Question

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

Answer 1

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
$$P\propto \underset{\text{at constant T}}{{\displaystyle \frac{1}{V}}|}$$

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

(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.
$$P\propto \underset{\text{constant V}}{T|}$$
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.