A constant volume gas thermometer work on:
A. Archimedes principle
B. Pascal’s law
C. Boyle’s law
D. Charles law
E. Gay Lussac’s law

Hint: From the ideal gas, compare the three parameters P,V,T with proportionality relation at constant volume and remember 3 laws corrected in the ideal gas equation.

Complete step-by-step answer:
From ideal gas solution
\[\text{PV = nRT}\]
Where P: Pressure
V: volume
T: Temperature
N: molecules
R: universal gas constant
For a constant volume system, the number of molecules are constant as well as the volume is constant.
Hence \[P\propto T\]
Pressure is proportional to temperature at constant volume.

(a) Archimedes Principle:
Archimedes principle states that upward buoyant force that is executed by body temperature in a fluid is equal to weight displaced.
\[F=\rho gV\]
F= Force
\[\rho\] = Density
G = gravity
V= volume

(b) Pascal’s law
Pascal’s law states that the pressure change at any point in confined incompressible fluid/liquid is transmitted such that the pressure change is constant everywhere.

(c) Boyle’s law:
Boyle’s law that the pressure of a given mass of an ideal gas is inversely proportional to its volume at constant temperature
\[P\propto \mathop{\left. \dfrac{1}{V} \right|}_{\text{at constant T}}\]

(d) Charles law:
Charles law states that volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.
\[V\propto \mathop{\left. T \right|}_{\text{constant P}}\]

(e) Gay – Iussac’s law
Gay Iussac’s law states that pressure of given mass of gas is directly proportional with the absolute temperature of gas when volume of the mass is constant.
\[P\propto \mathop{\left. T \right|}_{\text{constant V}}\]
Constant volume thermometer obeys Gay-Iussac’s law.
Option (e) is correct.

Note: The thermometer could be signified to work on Charles law when the thermometer was just a volume thermometer.
When a constant volume thermometer is taken then it obeys Gay-Iussac’s law.