A Carnot engine operates between two reservoirs of temperatures 900K and 300K.
Question: A Carnot engine operates between two reservoirs of temperatures $900 \mathrm{~K}$ and $300 \mathrm{~K}$. The engine performs 1200 $\mathrm{J}$ of work per cycle. The heat energy (in $\mathrm{J}$ ) delivered by the engine to the low temperature reservoir, in a cycle, is______ Solution: (600.00) Given; $T_{1}=900 K, T_{2}=300 K, W=1200 J$ Using, $1-\frac{T_{2}}{T_{1}}=\frac{W}{Q_{1}}$ $\Rightarrow 1-\frac{300}{900}=\frac{1200}{Q_{1}}$ $\Rightarrow \frac{2}{3}=\frac{1200}{Q_{1}} \Rightarr...
Read More →Prove that the line joining the points of contact of two parallel tangents of a circle passes through its centre
Question: Prove that the line joining the points of contact of two parallel tangents of a circle passes through its centre Solution: Suppose CD and AB are two parallel tangents of a circle with centre OConstruction: Draw a line parallel to CD passing through O i.e, OPWe know that the radius and tangent are perperpendular at their point of contact.OQC = ORA = 90∘Now, OQC + POQ = 180∘ (co-interior angles)⇒ POQ = 180∘ 90∘= 90∘Similarly, Now, ORA + POR = 180∘ (co-interior angles)⇒ POR = 180∘ 90∘= 90...
Read More →A golf ball has diameter equal to 4.2 cm.
Question: A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical. Solution: Surface area of ball $=4 \pi r^{2}$ $=4 \pi\left(\frac{4.2}{2}\right)^{2}$ $=17.64 \pi \mathrm{cm}^{2}$ Total surface area exposed $=\mathrm{SA}$ of ball $-200\left(\pi \mathrm{r}^{2}-\frac{4 \pi r^{2}}{2}\right)$ $=17.64 \pi-200 \pi r^{2}$ $=17.64 \pi-8 \pi$ $=80.5 \mathrm...
Read More →Write the free radical mechanism for
Question: Write the free radical mechanism for the polymerisation of ethene. Solution: Polymerization of ethene to polythene consists of heating or exposing to light a mixture of ethene with a small amount of benzoyl peroxide as the initiator. The reaction involved in this process is given below:...
Read More →PQ is a chord of length 4.8 cm of a circle of radius 3 cm.
Question: PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP Solution: Let TR =yand TP =xWe know that the perpendicular drawn from the centre to the chord bisects it. PR = RQNow, PR + RQ = 4.8⇒ PR + PR = 4.8⇒ PR = 2.4Now, in right triangle PORBy Using Pyhthagoras theorem, we havePO2= OR2+ PR2⇒ 32= OR2+ (2.4)2⇒ OR2= 3.24⇒ OR = 1.8Now, in right triangle TPRBy Using Pyhthagoras theorem, we haveTP2= T...
Read More →Explain the term copolymerisation
Question: Explain the term copolymerisation and give two examples. Solution: The process of forming polymers from two or more different monomeric units is called copolymerization. Multiple units of each monomer are present in a copolymer. The process of forming polymer BunaS from 1, 3-butadiene and styrene is an example of copolymerization Nylon 6, 6 is also a copolymer formed by hexamethylenediamine and adipic acid....
Read More →How can you differentiate between addition and condensation polymerisation?
Question: How can you differentiate between addition and condensation polymerisation? Solution: Addition polymerization is the process of repeated addition of monomers, possessing double or triple bonds to form polymers. For example, polythene is formed by addition polymerization of ethene. Condensation polymerization is the process of formation of polymers by repeated condensation reactions between two different bi-functional or tri-functional monomers. A small molecule such as water or hydroch...
Read More →A solid is in the form of a cylinder with hemispherical ends.
Question: A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. Solution: Volume of cylinder $=\pi r^{2} h$ $=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 12$ $=462 \mathrm{~cm}^{3}$ Volume of 2 hemisphere $=4 \pi r^{3}$ $=\frac{4}{3} \times \frac{22}{2} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}$ $=179.6 \mathrm{~cm}^{3}$ Therefore,...
Read More →In which classes,
Question: In which classes, the polymers are classified on the basis of molecular forces? Solution: On the basis of magnitude of intermolecular forces present in polymers, they are classified into the following groups: (i)Elastomers (ii)Fibres (iii)Thermoplastic polymers (iv)Thermosetting polymers...
Read More →An engine operates by taking a monatomic ideal gas through the cycle shown in the figure.
Question: An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close is Solution: From the figure, Work, $W=2 P_{0} V_{0}$ Heat given, $Q_{\text {in }}=W_{A B}+W_{B C}=n \cdot C_{V} \Delta T_{A B}+n C_{P} \Delta T_{B C}$ $=n \frac{3 R}{2}\left(T_{B}-T_{A}\right)+\frac{n 5 R}{2}\left(T_{C}-T_{B}\right)$ $\left(\because C_{v}=\frac{3 R}{2}\right.$ and $\left.C_{P}=\frac{5 R}{2}\right)$ $=\frac{3}{2}\left(P_{B} V_{B}-P_...
Read More →In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC
Question: In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D are, of lengths 6 cm and 9 cm respectively. If the area of △ABC = 54 cm2then find the lengths of sides of AB and AC. Solution: Construction: Join OA, OB, OC, OE AB at E and OF AC at F We know that tangent segments to a circle from the same external point are congruent.Now, we haveAE = AF, BD = BE = 6 cm and CD = CF = 9 ...
