# Gas Thermometer

## What is a Gas Thermometer?

According to gas laws, pressure of a gas varies as a linear function of temperature when the volume is kept constant. Similarly volume of a gas varies as a linear function of temperature when the pressure is kept constant. Gas thermometer uses these features of gases. They works on the principle of variation of pressure or volume as a linear function of change in temperature measured in absolute scale.

### Use of Gas Thermometers

Usage of gas thermometer works on the Zeroth law of thermodynamics.

This states that –

If two bodies individually are in thermal equilibrium with a third body then, the two bodies will also be in thermal equilibrium with each other.

• This principle makes the sense for use of a gas thermometers to calibrate other type of thermometers.
• Gas thermometers have wide range of temperature measurement from -260 \degree C to 800 \degree C .
• These thermometers are resistance to vibration and their readings can be taken from a far distance.

### Types of Gas Thermometers

According to the working principles, gas thermometers are classified into two types –

1. Constant Volume Gas Thermometer.
2. Constant Pressure Gas Thermometer.

Out of the above two types of gas thermometer, the constant volume gas thermometer is most widely used.

## Constant Volume Gas Thermometer

A constant volume gas thermometer works on the principle of Gay-Lussac’s law. It is the most commonly used type of gas thermometer. Setup and working procedure of a constant volume gas thermometer is shown in figure.

A constant volume gas thermometer is simply consists of a glass bulb connected by a glass capillary tube. The bulb is filled with certain amount of a gas. Helium, hydrogen or air are most commonly used in the bulb.

The capillary tube containing the bulb is connected to limb A of a mercury manometer. Limb B of the manometer is open to atmosphere. The two limbs A & B are connected through a flexible pipe forming an U-Tube manometer. A calibrated scale is attached in between the limbs of manometer for taking reference of readings of mercury levels in the limbs.

The limb B of manometer can be raised or lowered by a simple mechanism to adjust the mercury levels in the limbs as desired. At normal conditions, the mercury level in the limb A is at the reference level for measurement called Zero Point.

### Calibration of Thermometer

For calibrating the thermometer, bulb is kept in water bath tub maintained at triple point temperature T_{tp} and the corresponding gauge pressure of gas inside the bulb is measured. Let, difference in height of mercury levels in limbs A & B is h mm. Then, the absolute pressure of the gas contained in the bulb is obtained by using the relation –

P_{tp} = P_{atm} + \rho g h ……. (1)

Here, P_{atm} is the atmospheric pressure, \rho is the density of mercury and g is the acceleration due to gravity.

### Procedure of Measurement

Initially the setup is so arranged such that, the mercury level in limb A is at the marked Zero point level. For measurement, thermometer bulb is made in contact with the hot sample solution kept in a tub as shown in figure. After some time, the bulb comes in thermal equilibrium with the solution. The temperature of gas in the bulb increase and attains the temperature of solution in the tub. This increase in the temperature of bulb, causes the gas to expand and its volume increases. This will push the mercury in limb A and level dips from the zero point. Thus, the volume of gas in the bulb and capillary tube has got changed. This need to be corrected and the volume of gas is to be compressed up to the initial value. It is done by increasing the mercury pressure in the limb B by vertically moving it up or down.

For bringing the mercury level in limb A at zero point level, the limb B is vertically moved so that, the mercury level in the limb A is again rises at the reference Zero Point. In this way, the volume of the gas inside the bulb and the capillary tube is brought to the initial value. Thus, the volume of the system of gas remains constant. Thus, the increase in temperature of the bulb has resulted an increase of pressure of gas at constant volume.

The final pressure P_{t} of the gas in the bulb can be obtained by measuring the mercury column height Z above the reference Zero point level in limb A of manometer. Then from equation (1) –

P_{t} = P_{atm} + \rho g Z ……. (2)

### Calculation of Temperature

Change in pressure of a gas becomes the thermometric property for a constant volume gas thermometer. If temperature of the sample solution is T and the final pressure of gas in the bulb calculated by the relation (2) is found P_{t} , then governing thermometric relation can be expressed as –

T = 273.15 \times \left ( \frac { P_t }{ P_{tp} } \right ) \degree C

Because, 273.15 \degree C is the triple point temperature of water.

## Constant Pressure Gas Thermometer

In constant pressure gas thermometer, the pressure of the gas is maintained constant. Thus, the volume of the gas in the bulb varies linearly with the change in temperature of bulb.

The construction, set up and working principle of a constant pressure gas thermometer is same as that of a constant volume gas thermometer. It has only difference in the procedure of measurement.

### Procedure of Measurement

A constant pressure gas thermometer works on the principle of Charle’s Law. It states that –

• Charles law states that, the volume of a given mass of a gas is directly proportional to its absolute temperature if the pressure remains constant. Or,
• If the pressure remains constant then the volume of a given mass of gas increases or decreases by \left ( \frac {1}{273} \right ) of its volume at ( 0 \degree C ) for each ( 1 \degree C ) rise or fall in temperature respectively.

Its working procedure is almost similar to the procedure of working of a constant volume gas thermometer explained above. Only the difference is that, the mercury level is so adjusted in limbs A & B such that their difference, i.e., Z is maintained constant.

Here, change in volume of the gas becomes the thermometric property for a constant pressure gas thermometer. If temperature of the sample solution is T and the final volume of gas in the bulb calculated from thermodynamic relations is found V_{t} , then governing thermometric relation can be expressed as –

T = 273.15 \times \left ( \frac { V_t }{ V_{tp} } \right ) \degree C

Here, V_{tp} is the volume of gas when the bulb is kept at triple point temperature of water. It is obtained by the relation given by Ideal Gas Equation as follows –

P_{tp} \times V_{tp} = R \ T_{tp}

Or, \quad V_{tp} = 273.15 \left ( \frac {R}{P_{tp}} \right )

Here, P_{tp} is the absolute pressure of gas at triple point temperature of water and R is universal gas constant.

Advantages of gas thermometers are as follows –

1. Sensitivity of a gas thermometer is high due to the volumetric expansion being large enough.
2. Scale range of gas thermometers is large.
3. At certain conditions, the behavior of gas is almost similar to that of an ideal gas. Hence, gas thermometer gives accurate thermodynamic scale readings.
4. Thermal capacity of gases is low, so a small quantity of gas is required for a large change in volume for small change in temperature.

Advantages of gas thermometers are as follows –

1. It requires a lot of work and setup to determine temperature using gas thermometers.
2. Being a spacious and large setup it is hard to relocate it easily.
3. Its accuracy or precision comes down when used for measuring varying temperature with a faster rate.