Riemann surface
matlab

$$1001$$
Describe briefly the basic principle of the following instruments for making temperature measurements and state in one sentence the special usefulness of each instrument: constant-volume gas thermometer, thermocouple, thermistor.
(Wisconsin)

Solution:
Constant-volume gas thermometer: It is made according to the principle that the pressure of a gas changes with its temperature while its volume is kept constant. It can approximately be used as an ideal gas thermometer.
Thermocouple thermometer: It is made according to the principle that thermoelectric motive force changes with temperature. The relation between the thermoelectric motive force and the temperature is
$$\varepsilon=a+b t+c t^2+d t^3$$
where $\varepsilon$ is the electric motive force, $t$ is the difference of temperatures of the two junctions, $a, b, c$ and $d$ are constants. The range of measurement of the thermocouple is very wide, from $-200^{\circ} \mathrm{C}$ to $1600^{\circ} \mathrm{C}$. It is used as a practical standard thermometer in the range from $630.74^{\circ} \mathrm{C}$ to $1064.43^{\circ} \mathrm{C}$.
Thermister thermometer: We measure temperature by measuring the resistance of a metal. The precision of a thermister made of pure platinum is very good, and its range of measurement is very wide, so it is usually used as a standard thermometer in the range from $13.81 \mathrm{~K}$ to $903.89 \mathrm{~K}$.

Describe briefly three different instruments that can be used for the accurate measurement of temperature and state roughly the temperature range in which they are useful and one important advantage of each instrument. Include at least one instrument that is capable of measuring temperatures down to $1 \mathrm{~K}$.
(Wisconsin)

Solution:

Magnetic thermometer: Its principle is Curie’s law $\chi=C / T$, where $\chi$ is the susceptibility of the paramagnetic subst ance used, $T$ is its absolute temperature and $C$ is a constant. Its advantage is that it can measure temperatures below $1 \mathrm{~K}$.

Optical pyrometer: It is based on the principle that we can find the temperature of a hot body by measuring the energy radiated from it, using the formula of radiation. While taking measurements, it does not come into direct contact with the measured body. Therefore, it is usually used to measure the temperatures of celestial bodies.

Vapor pressure thermometer: It is a kind of thermometer used to measure low temperatures. Its principle is as follows. There exists a definite relation between the saturation vapor pressure of a chemically pure material and its boiling point. If this relation is known, we can determine temperature by measuring vapor pressure. It can measure temperatures greater than $14 \mathrm{~K}$, and is the thermometer usually used to measure low temperatures.

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