Answer to Question #160596 in Molecular Physics | Thermodynamics for joel

Question

State the assumptions that are made in the kinetic theory of gases and derive an expression for the pressure exerted by a gas which conforms to these assumptions, in terms of density and the root mean square velocity of its molecles

Answer 1

Answer

According to KTG assumption are as below

• The space-volume to molecules ratio is negligible as physics.
• There is no force of attraction between the molecules at the normal temperature and pressure.
• The force of attraction between the molecules builds when the temperature decreases and the pressure increases.
• There is a large space between the molecules resulting in continuous motion KTG.
• The free movement of molecules results in a collision which is perfectly elastic.
• The molecules have kinetic energy due to random movement. But the average kinetic energy of these molecules differs with temperaturE in MOTION.
• Molecules exert pressure on the walls of the container.
• derivation of expression-
  

As pressure

$P=\frac{m_T N}{3VN}\Sigma v^2\\=\frac{M_T}{3VN}\Sigma v^2\\ =\frac{\rho v_{rms}^2}{3}$