Question

In an experiment at a constant temperature (T), pressure (P) is inversely related to volume (V) and also at constant volume (V), pressure (P) is directly related to temperature (T). The formula according to the above information is (Take the proportionality constant as K).
A. $PVT = K$
B. $PVK = T$
C. $PV = K$
D. $\dfrac{{PV}}{K} = T$

Answer 1

Hint: An ideal gas is a theoretical gas made up of a large number of randomly moving point particles with no interparticle interactions. Scientists realised that correlations between pressure, volume, and temperature of a sample of gas could be produced that would hold to approximation for all gases near the end of the 18th century, and the gas laws were born.

Complete step by step answer:
Boyle's law says that the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant at constant temperature. The following is a summary of Boyle's law: When the temperature is constant, the volume of a given mass of a gas is inversely proportional to pressure. These equations can be used to describe the concept:
\[V \propto \dfrac{1}{P}\]

Joseph Louis Gay-Lussac discovered Gay-law, Lussac's also known as Amontons' law or the pressure law, in 1808. It says that the pressure exerted on the walls of an ideal gas's container is precisely proportional to its absolute temperature for a given mass and constant volume. Gay-law Lussac's may be expressed as a mathematical equation as:
\[P \propto T{\mkern 1mu} \]
Using 1 and 2 we can write as
\[\therefore P = \dfrac{{KT}}{V}\]

Note: The volume of a gas is exactly proportional to the number of molecules if the temperature and pressure remain constant. If the temperature and volume of the gas stay constant, the change in pressure is proportional to the number of molecules present. The pressure is inversely proportional to the volume if the quantity of gas molecules and the temperature stay constant. If the temperature varies but the quantity of gas molecules remains constant, the pressure or volume (or both) of the gas will vary in direct proportion to the temperature.