Unsolved Questions

A certain gas obeys the clausius equation of state p(v - b) = RT and has its internal energy given by . Show that the equation for a reversible adiabatic process is = constant.
The relation between u, p, and v for many gases is of the form u = a + bpv where a and b are constants. Show that for a reversible adiabatic process = Constant where
Air in a closed system expands reversibly and adiabatically from 3 MPa , 200°C to 3 times its initial volume , and then cools at constant volume until pressure drops to 1 MPa . Calculate work done and heat transfer per kg of air.
A mercury atom moves in a cubical box whose edge is 1m long. Its kinetic energy is equal to the average kinetic energy of an atom of an ideal gas at 1000 K. if the quantum numbers are n_x, n_y, n_z all equal to n, calculate n.
Show that, when ideal-gas atoms comes to equilibrium, and taking T = 300 K, P = 1000 Pa and m = 10^-26 kg, calculate
Defining the average speed (w) by the equation show that
Consider a function f defined by the relation first, differentiate partially with respect to Ω_B, and then with respect to Ω_A integrate twice to show
The number of molecules per cubic meter at 760 mm Hg, 273 K is approximately . If the average speed of an oxygen molecule at 273 K is 450 m/s, determine the number of collisions made with the container walls per square cm per sec.
Calculate the average and the rms speed s of the following groups of particles:
For a neutron flux of , determine the number of neutrons per unit volume and the “partial pressure” of the neutron gas, assuming that these neutrons have a Maxwellian velocity distribution at 400 K.
If a box of 1cm³ contains 10⁵ molecules of nitrogen at 27°C having rms speed of 1000 m/s, find the pressure exerted on the walls of the container. What will be the number of collisions per m²?
Show that the most probable kinetic and average energies are 1/2 kT and 3/2 kT respectively.
Prove the following:
Show that the number of molecules in a certain speed range is given by: