Calorimetry And Thermal Expansion Multiple Choice Question And Answers
Question 31. A block of ice at -10ºC is slowly heated and converted to steam at 100ºC. Which of the following curves represent the phenomenon qualitatively:
Answer: 1.
Question 32. 540 g of ice at 0°C is mixed with 540g of water at 80°C. What is the final temperature of the mixture?
- 0°C
- 40°C
- 80°C
- 0°C
Answer: 1. 0°C
Question 33. The thermal capacity of anybody is :
- A measure of its capacity to absorb heat
- A measure of its capacity to provide heat
- The quantity of heat required to raise its temperature by a unit degree
- The quantity of heat required to raise the temperature of a unit mass of the body by a unit degree
Answer: 3. The quantity of heat required to raise its temperature by a unit degree
Question 34. The figure shows the pressure-temperature phase diagram for water, the curves corresponding to sublimation, fusion, and vaporization respectively are
- AO, OB, and OC
- BO, OC, and AO
- OC, BO, and AO
- AO, OC, and BO
Answer: 1. AO, OB and OC
Question 35. An electric kettle takes a 4A current at 220V. How much time will it take to boil 1 kg of water at a temperature of 20°C? The temperature of boiling water is 100°C:
- 6.3 min
- 8.4 min
- 12.6 min
- 4.2 min
Answer: 1. 6.3 min
Question 36. The time taken by an 836 W heater to heat one liter of water from 10ºC to 40ºC is :
- 50 s
- 100 s
- 150 s
- 200 s
Answer: 3. 150 s
Question 37. 2 liters of water at 27°C is heated by a 1 kW heater in an open container. On average heat is lost to surroundings at the rate of 160 J/s. The time required for the temperature to reach 77°C is
- 8 min 20 sec
- 10 min
- 7 min
- 14 min
Answer: 1. 8 min 20 sec
Question 38. A piece of ice (heat capacity = 2100 J kg-1ºC-1 and latent heat = 3.36 × 105 J kg-1) of mass m grams is at –5 ºC 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:
- 8 gm
- 5 gm
- 6 gm
- 10 gm
Answer: 1. 8 gm
Question 39. Two large holes are cut in a metal sheet. If this is heated, distances AB and BC, (as shown)
- Both will increase
- Both will decrease
- AB increases, BC decreases
- AB decreases, BC increases
Answer: 1. Both will increase
Question 40. A steel scale is to be prepared such that the millimeter intervals are to be accurate within 6 ×10-5 mm. The maximum temperature variation from the temperature of calibration during the reading of the millimeter marks is (α = 12 × 10-6 k-1)
- 4.0°C
- 4.5°C
- 5.0°C
- 5.5°C
Answer: 3. 5.0°C
Question 41. Expansion during heating –
- Occurs only in a solid
- Increases the density of the material
- Decreases the density of the material
- Occurs at the same rate for all liquids and solids.
Answer: 3. Decreases the density of the material
Question 42. If a bimetallic strip is heated, it will.
- Bend towards the metal with a lower thermal expansion coefficient.
- Bend towards the metal with a higher thermal expansion coefficient.
- Twist itself into a helix.
- Have no bending.
Answer: 1. Bend towards the metal with a lower thermal expansion coefficient.
