IIT-JEE Part Test – 1 (Paper-I)

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CHEMISTRY

SECTION – I Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

1. Y g of non - volatile organic substance of molecular mass M is dissolved in 250 g benzene. Molal elevation constant of benzene is Kb. Elevation in its boiling point is given by

(A)b

M

K Y (B) b4K Y

M (C) bK Y

4M (D) bK Y

M

2. 20 g of a binary electrolyte (mol.wt. = 100) are dissolved in 500 g of water. The freezing point of the solution is –0.74°C, Kf = 1.86 K. molality–1. The degree of ionisation of the electrolyte is

(A) 50% (B) 75% (C) 100% (D) 0 3. The values of observed and calculated molecular weights of silver nitrate are 92.64 and 170

respectively. The degree of dissociation of silver nitrate is (A) 60% (B) 83.5% (C) 46.7% (D) 60.23% 4. Vapour density of PCl5(g) dissociating into PCl3(g) and Cl2(g) is 100. Hence, van’t Hoff factor for

the case: 5 3 2( ) ( ) ( )+��⇀↽��PCl g PCl g Cl g is

(A) 1.85 (B) 3.70 (C) 1.085 (D) 1.0425 5. 1.0 molal aqueous solution of an electrolyte X3Y2 is 25% ionized. The boiling point of the

solution is (Kb for H2O = 0.52 K kg/mol) (A) 375.5 K (B) 374.04 K (C) 377.12 K (D) 373.25 K 6. Xenon crystallizes in fcc lattice and the edge of the unit cell is 620 pm, then the radius of xenon

atom is (A) 438.5 pm (B) 219.25 pm (C) 536.94 pm (D) 265.5 pm 7. Potassium crystallizes in a body centred cubic lattice. What is the approximate number of until

cells in 4.0 g of potassium? Atomic mass of potassium = 39. (A) 3.09 × 1022 (B) 3.89 × 1023 (C) 3.09 × 1010 (D) None of these 8. When heated above 916°C, iron changes its crystal structure from bcc to ccp structure without any

change in the radius of atom. The ratio of density of the crystal before heating and after heating is (A) 1.089 (B) 0.918 (C) 0.725 (D) 1.231

SECTION – II Multiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct.

9. Select the correct statements:

(A) For CsCl unit cell (edge-length = a), rc + ra = 3

a2

(B) For NaCl unit cell (edge-length =� ), rc + ra = 2

�

(C) The void space in a b.c.c. unit cell is 0.68 (D) The void space % in a face-centered unit cell is 26%

IIT-JEE Part Test – 1 (Paper-I)

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10. Hexagonal closest-packed structure and a cubic closest-packed structure for a given element would be expected to have

(A) the same co-ordination number (CN) (B) the same packing fraction (C) different co-ordination number (D) different packing fraction 11. Select the correct statements (A) In closest packing of x-atoms, there are 2x tetrahedral holes, & x-octahedral holes (B) If anion B constitutes ccp and all the octahedral voids are occupied by cation (A), the crystal

has the same molecular formula AB, if the cation (A) occupies the alternate tetrahedral voids (C) In Schottky defects, density of the lattice decreases (D) None of these 12. According to Raoult’s law the relative decrease in the solvent vapour pressure over the solution is

not equal to (A) the mole fraction of the solvent (B) the mole fraction of solute (C) the number of moles of solute (D) all of these 13. Glasses and plastics are: (A) amorphous solids (B) supercooled liquids (C) isotropic (D) ferromagnetic

SECTION – III Comprehension Type

This section contains 2 groups of questions. Each group has 2 & 3 multiple choice questions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Questions Nos. 14 to 15

A spinel is an important class of oxides consisting of two types of metal ions with the oxide ions arranged in ccp layers. The normal spinel has one eighth of the tetrahedral holes occupied by one type of metal ion and one half of the octahedral holes occupied by another type of metal ion. Such a spinel is formed by Zn2+. Al3+ and O2–. The neutrality of the crystal being maintained.

