Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The relation between volume V, pressure P and absolute temperature T of an ideal gas is PV=XT, where X is a constant. The value of X depends uponA. the mass of gas molecule B. the average kinetic energy of the gas moleculesC. p, V and TD. The number of gas molecules in V

Last updated date: 20th Jun 2024
Total views: 54.9k
Views today: 1.54k
Verified
54.9k+ views
Hint First, we will derive the ideal gas equation using the different laws such as Boyle’s law, Charles’s law and Avogadro’s law. Then we will equate the both equations and find the value of x.

Complete step-by-step solution The ideal gas law is the equation of state of ideal gas.
Derivation of ideal gas equation
Let pressure exerted by the gas=P, Temperature=T, Volume of the gas=V, moles=n, universal gas constant=R
Acc. To Boyle’s law,
It states that volume is inversely proportional to pressure given temperature remains the same.
\[V \propto \dfrac{1}{P}\]
Acc. To Charle’s law,
It states that volume of the gas occupied is directly proportional to temperature given pressure is constant.
\[V \propto T\]
\[V \propto n\]
Combining all three equations
\[V \propto \dfrac{{nT}}{P}\]
Ideal gas equation,
\[PV = nRT\] , R= Universal Gas Constant=8.314J/mol-K ……(1)
We are given that
\[PV = xT\] …….(2)
Comparing the two equations
\[x = nR\]
\[n = \dfrac{N}{{{N_a}}}\] , N= number of molecules of the gas