Elasticity Notes Exercise - I

ELASTICITY Exercise - I UNSOLVED PROBLEMS Q.1 The block oxide of copper is prepared in four different ways and the following observations noted: Copper (in g) Copper oxide (in g) 5.015 6.284 8.286 10.357 18.443 23.169 12.011 15.051 What do you infer form this data ? Q.2 Given below are date on masses of two combining substances yielding more than one compound. Try to discover a striking feature hidden in these date. Carbon Oxygen Compound (parts by mass) (parts by mass) Q.5 (a) Avogadro’s hypothesis is: “Equal volumes of all gases under the same conditions of temperature and pressure have the same number of molecules”. Suppose we replaced ‘molecules’ by ‘atoms’ in this hypothesis. (By atoms we refer to indivisible entities in chemical reactions, unlike mol ecules, which can split into atoms). Would the modified hypothesis be correct ? Would it explain the data in 9.4? (b) What is the atomicity of nitrogen, oxygen, and hydrogen suggested by the data in 9.4 ? (atomicity is the number of atoms in a molecule). Q.6 A drop of olive oil of 1 mm diameter when transferred lightly over water dusted with lycopodium powder spreads out into a circular thin film of diameter 28.1 cm. Estimate the size of a molecule of the oil assuming that the film is only one molecule thick. 464.9 9.3 Carbon 334.6 854.5 626.7 2086.2 Hydrogen 111.2 146.4 Carbon monoxide Carbon dioxide Compound Methane Ethylene Q.7 A steel wire of length 4,7 m and cross-section 3.0 x 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-section 4.0 x 10--5 m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper ? Element 150.0 266.4 Sulphur 75.6 68.8 Compound I II Q.8 Figure 9.21 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material ? Q.3 Given the chemical formula for methane to be CH4, obtain the ratio of mass of a carbon atom to the mass of a hydrogen atom from the data in Exercise 9.2, and predict some possible chemical formulae for ethylene. 250 200 150 100 50 0 0.001 0.002 0.003 0.004 Strain A Strain Stress Q.9 The stress-strain graphs for martyries A and B are shown in Fig. 9.22 Stress Q.4 The following table gives observations on two gaseous reactions. In each set, the temperature and pressure conditions are kept fixed. A. Nitrogen gas Hydrogen gas Ammonia gas (cm3) (cm3) (cm3) 623.3 1830.0 1253.4 349.0 1051.2 685.6 84.7 251.9 170.7 B. Hydrogen gas Oxygen gas Water vapour (cm3) (cm3) (cm3) 307.9 156.6 309.1 435.9 217.8 423.6 851.1 473.1 856.0 What do you infer from these data? Can you understand the law you have inferred empirically on the basis of the atomic picture and Avogardo’s hypothesis? 300 B Strain The graphs are drown to the same scale. (a) Which of the material has greater Young’s modulus (b) Which material is more ductile ? (c) Which is more brittle ? (d) Which of the two is stronger material ? ELASTICITY Stress Stress Q.10 Two different types of rubber are found to have the stress-strain curves as shown in Fig. 9.23. \ Rubber (B) Rubber (A) Strain Strain (a) In which significant ways do these curves differ from the stress - strain curve of a metal wire shown in fig. 9.12 ? (b) A heavy machine is to be installed in a factory. To absorb vibrations of the machine, a block of rubber is placed between the machinery and the floor. Which of the two rubbers A and B would you prefer to use for this purpose ? Why ? (c) which of the tow rubber materials would you choose for a car tire ? Q.11 Read each of the statements below carefully and state, with reasons, if it is true of false. (a) The modulus of elasticity of rubber is greater than that of steel (b) The stretching of a coil is determined by its shear modulus (c) When a materials under tensile stress, the restoring force is due to inter -atomic repulsion (d) A piece of rubber under an ordinary stress can display 1000% strain; yet when unloaded it returns to its original length. This shows that the restoring forces in a rubber piece are strictly conservative (e) Elastic forces re strictly conservative when Hooks’s law is obeyed Q.12 Two wires of diameter 0.25 cm, one made of steel and other made of brass are loaded as shown in Figure. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Young’s modulus of steel is 2.0 x 1011 Pa and that of brass is 0.91 x 1011 Pa. Compute the elongations of steel and brass wires. (1 Pa = 1 N n-2) 1.5m steel 4.0 kg 1.0m steel Q.14 A silica glass rod has a diameter of 1 cm and is 10 cm long. Using the data from table 9.1, estimate the largest mass that can be hung from it without breaking it. Q.15 Compute the bulk modulus of water from the following data: initial volume =100.0 litre, Pressure increase = 100.0 atm. ( 1 atm=1.013 x 105), Final volume = 100.5 litre. Compare the bulk nodulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large. (1 Pa = 1 N m-2) Q.16 What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is 1.03 x 103 kg m-3 ? ( Compressibility of water is 45.8 x 10-11 Pa-1; 1 Pa = 1 N m-2) Q.17 You will appreciate from Exercise 9.3 that date on chemical combinations can at best yield ratios of atomic masses of different elements. This is why atomic masses are defined with respect to some ‘reference atom’. In early chemistry, hydrogen was chosen to be the reference and assigned a unit mass. In the so called chemical scale, oxygen was assigned a mass of `6 units. By international agreement, the unified atomic mass unit (u) is defined to be such that the isotope 12c has a mass exactly equal to 12 u. The difference between these different scales is slight but important for precision measurements. The mass of 137Cs atom is 136.90707 u on the unified atomic scale. The mass of 1H is 1.0078252 u on the same scale. What is the mass of 137Cs atom with respect to the hydrogen reference scale ? Q.18 Why are atomic masses (on say the unified scale) not exact integers ? Why is there a slight difference in the atomic mass of an element on different scales ? Q.19 (a) If data on chemical combination give only relative atomic masses, how does one know the absolute mass of an atom of say oxygen ? (b) Express 1 u in terms of Kg, given that the experimental value of Avogadro’s number is NA = 6.022045 x 1023 mole-1 6.0 kg Q.13 The edges of an aluminium cube are 10 cm long. On face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face ? ( 1 Pa = 1 N m-2) Q.20 Figure 9.1 in the text gives a plot of interatomic potential energy as function of the distance between two hydrogen atoms. Answer the following : (a) if interatomic forces are electrical in nature, why do they not obey Coulomb’s law; i.e. why do they fall of as 1 / r7 for a large distance (instead of as 1 / r7 ELASTICITY expected on the basis of Coulomb’s law). (c) if the potential energy minimum is at r = R0 = 0.74 Å, is the force attractive of repulsive at r = 0.5 Å, 1.9 Å and  Q.21 How much energy is needed to dissociate 0.05% of hydrogen gas occupying a volume of 5.6 liters under STP ? The binding energy of a hydrogen molecule is 4.75 eV. Q.22 The interatomic separation in a neutral H 2 molecule is 0.74 Å and the binding energy is 4.75 eV. If an electron of the molecule is removed, the resulting molecular ion H2 has a binding energy of 2.8 eV.. Would you expect the separation between two protons in H2 greater or less than 9.74 Å ? Q.23 Explain (a) An energy of about 1.3 eV is need to create free Na+ and Cl- ions. [By this we mean that the Na+ and Cl- configuration at large distances has energy 1.3 eV. Higher than neutral Na and Cl atoms at large distances]. In spite of this initial investment the sodium chloride molecule prefers ionic binding. Why? (b) A related question is why does H2 prefer a covalent binding ? Why does it not prefer ionic binding H+ Hlike Na+ Cl- ? Q.24 The interatomic separation in an O2 molecule is 1.2 Å and its binding energy is about 4.4 eV. The intermolecular potential energy between two oxygen molecules has a minimum at 2.9 Å. The two potential energy curves have roughly similar shapes. Would you expect the minimum of intermolecular potential energy in oxygen to be greater of less than 4.4 eV ? Check your expectation with the answer given in the text. Q.25 In which principal aspects are intermolecular forces different from interatomic forces ? In which aspects are they similar ? Q.26 Estimate the average intermolecular binding energy per molecular of (i) mercury, (ii) water if their latent heats of vaporization are 2.72 x 105 J kg-1 and 2.26 x 106 J kg-1 respectively. Is it correct to think that this substance apart from one another, i.e. the negative of the minimum of potential energy between two molecules ? Q.27 Answer the following: (a) If intermolecular potential energy has a minimum at some separation r = r, what is it that prevents all molecules of the given substance from collapsing to the condensed state where every pair has separation equal or r0 ? (b) Intermolecular attracting is the crucial thing for gas to liquid transition, while a repulsive potential energy at short distances is crucial for liquid to solid transition. Explain this important qualitative insight into the nature of phase transitions (Read section 9.3) (c) give an example of an unusual phase of matter in nature, which arises due to the highly non- spherical shape of its molecules. Q.28 Four in identical hollow cylindrical columns of steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the to distribution to be uniform, calculate the compressional strain of each column. The Young’s modulus of steel is 2.0 x 1011 Pa ( 1 Pa = 1 N m-2). Q.29 Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.25, are used to investigate behavior of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.5 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil ? Q.30 A composite wire of uniform diameter 3.0 mm consists of a copper wire of length 2.2 m and a steel wire of length 1.6 m stretches under a load by 0.7 mm. Calculate is 2.0 x 1011 Pa (1 Pa = 1 N m-2 ). Diamond cones Metal gasket Q.31 (a) You have discovered in Exercises 9.1 and 9.2 the ‘law of constant proportions’ and the ‘low of multiple proportions’. Which of these two laws in your view suggests the atomic hypothesis ? Explain carefully. (b) Would you regard Dalton’s atomic hypothesis a fundamental improvement over the atomic views of ancient Indians and Greeks ? Justify your answer.