14. The formula of the spinel is

(A) ZnAl2O4 (B) Zn2AlO4

(C) both (A) and (B) (D) None of these

15. Types of hole occupied by Zn2+ ion is

(A) octahedral (B) tetrahedral

(C) both (A) and (B) (D) None of these

Paragraph for Questions Nos. 16 to 18

The vapour pressure of a solvent in a solution is lower than that of pure solvent, at the same

temperature. A higher temperature is needed to raise the vapour pressure up to the atmospheric pressure, when boiling begins. However, increase is small, like 0.1 mol kg–1 aqueous sucrose solution boils at 100.05°C.

Sea water, an aqueous solution, which is rich in Na+ and Cl– ions, freezes at about 1°C lower than frozen water. At the freezing point of a pure solvent, the rates at which two molecules stick together to form the solid and leave it to return to liquid state are equal when solute is present.

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Fewer solvent molecules are in contact with surface of solid. However, the rate at which the solvent molecules leave the surface of solid remains unchanged. That is why temperature is lowered to restore the equilibrium. The freezing point depression in an ideal solution is proportional to molality of the solute.

16. An aqueous solution of 0.1 mol kg–1 concentration of sucrose should have freezing point of (approx) (Given : Kf = 1.86)

(A) – 0.2°C (B) 0.2°C (C) 2°C (D) – 2°C 17. When 250 mg of eugenol is added to 100 gm of camphor (Kf = 39.7), it lowered the freezing point

by 0.62°C. The molar mass of eugenol is (A) 1.6 × 102 gm/mole (B) 1.6 × 104 gm/mole (C) 1.6 × 103 gm/mole (D) 200 gm/mole 18. The freezing point of a 5 % by mass CH3COOH (aq.) solution is –1.576°C. The van’t Hoff factor

is (Kf of water = 1.86) (A) 0.97 (B) 2 (C) 0.5 (D) none of the above

SECTION – IV Integer Answer Type

This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following:

19. The coordination number of each atom in bcc is ________

20. The number of molecules in a unit cell of fluorite is ________

21. If effective number of particle along any body diagonal of unit cell in some cubical arrangement is 0.25 and along any face diagonal is 0.75. Find the effective number of particles per unit cell.

22. A very small amount of non-volatile solute (that does not dissociate) is dissolved in 56.8 cm3 of benzene (density 0.889gcm–3). At room temperature, the vapour pressure of this solution is 99.88 mm Hg while that of benzene is 100mm Hg. Find the molality of this solution. If the freezing temperature of this solution is 0.73 degree lower than that of benzene. What is the approximate value of molal freezing point depression constant of benzene in K ?

23. Analysis shows that nickel oxide has the formula Ni0.98O. What fraction of the nickel exist as Ni3+ ions in % ?

24. Copper crystal has a face centred cubic structure. Atomic radius of copper atom is 128 pm. What is the approximate value of density of copper metal? Atomic mass of copper is 63.5.

25. A mixture of two immiscible liquids nitrobenzene & water boiling at 99°C has a partial vapour pressure of water 733 mm & that of nitrobenzene 27 mm. The ratio of the weights of nitrobenzene to the water in the distillate is __________

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26. Depression of freezing point of 0.01 molal aq. CH3COOH solutions is 0.02046°. 1 molal urea solution freezes at –1.86°C. Assuming molality equal to molarity, pH of CH3COOH solution is ________

27. 2.56 gm of sulphur in 100 gm of CS2 has depression in F.P. of 0.010°, Kf = 0.1° (molal)–1. Hence atomicity of sulphur in CS2 is _________

28. At 300 K, the vapour pressure of an ideal solution containing 1 moles of A and 3 moles of B in 5.5 dm of Hg. At same temp, if one mole of B is added to this solution, the vapour pressure of solution is increased by 0.1 dm of Hg. Find VP of B in pure state.

MATHEMATICS

SECTION – I Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

29. Consider the straight line ax + by = c where a, b, c ∈ R+. This line meets the coordinate axes at 'P' and 'Q' respectively. If the area of triangle OPQ, 'O' being origin, does not depend upon a, b and c, then (A) a, b, c are in G.P. (B) a, c, b are in G.P.

