Kinetic Theory ...

Three perfect gases at absolute temperatures $$\mathrm{T}_{1},\ \mathrm{T}_{2}$$ and $$\mathrm{T}_{3}$$ are mixed. The masses of molecules are $$\mathrm{m}_{1},\ \mathrm{m}_{2}$$ and $$\mathrm{m}_{3}$$ and the number of molecules are $$\mathrm{n}_{1},\ \mathrm{n}_{2}$$ and $$\mathrm{n}_{3}$$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

An ideal gas goes through a reversible cycle $$a\rightarrow b\rightarrow c\rightarrow d$$ has the V- T diagram shown below. Process $$d\rightarrow a $$ and $$b\rightarrow c$$ are adiabatic.
The corresponding P-V diagram for the process is ( all figure are schematic and not drawn to scale).

In the nuclear fusion reaction, $$_{1}^{2}\mathrm{H}+_{1}^{3}\mathrm{H}\rightarrow_2^4{He}$$ $$+\ {n}$$ given that the repulsive potential energy between the two nuclei is $$7.7\times 10^{-14}\ {J}$$, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant $$\mathrm{k}=1.38\times 10^{-23}\mathrm{J}/\mathrm{K}$$]

An ideal gas is enclosed in a cylinder at pressure of $$2 \,atm$$ and temperature, $$300 \,K$$. The mean time between two successive collisions is $$6 \times 10^{-8} \,s$$. If the pressure is doubled and temperature is increased to $$500 \,K$$, the mean time between two successive collisions will be close to:

$$'N'$$ moles of a diatomic gas in a cylinder are at a temperature $$'T'$$. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas gets converted into monatomic gas. What is the change in the total kinetic energy of the gas ?

Which of the following shows the correct relationship between the pressure $$'P'$$ and density $$\rho$$ of an ideal gas at constant temperature ? 

One $$kg$$ of a diatomic gas is at a pressure of $$ 8\times 10^{4}\ \mathrm{N}/\mathrm{m}^{2}$$. The density of the gas is $$4$$ $$\mathrm{k}\mathrm{g}/\mathrm{m}^{3}$$. What is the energy of the gas due to its thermal motion ? 

The gas mixture constists of $$3$$ moles of oxygen and $$5$$ moles of argon at temperature $$T$$. Considering only translational and rotational modes, the total internal energy of the system is:

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4:3. The ratio of their densities is

A gas molecule of mass $$M$$ at the surface of the Earth has kinetic energy equivalent to $$0^oC$$. If it were to go up straight without colliding with any other molecules, how high it would rise?
Assume that the height attained is much less than radius of the earth. ($$k_B$$ is Boltzmann constant)