Kinetic Theory ...

2 moles of an ideal gas A ($$ {C}_{P} $$ $$= 4R$$) and 4 moles of an ideal gas B ($$ {C}_{V} $$ $$= \dfrac {3R}{2}$$) are taken together in a container and allowed to expand reversibly and adiabatically from 49L to 64L, starting from an initial temperature of $$ {47}^{0} $$C. The final temperature of the gas is :

The ratio of translational and rotational kinetic energies at 100 K temperature is 3 : 2. Then the internal energy of one mole gas at that temperature is $$[R = 8.3 J/mol-K]$$

A monoatomic ideal gas ($$ {C}_{V} = \dfrac {3}{2} R$$) is allowed to expand adiabatically and reversibly from initial volume of 8L at 300 K to a volume of $$ {V}_{2} $$ at 250 K. $$ {V}_{2} $$ is: 

On heating 128 g of oxygen gas from 0$$^{\circ}$$C to 100$$^{\circ}$$C, $$C_V$$ and $$C_P$$ on an average are 5 and 7 cal mol$$^{-1}$$ degree$$^{-1}$$, the value of $$\Delta$$U and $$\Delta$$H are respectively :

$$S_1$$: At extermely high temperature degree of freedom of monatomic gas become 5. due to activation of vibrational degree of freedom.
$$S_2$$: For a uniformly charged solid non-conducting sphere potential is maximum at it's centre.
$$S_3$$: Breaking stress of wire depends on its corss-sectional Area.
$$S_4$$: Only time varying magnetic field produces induced electric field which have lines of force.

The heat capacity of a certain amount of a particular gas at constant pressure is greater than that at constant volume by 29.1 J/K. Match the items given in Column I with the items given in Column II.

Consider a classroom of dimensions $$(5 \times 10 \times 3)\ $$m$$^3$$ at temperature $$20^{o}$$C and pressure $$1$$ atm. There are $$50$$ people in the room, each losing energy at the average of $$150$$ watts. Assuming that the walls, ceiling, floor, and furniture are perfectly insulated and none of them is absorbing heat. How much time will be needed for raising the temperature of air in the room to the body temperature (37$$^{o}C$$)? [For air $$C_p = \dfrac{7}{2} R$$ and neglect the loss of air to the outside as the temperature rises]

At what temperature does the mean kinetic energy of hydrogen atoms increase to such an extent that they will escape out of the gravitational field of earth forever?

$$1$$ mole of an ideal gas $$A\ ({ C }_{ v,m }=3R)$$ and $$2$$ moles of an ideal gas $$B\ \left( { C }_{ v,m }=\cfrac { 3 }{ 2 } R \right)$$ are taken in a container and expanded reversibly and adiabatically from $$1$$ litre to $$4$$ litres starting from initial temperature of $$320K$$. $$\Delta E$$ or $$\Delta U$$ for the process is:

In a certain gas $$\displaystyle \frac{2}{5}$$th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. The average translation energy of one such molecule, when the temperature is $$27^{\circ}C$$ is given by $$x\times 10^{-23}\ J$$,then find $$x$$?