(C) a, b, c are in A.P. (D) a, c, b are in A.P. 30. A light ray emerging from the point source placed at P(2, 3) is reflected at a point 'Q' on the

y–axis and then passes through the point R(5, 10). Coordinate of 'Q' is (A) (0, 3) (B) (0, 2) (C) (0, 5) (D) none of these 31. The axes being inclined at an angle of 60o, the angle between the two straight lines 2 5y x= + and

2 7 0y x+ + = is

(A) 90o (B) ( )–1tan 5 / 3 (C) ( )–1tan 3 / 2 (D) ( )–1tan 5 / 3

32. If the circle (x – a)2 + y2 = 25 intersect the circle x2 + (y – b)2 = 16 in such a way that common chord is of maximum length, then value of a2 + b2 is

(A) 8 (B) 10 (C) 9 (D) 41 33. If the circle x2 + y2 + ax + c = 0 lies inside the circle x2 + y2 + bx + c = 0 then (A) ab < 0, c > 0 (B) ab < 0, c < 0 (C) ab > 0, c > 0 (D) ab > 0, c < 0

34. If the distance from the origin to the centres of the three circles x2 + y2 – 2λi x = c2, (i = 1, 2, 3) are in G.P., then the lengths of the tangents drawn to them from any point on the circle x2 + y2 = c2 are in

(A) A.P. (B) G.P. (C) H.P. (D) None of these 35. The equation of the line which is reflection of the line PQ, where P is (1, 2) and Q (6, 3), on the

line 2x + 3y + 5 = 0 is (A) y + 5x – 19 = 0 (B) x – 5y + 19 = 0 (C) y + 5x + 19 = 0 (D) x + 5y – 19 = 0 36. If two lines represented by the equation ax3 + bx2y + cxy2 + dy3 = 0 are at right angles then

a2 + d2 + ac + bd is equal to (A) –1 (B) 0 (C) 1 (D) ab + cd

IIT-JEE Part Test – 1 (Paper-I)

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SECTION – II Multiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct.

37. In an acute triangle ABC, if the coordinates of orthocentre 'H' are (4, b), centroid 'G' are (b, 2b – 8) and circumcentre 'S' are (– 4, 8), then 'b' can not be

(A) 4 (B) 8 (C) 12 (D) – 12 38. Let the algebraic sum of the perpendicular distances from the points A(2, 0), B(0, 2), C(1, 1) to a

variable line be zero. Then all such lines (A) are concurrent (B) passes through a fixed point (1, 2) (C) touches some fixed circle (D) passes through a fixed point (1, 1) 39. Equation of a straight line passing through the point (4, 5) and equally inclined to the lines

3x = 4y + 7 and 5y = 12x + 6 is (A) 9x – 7y = 1 (B) 9x + 7y = 71 (C) 7x + 9y = 73 (D) 7x – 9y + 17 = 0 40. Tangents drawn from the point (α, α2) to the curve x2 + 3y2 = 9 include an acute angle between

them if α is equal to

(A) tan 4 (B) cosec 1

3

(C)1

ee

+ (D) 1

22

+

41. A line which makes an acute angle θ with the positive direction of x-axis is drawn the point A (4, 3) to meet the line x = 8 at B and y = 6 at C, then

(A) AB = 4 sec θ (B) AC = 3 cosec θ

(C) ( ) ( )2 2

16 91

AB AC+ = (D)

( )2 4sin 3cosAB AC

sin 2

θ + θ+ =

θ

SECTION – III Comprehension Type

This section contains 2 groups of questions. Each group has 2 & 3 multiple choice questions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Question Nos. 42 to 43

Consider a triangle PQR with coordinates of its vertices as P(–8, 5); Q(–15, –19) and R(1, –7). The bisector of the interior angle of P has the equation which can be written in the form ax + 2y + c = 0.

