the rest of the universe. • the total entropy of the universe keeps increasing.