Kinetic Theory ...

A particle moving along x-axis is acted upon by a single force $$F=F_0e^{-kx}$$, where $$F_0$$ and K and constants. The particle is released from rest at x=0. It will attain a maximum KE of

Figure shows a hypothetical speed distribution for particles of a certain gas $$P ( v ) = C r ^ { 2 } \text { for } 0 < v \leq v _ { 0 } \text { and } P ( v ) = 0 \text { for } v > V _ { 0 }$$

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

N moles of an ideal diatomic gas is contained in a cylinder at temperature $$T.$$ On supplying some heat to cylinder, $$N/3$$ moles of gas disassociated into atoms while temperature remains constant. Heat supplied to the gas is

The respective speeds of the molecules are $$1,2,3,4$$ and $$5\,km, {s}^{-1}$$. The ratio of their r.m.s. velocity and the average velocity will be 

A box contains N molecules of a perfact gas at temperature $$T_{1}$$ and pressure $$P_{1}$$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is $$P_{2}$$ and temperature $$T_{2}$$, then

One mole of an ideal gas undergoes a cyclic change as shown in the figure. The process AB is isothermal. The pressure and volume at point A is $$2.1 \times {10^5}$$ and 22.4 liters, respectively. The temperature at C is

The pressure of the gas contained in a closed vessel is increased by $$0.4\%$$ when heated by $$1^oC$$. The initial temperature of the gas must be

Energy associated with each molecule per degree of freedom of a system at room temperature ($$27^{o}C$$) will be ($$k$$ is Boltzmann;s constant)

For a particle moving along x-axis, acceleration is given as $$a=2v^2$$. If the speed of the particle is $$v_0$$ at $$x=0$$, find speed as a function of $$x$$.