### Kinetic Theory

goals
A cylindrical is containing nitrogen at $2\ atm$ and temperature $17^{\circ}C$. The radius of a nitrogen molecule to be roughly $1\ A^{\circ}$. Molecule mass of nitrogen $= 28.0\ u$, Boltzmann constant, $k = 1.38 \times 10^{-23} JK^{-1}$.
In a process the pressure of gas is inversely proportional to the square of volume If temperature of the gas is increased then work done by the gas
At what temperature the kinetic energy of a gas molecular is one-half of its value of ${30}^\circ C$ ?
It is possible to make crystalline solids that are only one layer of atoms thick. Such two dimensional crystals can be created by depositing atoms on a very flat surface. The atoms in such a two dimensional crystal can move only within the plane of the crystal, At very low temperature the molar heat capacity of such a crystal is C$_1$ and at room temperature it is C$_2$
Two closed identical conducting containers are found in the laboratory of an old scientist. For the verification of the gas some experiments are performed on the two boxes and the results are noted
Experiment 1: When the two containers are weight
$W_{A}$ = 225g
$W_{B}$ = 160g and mass of evacuated container
$W_{C}$ = 100g.
Experiment 2:
When two containers are given same amount of heat same temperature rise is recorded. The pressure changes are found
$\triangle P_{A}$ = 2.5 atm, $\triangle P_{B}$ = 1.5 atm

Required data for unknown gas: Mono (molar gas)
$He=4g, Ne=20g, Ar=40g, Kr=84g, Xe=131g Rd=222g$

Dia (molar gas)
$H_{2} = 2g, F_{2}= 19g, N_{2} = 28g, O_{2}= 32, Cl_{2} = 71g$