The atmosphere on a planet is possible only if [ where `v_(rms)` is root mean square speed of gas molecules on planet and `v_(e)` is escape speed on its surface ]

On any planet, the presence of atmosphere implies ( C_(rms)= root mean square velocity of molecules and v_(s)= escape velocity)

On any planet, the presence of atmsophere implies: [c_(r.m.s) = root mean square velocity of molecules and v_e = escape velocity]

The root mean square speed of a group of gas moecules, having speeds v_(1),v_(2),....v_(N) is

If v_(rms) is the rms speed of molecules in a gas and v is the speed of sound waves in the gas, then the ratio (v_(rms))/v is

If v_(rms) is the rms speed of molecules in a gas and v is the speed of sound waves in the gas, then the ratio (v_(rms))/v is

Define root mean square speed (v_(rms)) . Write down its equations.

Atmosphere of a planet contains only an ideal gas of molar mass M_(0) . The temperature of the atmosphere varies with height such that the density of atmosphere remains same throughout. The planet is a uniform sphere of mass M and radius ‘a’. Thickness of atmosphere is small compared to ‘a’ so that acceleration due to gravity can be assumed to be uniform throughout the atmosphere. (a) Find the temperature difference between the surface of the planet and a point at height H in its atmosphere (b) If the rms speed of gas molecules near the surface of the planet is half the escape speed, calculate the temperature of the atmosphere at a height H above the surface. Assume (C_(p))/(C_(V)) = gamma for the atmospheric gas

The speed of sound in a gas is v and the root mean square speed of gas molecules is v_(rms) . If the ratio of the specific heats of the gas is 1.5 then the ratio v//v_(rms) is