42. The distance between the orthocenter and the circumcentre of the triangle PQR is (A) 25/2 (B) 29/2 (C) 37/2 (D) 51/2 43. Radius of the incircle of the triangle PQR is (A) 4 (B) 5 (C) 6 (D) 8

Paragraph for Question Nos. 44 to 46

A circle C whose radius is 1 unit, touches x-axis at point A. The centre Q of C lies in first quadrant. The tangent from origin O to the circle touches it at T and a point P lies on it such that ∆OAP is a right-angled triangle at A and its perimeter is 8 units.

44. The length of PQ is

(A) 1

2 (B)

4

3 (C)

5

3 (D) None of these

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45. Equation of circle C is

(A) ( ){ } ( )2 2

– 2 3 –1 1x y+ + = (B) ( ){ } ( )2 2

– 3 – 2 –1 1x y+ =

(C) ( ) ( )2 2

– 3 –1 1x y+ = (D) None of these

46. Equation of tangent OT is

(A) – 3 0x y = (B) – 2 0x y = (C) – 3 0y x = (D) None of these

SECTION – IV Integer Answer Type

This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following:

47. A variable line through the point (6/5, 6/5) cuts the co–ordinate axes at the points A and B. If the point P divides AB internally in the ratio 2 : 1, given that the locus of P is 5xy = t(2x + y), find the value of t.

48. The area of the region in the x-y plane defined by [x]2 + [y]2 = 5 is ________ sq. units. 49. Secants are drawn from the point P(–1, 3) to the curve x2 + y2 – 2x + 4y – 8 = 0, which meets the

circle at A and B. The minimum value of PA + PB is _________ 50. The number of common tangents that can be drawn to the circle x2 + y2 – 4x – 6y – 3 = 0 and

x2 + y2 + 2x + 2y + 1 = 0 is ________ 51. The minimum distance of 4x2 + y2 + 4x – 4y + 5 = 0 from the line – 4x + 3y = 3 is _______ 52. The sides of a triangle have the combined equation x2 – 3y2 – 2xy + 8y – 4 = 0. The third side,

which is variable always passes through the point (–5, –1). If the range of values of the slope of the third line so that the origin is an interior point of the triangle, lies in the interval (a, b) then

find 2

1a

(5b)

+

.

53. If the equation of the line(s) through the point of intersection of the lines x – 3y + 1 = 0,

2x + 5y – 9 = 0 and whose distance from the origin is 5 is 2x + y = k, then k equals

54. C1 is a circle with centre at the origin and radius equal to r and C2 is a circle with centre at (3r, 0) and radius equal to 2r. The number of common tangents that can be drawn to the two circles are

55. The circle x2 + y2 + 4x – 7y + 12 = 0 cuts an intercept on y-axis of length ____

56. If the line 0y x+ = bisects two chords drawn form point 1 2 1– 2

,2 2

a a +

to the circle

( )2 22 2 – 1 2x y a x+ + ( )– 1– 2 0,a y = then lies in the interval ( ) ( )– ,– ,∞ λ ∪ λ ∞ the

numerical quantity λ should be equal to _____

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PHYSICS

SECTION – I Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

57. Figure (Five straight lines numbered 1, 2, 3, 4 and 5) shows graph of change in temperature ∆T versus heat supplied Q for different processes performed on a gas of one mole.

(i) line 4 and 5 (coinciding with Q and ∆T axis respectively) represent isothermal and adiabatic processes respectively

(ii) line 2 represents isochoric process for diatomic gas (iii) line 1 and 3 represent isobaric process for a diatomic gas

and isochoric process for a monoatomic gas respectively

(iv) line 2 represents isobaric process for a monoatomic gas. Correct answers are (A) (i), (ii), (iii) (B) (ii), (iii), (iv) (C) (i) and (iv) (D) (i), (ii), (iii), (iv)

58. A rod of length 40 cm has the coefficient of linear expansion α1 = 6 × 10−6/°C. Another rod of length l has the coefficient of linear expansion α2 = 4 × 10−6/°C. If the difference in the lengths of the two rods always remain same at all temperatures, then the value of l is

(A) 26 cm (B) 60 cm (C) 80 cm (D) 32 cm 59. The heat (Q) supplied to a solid, which is otherwise thermally isolated from its surroundings, is

plotted as a function of its absolute temperature, θ. It is found that they are related by the equation, Q = aθ2 + bθ4. (a, b are constants). The heat capacity of the solid is given by

(A) 3 5

3 5a b

θ θ+ (B) 3a bθ + θ

(C) 3

3 5a b

θ θ+ (D) 32 4a bθ + θ

60. An ideal gas undergoes a thermodynamics cycle as shown in figure. Which of the following graphs represents the same cycle ?

