Describe the construction and working of different types of gas thermometers.

Construction:

The constant-volume gas thermometer consists of a closed glass or metal container that holds a fixed amount of gas. The container is connected to a pressure-measuring device, such as a manometer or a pressure gauge.
The gas inside the container is usually an inert gas, such as helium or hydrogen, which is less likely to react under varying conditions of temperature.
The key feature of this thermometer is that the volume of the gas is kept constant, and the pressure of the gas is measured.

Working:

According to Gay-Lussac’s Law, the pressure of a gas is directly proportional to its absolute temperature when the volume is kept constant.

Where:
- is the pressure of the gas,
- is the absolute temperature (in Kelvin).
When the temperature of the gas increases, the kinetic energy of the gas molecules increases, causing them to collide with the walls of the container more frequently and with greater force, resulting in a higher pressure.
By measuring the pressure at a given temperature and using a known reference point (like the freezing point of water), the temperature of the gas can be determined.

Applications:

Used in high-precision temperature measurements and calibration of other thermometers.
Common in scientific research due to its accuracy, especially when measuring low temperatures.

Construction:

The constant-pressure gas thermometer consists of a gas-filled container connected to a piston or movable boundary, allowing the gas to expand or contract freely while maintaining a constant pressure.
The gas inside the container is also typically an inert gas.
A calibrated scale is attached to the piston, which moves in response to changes in the volume of gas.

Working:

According to Charles’ Law, the volume of a gas is directly proportional to its absolute temperature when the pressure is kept constant.

Where:
- $V$ is the volume of the gas,
- is the absolute temperature (in Kelvin).
When the temperature increases, the gas molecules move faster and collide with the walls of the container with greater force. This increases the volume of the gas as it pushes the piston outward.
By measuring the change in volume of the gas at constant pressure, the temperature can be inferred.

Applications:

Used in industries where temperature needs to be controlled with constant pressure, such as in thermodynamic studies.
Used in calibration standards for other types of thermometers.

Construction:

A variation of the constant-volume gas thermometer uses mercury as the working fluid.
The thermometer consists of a long glass tube filled with mercury. The tube has a capillary tube at one end that allows the mercury to expand or contract with temperature changes.
The temperature is determined by the height of the mercury column inside the tube, which increases as the temperature rises.

Working:

Mercury expands when the temperature increases due to the increased kinetic energy of the mercury atoms. As the mercury expands, the column of mercury rises in the tube.
The height of the mercury column is calibrated against known temperatures, and the temperature is read directly from a scale marked on the thermometer.

Applications:

Commonly used in traditional thermometers for measuring body temperature, air temperature, and other general temperature measurements.
Less commonly used today due to environmental concerns about mercury toxicity.

Construction:

This type of thermometer uses an ideal gas inside a sealed container and is connected to a pressure gauge or a manometer.
The gas should ideally behave as an ideal gas (this is typically a very good approximation for gases like helium or hydrogen).

Working:

The temperature of the gas is determined using the Ideal Gas Law, which states:

Where:
- is the pressure of the gas,
- $V$ is the volume,
- $n$ is the number of moles of gas,
- $R$ is the ideal gas constant,
- $T$ is the absolute temperature (in Kelvin).
If the volume and the amount of gas are kept constant, the pressure will be proportional to the temperature. By measuring the pressure and knowing the other variables, the temperature of the gas can be calculated.

Applications:

Used for high-precision temperature measurements in scientific experiments, particularly in laboratories studying thermodynamic properties of gases.

Construction:

This is a specific type of constant-pressure gas thermometer that uses hydrogen gas due to its low molecular weight and its ability to provide accurate temperature measurements.
The hydrogen gas is placed inside a container that is connected to a movable piston, and the pressure is carefully monitored.

Working:

The working principle is similar to the constant-pressure gas thermometer described earlier.
Hydrogen gas expands when heated, causing the piston to move. The movement of the piston is used to determine the temperature based on the known relationship between volume and temperature (Charles’ Law).

Applications:

Often used in scientific research where precise temperature measurements are critical, such as in cryogenics or extremely low-temperature environments.