Answer to Question #120756 in Molecular Physics | Thermodynamics for Abhishek

Question

With the help of a neat and labelled diagram, explain the working of a constant volume gas therm ometer.

Answer 1

The schematic diagram of a constant-volume gas thermometer is shown in Fig.1. The

volume of an ideal gas in the sensing bulb D is kept constant by adjusting the level of

mercury in the arm B of the manometer. The arm B and the arm A are connected by a

flexible tube to form a U-tube manometer. The arm B is also connected to the gas bulb

D via a capillary tube C, while the other arm A of the manometers is open to

atmosphere and can be moved vertically to adjust the mercury level, so the mercury

just touches the mark L of the capillary. The pressure in the bulb b is used as a

thermometric property and can be given by

$$p=p_{atm}+\rho gh$$

The gas bulb D is first placed in constant-temperature bath at the triple point

temperature $T_{tp}$ of water and the level of mercury is adjusted to touch the mark L by

moving the manometer arm A up and down. 

As the volume of the bulb becomes constant and the height difference of the mercury

in the two arms is recorded as $h_{tp}$ the pressure, $p_{tp}$ corresponding to the mercury column

at the triple point.

Now the bulb is brought in contact with a system whose temperature T, is to be

measured. Again, in a similar manner, by keeping the volume of gas in the bulb

constant, the height difference of the mercury in the two arms is recorded and the

corresponding new pressure p is calculated by Eq. (2).

From the ideal gas equation, the new temperature is given by

$$T=273.15\frac{p}{p_{tp}}$$