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Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17 0C. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of `N_2`=28.0
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A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom
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From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 `cm^3` `s^(–1)`. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 `cm^3` `s^(–1)`. Identify the gas. [Hint : Use Graham’s law of diffusion: R1/R2 = ( M2 /M1 )1/2, where R1, R2 are diffusion rates of gases 1 and 2, and M1 and M2 their respective molecular masses. The law is a simple consequence of kinetic
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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 ` n^2` = `n^1` exp [ -mg (`h_2` – `h_1`)/ kB T] where` n-2`, `n-1` refer to number density at heights `h_2` and `h_1` respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: `n_2`
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Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms : [Hint : Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few
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What is the area of the triangle ADE in the following figure?
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What will be the change in the volume of a cube when its side becomes 10 times the original
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Area of a rhombus is equal to __________ of its
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If the area of a face of a cube is 10 `cm^2`, then the total surface area of the cube is
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1L = 1000
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Amount of region occupied by a solid is called its surface
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160 `m^3` of water is to be used to irrigate a rectangular field whose area is 800 `m^2`. What will be the height of the water level in the
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Find the area of a rhombus whose one side measures 5 cm and one diagonal as 8
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The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the
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Find the area of polygon ABCDEF, if AD = 18cm, AQ = 14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm, and FM, EP, QC and BN are perpendiculars to diagonal
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A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces
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A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out
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A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final
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What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w
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If the height of a cylinder becomes `1/4` of the original height and the radius is doubled, then which of the following will be
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