Read More →Solve the following
Question: Is, a homopolymer or copolymer? Solution: is a homopolymer because it is obtained from a single monomer unit, NH2CHRCOOH....
Read More →Define the term polymerisation.
Question: Define the term polymerisation. Solution: Polymerization is the process of forming high molecular mass (103 107u) macromolecules, which consist of repeating structural units derived from monomers. In a polymer, various monomer units are joined by strong covalent bonds....
Read More →Find the mass of a 3.5 m long lead pipe,
Question: Find the mass of a 3.5 m long lead pipe, if the external diameter of the pipe is 2.4 cm, thickness of the metal is 2 mm and the mass of 1 cm3of lead is 11.4 grams. Solution: Length of the pipe (h) = 3.5 cm = 300 cm External radius of the pipe $(R)=\frac{2.4}{2}=1.2 \mathrm{~cm}$ Thickness of pipe $=2 \mathrm{~mm}$ $=0.2 \mathrm{~cm}$ So internal radius of pipe $=1.2-0.2$ $=1 \mathrm{~cm}$ Thus volume of pipe $=\pi\left(R^{2}-r^{2}\right) h$ $=\frac{22}{7} \times\left((1.2)^{2}-1^{2}\ri...
Read More →How do you explain the functionality of a monomer?
Question: How do you explain the functionality of a monomer? Solution: The functionality of a monomer is the number of binding sites that is/are present in that monomer. For example, the functionality of monomers such as ethene and propene is one and that of 1, 3-butadiene and adipic acid is two....
Read More →Distinguish between the terms homopolymer and copolymer and give an example of each.
Question: Distinguish between the terms homopolymer and copolymer and give an example of each. Solution:...
Read More →What are natural and synthetic polymers?
Question: What are natural and synthetic polymers? Give two examples of each type. Solution: Natural polymers are polymers that are found in nature. They are formed by plants and animals. Examples include protein, cellulose, starch, etc. Synthetic polymers are polymers made by human beings. Examples include plastic (polythene), synthetic fibres (nylon 6, 6), synthetic rubbers (Buna S)....
Read More →A toy is in the form of a cone mounted on a hemisphere
Question: A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. Determine the surface area of the toy. (Use = 3.14) Solution: Radius of hemisphere and the cone are the same.So, r = 3 cmSurface area of the cone $=\pi r l$ $=3.14 \times 3 \times \sqrt{3^{2}+4^{2}}$ $=47.1 \mathrm{~cm}^{2}$ Surface area of the hemisphere $=2 \pi r^{2}$ $=2 \times 3.14 \times 9$ $=56.52 \mathrm{~cm}^{2}$ Total surf...
Read More →What are natural and synthetic polymers?
Question: What are natural and synthetic polymers? Give two examples of each type. Solution: Natural polymers are polymers that are found in nature. They are formed by plants and animals. Examples include protein, cellulose, starch, etc. Synthetic polymers are polymers made by human beings. Examples include plastic (polythene), synthetic fibres (nylon 6, 6), synthetic rubbers (Buna S)....
Read More →Explain the terms polymer and monomer.
Question: Explain the terms polymer and monomer. Solution: Polymers are high molecular mass macromolecules composed of repeating structural units derived from monomers. Polymers have a high molecular mass (103 107u). In a polymer, various monomer units are joined by strong covalent bonds. Polymers can be natural as well as synthetic. Polythene, rubber, and nylon 6, 6 are examples of polymers. Monomers are simple, reactive molecules that combine with each other in large numbers through covalent b...
Read More →Arrange the following polymers in increasing order of their intermolecular forces.
Question: Arrange the following polymers in increasing order of their intermolecular forces. (i)Nylon 6, 6, Buna-S, Polythene. (ii)Nylon 6, Neoprene, Polyvinyl chloride. Solution: Different types of polymers have different intermolecular forces of attraction. Elastomers or rubbers have the weakest while fibres have the strongest intermolecular forces of attraction. Plastics have intermediate intermolecular forces of attraction. Hence, the increasing order of the intermolecular forces of the give...
Read More →Three rods of identical cross-section and lengths are made of three different materials
Question: Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $\mathrm{K}_{1}, \mathrm{~K}_{2}$ and $\mathrm{K}_{3}$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100^{\circ} \mathrm{C}$ and the other at $0^{\circ} \mathrm{C}$ (see figure). If the joints of the rod are at $70^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ in steady state and there is no ...
Read More →A right angled triangle with sides 3 cm and 4 cm
Question: A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated. Solution: The double cone so formed is as in figure. Hypotenuse AC $=\sqrt{3^{2}+4^{2}}$ $=5 \mathrm{~cm} .$ Area of $=\frac{1}{3} \times \frac{22}{7} \times \frac{12}{5} \times \frac{12}{5} \times 5$ $=\frac{1056}{35}$ $=30 \frac{6}{35}$ $\triangle A B C=\frac{1}{2} \times A B \times A C$ $=\frac{1}{2} \times A C \times O B$ $=\frac{1}{2} \times 4 \tim...
Read More →Explain the difference between Buna-N and Buna-S.
Question: Explain the difference between Buna-N and Buna-S. Solution: Buna N is a copolymer of 1, 3butadiene and acrylonitrile. Buna S is a copolymer of 1, 3butadiene and styrene....
Read More →Classify the following as addition and condensation polymers:
Question: Classify the following as addition and condensation polymers: Terylene, Bakelite, Polyvinyl chloride, Polythene. Solution: Addition polymers: Polyvinyl chloride, polythene Condensation polymers: Terylene, bakelite...
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