Q13.14 Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms :
|Substance||Atomic Mass (u)||Density (103 Kg m3)|
Q13.13 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, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres
where n2, n1 refer to number density at heights h2 and h1 respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
where is the density of the suspended particle, and , that of the surrounding medium. [ s Avogadro’s number, and R the universal gas constant.] [Hint: Use Archimedes principle to find the apparent weight of the suspended particle.]
Q 13.12 From a certain apparatus, the diffusion rate of hydrogen has an average value of . The diffusion of another gas under the same conditions is measured to have an average rate of . Identify the gas.
Q13.11 A metre long narrow bore held horizontally (and closed at one end) contains a long mercury thread, which traps a column of air. What happens if the tube is held vertically with the open end at the bottom ?
Q13.10 Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at and temperature . Take the radius of a nitrogen molecule to be roughly . Compare the collision time with the time the
molecule moves freely between two successive collisions (Molecular mass of ).
Q13.9 At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at ? (atomic mass of , of ).
Q13.8 Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not, in which case is vrms the largest ?
Q13.7 Estimate the average thermal energy of a helium atom at (i) room temperature (), (ii) the temperature on the surface of the Sun (), (iii) the temperature of million kelvin (the typical core temperature in the case of a star).
Q13.6 Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity at a temperature of and pressure.
Q13.5 An air bubble of volume rises from the bottom of a lake deep at a temperature of . To what volume does it grow when it reaches the surface, which is at a temperature of ?
Q13.4 An oxygen cylinder of volume litres has an initial gauge pressure of atm and a temperature of . After some oxygen is withdrawn from the cylinder, the gauge pressure drops to atm and its temperature drops to . Estimate the mass of
oxygen taken out of the cylinder (, molecular mass of ).
Q13.3 Figure 13.8 shows plot of versus P for kg of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true: ?
(c) What is the value of where the curves meet on the y-axis?
(d) If we obtained similar plots for kg of hydrogen, would we get the same
value of at the point where the curves meet on the y-axis? If not, what mass
of hydrogen yields the same value of (for low pressure high temperature
region of the plot) ? (Molecular mass of , of ,
Q13.2 Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, ). Show that it is .
Q13.1 Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 Å.