# Presentation: 446291

## Temperature

- Ruslan Prozorov
*5 September 2008*
- Physics 590B

## what is temperature?

- bodily sensation (hot vs cold) – not helpful
- Temperature is a property of matter. Temperature is one of the principal parameters of thermodynamics. On the microscopic scale, temperature is defined as the average energy of microscopic motions of a single particle in the system per degree of freedom. On the macroscopic scale, temperature is the unique physical property that determines the direction of heat flow between two objects placed in thermal contact.
- Internal energy, U, and entropy, , are the fundamental parameters describing any system. The temperature is DEFINED as

- the conventional temperature

- and entropy

## entropy

## thermal fluctuations: the “evil” force

- Boltzmann constant
- a way to reconcile the mathematical stat mech with observable temperature and the universal gas law
- thermal fluctuations – randomizing force

## Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist

## Slide 6

## laws of thermodynamics

- 0. if two systems are in equilibrium with a third system, they must be in equilibrium
- 1. heat is form of energy. Energy is conserved.
- 2. entropy of a closed system increases until it reaches maximum (at equilibrium)
- 3. entropy approaches constant value when temperature goes to zero

## Slide 8

## early temperature scales

- In 1724 Daniel Gabriel Fahrenheit produced a temperature scale which now (slightly adjusted) bears his name. He could do this because he manufactured thermometers, using mercury (which has a high coefficient of expansion) for the first time and the quality of his production could provide a finer scale and greater reproducibility, leading to its general adoption.
- In 1742 Anders Celsius proposed a scale with zero at the boiling point and 100 degrees at the melting point of water, though the scale which now bears his name has them the other way around

## the absolute scale

- The kelvin unit and its scale, by international agreement, are defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water

- The single combination of pressure and temperature at which water, ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C) and a partial vapor pressure of 611.73 pascals (6.1173 millibars, 0.0060373057 atm).

## Slide 11

## temperature ranges

## high temperatures - briefly

- Thermocouples up to ~ 1500 K

## Primary Thermometers

## Helium Vapor Pressure Thermometry

## Helium melting curve thermometer

## Nuclear orientation thermometry (1-40 mK)

- a magnetic field into *2I+1*
- hyperfine levels.
- 60Co is substituted into
- 59Co (*B*s=10 Telsa), which gives
- The relative occupation of each
- level is given by the Boltzmann
- factor. Each level has its own
- anisotropic γ-decay properties.
- W(θ,T) can be computed.

- 19 September 2006

- CMP Lunch

## Coulomb blockade thermometer

- Coulomb blockade, named after Charles-Augustin de Coulomb, is the increased resistance at small bias voltages of an electronic device comprising at least one low-capacitance tunnel junction.
- A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting electrodes.
- According to the laws of classical electrodynamics, no current can flow through an insulating barrier. According to the laws of quantum mechanics, however, there is a nonvanishing (larger than zero) probability for an electron on one side of the barrier to reach the other side (see quantum tunnelling). When a bias voltage is applied, this means that there will be a current flow. In first-order approximation, that is, neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical terms, the tunnel junction behaves as a resistor with a constant resistance, also known as an ohmic resistor. The resistance depends exponentially on the barrier thickness. Typical barrier thicknesses are on the order of one to several nanometers.
- An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite capacitance. The insulator is also called dielectric in this context, the tunnel junction behaves as a capacitor.
- Due to the discreteness of electrical charge, current flow through a tunnel junction is a series of events in which exactly one electron passes (tunnels) through the tunnel barrier (we neglect events in which two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementary charge by the tunnelling electron, causing a voltage buildup U = e / C, where e is the elementary charge of 1.6×10-19 coulomb and C the capacitance of the junction. If the capacitance is very small, the voltage buildup can be large enough to prevent another electron from tunnelling. The electrical current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the differential resistance around zero bias is called the Coulomb blockade.
- In order for the Coulomb blockade to be observable, the temperature has to be low enough so that the characteristic charging energy (the energy that is required to charge the junction with one elementary charge) is larger than the thermal energy of the charge carriers. For capacitances above 1 femtofarad (10-15 farad), this implies that the temperature has to be below about 1 kelvin. This temperature range is routinely reached for example by dilution refrigerators.
- To make a tunnel junction in plate condenser geometry with a capacitance of 1 femtofarad, using an oxide layer of electric permeability 10 and thickness one nanometer, one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by electron beam lithography and appropriate pattern transfer technologies, like the Niemeyer-Dolan technique, also known as shadow evaporation technique.
- Another problem for the observation of the Coulomb blockade is the relatively large capacitance of the leads that connect the tunnel junction to the measurement electronics.

## Slide 19

## Magnetic susceptibility

## NMR thermometer

## noise

## thermometers

- clinical thermometer

- Galileo thermometer

- The word thermometer (in its French form) first appeared in 1624 in *La Récréation Mathématique* by J. Leurechon, who describes one with a scale of 8 degrees

## thermocouple

## thermocouples

- In 1821, the German–Estonian physicist Thomas Johann Seebeck discovered that when any conductor (such as a metal) is subjected to a thermal gradient, it will generate a voltage. This is now known as the thermoelectric effect or Seebeck effect. Any attempt to measure this voltage necessarily involves connecting another conductor to the "hot" end. This additional conductor will then also experience the temperature gradient, and develop a voltage of its own which will oppose the original. Fortunately, the magnitude of the effect depends on the metal in use. Using a dissimilar metal to complete the circuit creates a circuit in which the two legs generate different voltages, leaving a small difference in voltage available for measurement. That difference increases with temperature, and can typically be between 1 and 70 microvolts per degree Celsius (μV/°C) for the modern range of available metal combinations. Certain combinations have become popular as industry standards, driven by cost, availability, convenience, melting point, chemical properties, stability, and output. This coupling of two metals gives the thermocouple its name.
- Thermocouples measure the temperature difference between two points, not absolute temperature. In traditional applications, one of the junctions—the cold junction—was maintained at a known (reference) temperature, while the other end was attached to a probe.
- Having available a known temperature cold junction, while useful for laboratory calibrations, is simply not convenient for most directly connected indicating and control instruments. They incorporate into their circuits an artificial cold junction using some other thermally sensitive device, such as a thermistor or diode, to measure the temperature of the input connections at the instrument, with special care being taken to minimize any temperature gradient between terminals. Hence, the voltage from a known cold junction can be simulated, and the appropriate correction applied. This is known as cold junction compensation.

## Slide 26

## silicone diodes

## GaAlAs diodes

## Resistance thermometers

- Resistance thermometers, also called resistance temperature detectors (RTDs), are temperature sensors that exploit the predictable change in electrical resistance of some materials with changing temperature.

## Slide 30

## Slide 31

## Pt resistance thermometers

## Rhodium-Iron RTDs

## Slide 34

## negative T coefficient: Cernox

## Germanium resistance

## Slide 37

## Carbon-Glass

## Ruthenium oxide

## capacitance

## Slide 41

## Slide 42