What is the value of \(\gamma\) to monoatomic gas ?

Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197g mol^-1 .

The volume of a given mass of a gas at 27⁰C, 1 atm is 100 cc. What will be its volume at 327⁰C?

What is the minimum possible temperature on the basis of Charle's law ?

 What would be the effect on rms velocity of gas molecules, if the temperature of the gas is increased by a factor 4 ?

What is the number of degree of freedom of a bee flying in a room?

The specific heat of argon at constant volume is 0.075kg^-1K^-1, then what will be its atomic weight?[Given, R = 2 cal mol^-1K^-1]

How is mean free path depends on number density of the gas?

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters \(1\overset { 0 }{ A } \) and \(2\overset { 0 }{ A } \). The gases may be considered under identical conditions of temperature, pressure and volume.

If there are f degrees of freedom with n moles of a gas, then find the internal energy possessed at a temperature T.

What is the rms speed of hydrogen gas molecules at STP.  Given,  density is  0.09 kg m^-3.

A gas is contained in a closed vessel. How pressure due to the gas will be affected if force of attraction between the molecules disseppear sudenly?

What is basic law followed by equipartition of energy?

Explain qualitatively, how the extent of Brownian motion is affected by the
(a) size of the Brownian particle,
(b) density of the medium,
(c) temperature of the medium,
(d) viscosity of the medium?

An oxygen cylinder of volume 30 L has an initial gauge pressure of 15 atm and a temperature of 27⁰ C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17⁰ C.Estimate the mass of oxygen taken out of the cylinder (R = 8.31 mol^-1K^-1 , molecular mass of O₂= 32 u).
Whenever masses are taken out of the closed system, no more it is a  closed removed should be calculated and then by multiplying with molecular mass of the gas, the same can be converted into mass of the gas removed.

Calculate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2 atm and temperature 17^oC.Take the radius of a nitrogen molecule to be roughly \(1.0\mathring { A } \)  Compare the collision time with the time,the molecule moves freely between two successive collisions.Molecular mass of \({ N }_{ 2 }=28.0u\)

Estimate the average thermal energy of a helium atom at (i) room temperature (27 °C), (ii) the temperature on the surface of the Sun (6000 K), (iii) the temperature of 10 million kelvin (the typical core temperature in the case of a star).

Explain,
(i) why there is no atmosphere on moon.
(ii) there is fall in temperature with altitude

The molecules of a given mass of a gas have root mean square speeds of 100 ms^-1 at 27⁰ C and 1.00 atm pressure. What will be the root mean square speeds of the molecules of the gas at 127⁰C and 2.0 atm pressure?

An electric bulb of volume 250 cm³ was sealed off during manufacture at a pressure of 10^-3 mm of mercury at 27⁰C. Compute the number of air molecule contained in the bulb.Given that, molecules contained in the bulb. Given that, R = 8.31 J/mol/K N_A= \(6.02\times { 10 }^{ 23 }{ mol }^{ -1 }\).

A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity,e.g. does not have uniform density(and pressure). As you might except, its density decreases with height. The precise dependence is given by the so called law of atmosphere.
n₂ = n₁ exp [- mg(h₂ - h₁)/ k_BT]
Where, n₂ and n₁ refer to number density at heights h₂ and h_1, respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column.
\({ n }_{ 2 }={ n }_{ 1 }\quad exp\left[ -mg\quad { N }_{ A }(\rho -{ \rho }^{ ' })({ h }_{ 2 }-{ h }_{ 1 })/(\rho RT) \right] \)
Where, \(\rho \) is the density of the suspended particle and \({ \rho }^{ ' }\), that of surrounding medium.
[\(\because \) N_A is Avogadro's number and R is the universal gas constant.]