(A) (B)

(C)

(D)

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61. The figure, shows the graph of logarithmic reading of pressure and volume for two ideal gases A and B undergoing adiabatic process. From figure it can be concluded that

(A) gas B is diatomic (B) gas A and B both are diatomic (C) gas A is monoatomic

(D) gas B is monoatomic & gas A is diatomic

62. Three bodies A, B and C of masses m, m and3 m respectively are supplied heat at a constant rate. The change in temperature θ versus time t graph for A, B and C are shown by I, II, and III respectively. If their specific heat capacities are SA, SB and SC respectively then which of the following relation is correct ? (Initial temperature of body is 0°C)

(A) SA > SB > SC (B) SB = SC < SA (C) SA = SB = SC (D) SB = SC > SA 63. Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at

300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is.

(A) 30 K (B) 18 K (C) 50 K (D) 42 K

64. The two ends of a uniformly tapered rod are maintained at temperatures 100oC and 0oC respectively. Under steady state, the temperature of the section AA′ exactly at the mid point

(A) is 50oC (B) is more than 50oC

(C) is less than 50oC (D) none of these

SECTION – II Multiple Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct.

65. A 100 cm long cylindrical flask with inner and outer diameters 2 cm and 4 cm respectively is completely filled with ice as shown in the figure. The constant temperature outside the flask is 40oC. (Thermal conductivity of the flask is 0.693 W/moC, Lice = 80 cal/gm), then

(A) Rate of heat flow from outside to the flask is 80π J/s

(B) The rate at which ice melts is Kg / s4200

π

(C) The rate at which ice melts is 100π Kg/s (D) Rate of heat flow from outside to flask is 40π J/s.

66. An ideal gas is heated from temperature T1 to T2 under various conditions. The correct statement(s) is/are

(A) ∆ U = nCv(T2 − T1) for isobaric, isochoric and adiabatic process (B) work is done at expense of internal energy in an adiabatic process and both have equal values (C) ∆ U = 0 for an isothermal process (D) C = 0 for an adiabatic process

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67. A gaseous mixture consists of 8 g of oxygen and 20 g of argon. The gases are assumed to be ideal. Then ( given molecular weight of argon is 40 and R = 8.3 J/mol − K)

(A) γ of the gas mixture is 1.55 (B) Cv of the gas mixture is 15.2 J mol−1 K−1 (C) Cp of the gas mixture is 23.56 J mol−1 K−1 (D) None of the above are correct

68. A system of n moles of an ideal gas is taken through the process 1-2-3-4-1. If ∆U, W, Q represents change in internal energy, work done by the system and heat supplied to the system respectively, then

(A) |∆u|1−2−3 > |∆u|4−1 (B) |W|1−2−3 < |W|4−1 (C) volume at 4 is greater than volume at 2.

(D) If temperature at 1, 2 and 3 are T0, 4T0 and 9T0 respectively, Q for the cyclic process is 9.6nRT0

69. The two ends of a uniform rod of thermal conductivity k are maintained at different but constant

temperatures. The temperature gradient at any point on the rod is .ddlθ

The heat flow per unit time

per unit cross section of the rod is I. Then

(A) ddlθ

is same for all points on the rod

(B) I will decrease as we move from higher to lower temperature

(C) d

I kdlθ=

(D) All the above options are incorrect

SECTION – III Comprehension Type

This section contains 2 groups of questions. Each group has 2 & 3 multiple choice questions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph for Questions Nos. 70 to 71

Radiation is the fastest method of transporting heat energy from a hot body. The radiations travel with a velocity of 3 × 108 ms−1. The radiation laws like Stefan’s law, Wein’s law exhibit a study of the same. The other modes of transfer of heat requires a medium. The temperature scale used in expressing such temperatures is Kelvin scale. Having a non-conducting medium between two surfaces may reduce the transfer of heat.

70. Two thin blankets are better than one thick blanket in controlling the effect of cold air since. (A) perforation in thick blanket will be bigger (B) perforation in thin blanket will be smaller (C) air between the thin blankets stops transfer of heat (D) thin blankets radiate more energy 71. Two spheres with emissive powers 0.6 and 0.8 of radii 2 cm and 4 cm are heated to temperatures

of 27°C and 157°C and placed at a room of absolute temperature 0 K. The ratio of heat radiated per second is

(A) 0.059 (B) 1.6 × 10−4 (C) 0.079 (D) 0.831

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Paragraph for Questions Nos. 72 to 74

A double-pane window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m2 and thickness 0.01 m separated by 0.05 m thick stagnant air space. In the steady state, the room-glass interface and the glass-outdoor interface are at constant temperatures of 27°C and 0°C respectively. The thermal conductivity of glass is 0.8 and of air 0.08 W m−1 K−1

72. The temperature of the outer glass-air interface is (A) 26.5°C (B) 25.5°C (C) 24.5°C (D) 23.5°C 73. The temperatures of the inner glass-air interface is (A) 2.5°C (B) 2.0°C (C) 1.5°C (D) 0.5°C 74. The rate of flow of heat through the window pane is nearly equal to (A) 1000 J s−1 (B) 2000 J s−1 (C) 3000 J s−1 (D) 4000 J s−1

SECTION – IV Integer Answer Type

This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following:

75. Two containers A and B are connected by a conducting solid cylindrical rod of length 242

7cm

and radius 8.3cm. Thermal conductivity of the rod is 693 watt/mole - K. The container A contains two mole of oxygen gas and the container B contains four mole of helium gas. At time t = 0 temperature difference of the containers is 50oC. After what time (in seconds) temperature difference between them will be 25oC. Transfer of heat takes place through the rod only. Neglect

radiation loss. Take R = 8.3 J/mole - K and 22

7π = .

76. A diatomic ideal gas is compressed adiabatically to 1

32 of its initial volume. If the initial

temperature of the gas is Ti (in Kelvin) and the final temperature is aTi, the value of a is 77. 600 J of heat is added to a monatomic gas in a process in which the gas performs a work of 150 J.

The molar heat capacity for the process is ____ R

78. A piece of ice (heat capacity = 2100 J kg−1°C–1 and latent heat = 3.36 ×105J kg−1) of mass m grams is at −5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

79. An ideal heat engine working between temperature T1 and T2 has an efficiency η, the new efficiency if both the source and sink temperature are doubled, well be _______ η.

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80. A slab of stone of area 0.34 m2 and thickness 10 cm is exposed on the lower face to steam at 100oC. A block of ice at 0oC rests on the upper face of the slab. In one hour, 3.6 kg of ice is melted. Assume that the heat loss from the sides is negligible. The latent heat of fusion of ice is 3.4 × 105 J kg−1. What is the thermal conductivity of the stone in units of Js−1 m−1oC−1 ?

81. A solid cube of side a, density d and specific heat s is at temperature 400K. It is placed in an ambient temperature at 200K.

Take : a = 0.9m, d = 4.8 × 103 kg/m3, s = 2.0 × 103 J/kg/K, Stefan's constant σ = 6 × 10−8 W/K4–m2. Consider the cube to be a black body. If the time for the temperature of the cube to drop by 5K is 1000X seconds, find X in nearest integer

82. For a thermodynamics system, the pressure volume & temperature are related as 2T

PV

α= ,

where α is a positive constant. The work done by this system in a constant pressure process, if the temperature changes from T0 to 2T0. is ______ 2

0Tα (The gas is non-ideal)

83. An ideal gas is taken through the cycle A → B → C → A, as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process C → A is negative of _____J.

84. A vessel contains 1 mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas is

P. An identical vessel containing one mole of the gas (molar mass 4) at a temperature 2T has a pressure of ________P.

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