Question 43. Two holes of unequal diameters d1 and d2(d1 > d2) are cut in a metal sheet. If the sheet is heated-
- Both d1and d2 will decrease
- Both d1 and d2 will increase
- d1 will increase d2 will decrease
- d1 will decrease, d2 will increase
Answer: 2. Both d1 and d2 will increase
Question 44. Two bars of copper having the same length but unequal diameter are heated to the same temperature. The change in length will be –
- More in thinner bar
- More in thicker bar
- Same for both the bars
- Determined by the ratio of length and diameter of the bars
Answer: 3. Same for both the bars
Question 45. A metallic bar is heated from 0ºC to 100ºC. The coefficient of linear expansion is 10-5K-1. What will be the percentage increase in length
- 0.01%
- 0.1%
- 1%
- 10%
Answer: 2. 0.1%
Question 46. A pendulum clock has an iron pendulum 1m long (αiron = 10-5/ºC). If the temperature rises by 10ºC, the clock-
- Will lose 8 seconds per day
- Will lose 4.32 seconds per day
- Will gain 8 seconds per day
- Will gain 4.32 seconds per day
Answer: 2. Will lose 4.32 seconds per day
Question 47. Two rods of lengths l1and l2 are made of materials whose coefficient of linear expansions is α1 are α2. If the difference between two lengths is independent of temperature –
- \(\frac{\ell_1}{\ell_2}=\frac{\alpha_1}{\alpha_2}\)
- \(\frac{\ell_1}{\ell_2}=\frac{\alpha_2}{\alpha_1}\)
- \(\ell_2^2 \alpha_1=\ell_1^2 \alpha_2\)
- \(\frac{\alpha_1^2}{\ell_1}=\frac{\alpha_2^2}{\ell_2}\)
Answer: 2. \(\frac{\ell_1}{\ell_2}=\frac{\alpha_2}{\alpha_1}\)
Question 48. If α, β, γ are respectively the linear, superficial and cubical expansivity of a homogeneous solid, then –
- α : β : γ = 1 : 2 : 3
- α : β : γ = 3 : 2 : 1
- α : β : γ = 2 : 3 : 1
- α : β : γ = 3 : 1 : 3
Answer: 1. α : β : γ = 1 : 2 : 3
Question 49. The coefficient of linear expansion of steel and brass are 11 × 10-6/ºC and 19 × 10-6/ºC respectively. If their difference in lengths at all temperatures has to be kept constant at 30cm, their lengths at 0ºC should be –
- 71.25 cm and 41.25 cm
- 82 cm and 52 cm
- 92 cm and 62 cm
- 62.25 cm and 32.25 cm
Answer: 1. 71.25 cm and 41.25 cm
Question 50. A solid ball of metal has a spherical cavity inside it. If the ball is heated, the volume of the cavity will –
- Increase
- Decrease
- Remains unchanged
- Have its shape changed
Answer: 1. Increase
Question 51. If the length of a cylinder on heating increases by 2%, the area of its base will increase by
- 0.5%
- 2%
- 1%
- 4%
Answer: 4. 4%
Question 52. A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10ºC, and the coefficient of linear expansion of the metal of the rod is 2 × 10-6 perºC, the period of the pendulum will have a percentage increase of –
- – 2 × 10-3
- – 1 × 10-3
- 2 × 10-3
- 1 × 10-3
Answer: 4. 1 × 10-3
Question 53. The volume of a solid decreases by 0.6% when it is cooled to 50ºC. Its coefficient of linear expansion is –
- 4 × 10-6K
- 5 × 10-5K
- 6 × 104K
- 4 × 10-5K
Answer: 4. 4 × 10-5K
Question 54. Which of the following graphs represents variation in density of water with temperature best –
Answer: 4.
Question 55. A rectangular block is heated from 0ºC to 100ºC. The percentage increase in its length is 0.10% What will be the percentage increase in its volume?
- 0.03 %
- 0.10%
- 0.30%
- None of these
Answer: 3. 0.30%
Question 56. A thin copper wire of length l increases in length by 1% when heated from 0ºC to 100ºC. If a then cooper plate of area 2l × l is heated from 0ºC to 100ºC, the percentage increase in its area will be
- 1%
- 2%
- 3%
- 4%
Answer: 2. 2%
Question 57. If Ι is the moment of inertia of a solid body having α -coefficient of linear expansion then the change in Ι corresponding to a small change in temperature ΔT is
- \(\frac{1}{2}\) α Ι ΔT
- 2α Ι ΔT
- 2 α Ι ΔT
- 3 α Ι ΔT
Answer: 3. 2 α Ι ΔT
Question 58. A liquid with a coefficient of volume expansion γ is filled in a container of a material having the coefficient of linear expansion α .Ιf the liquid overflows on heating, then.
- γ > 3α
- γ < 3α
- γ = 3α
- None of these
Answer: 1. γ > 3α
Question 59. Two rods having lengths l1 and l2, made of materials with the linear expansion coefficient α1 and α2, were soldered together. The equivalent coefficients of linear expansion for the obtained rod:-
⇒ \(\frac{\ell_1 \alpha_2+\ell_2 \alpha_1}{\ell_1+\ell_2}\)
⇒ \(\frac{\alpha_1 \alpha_2}{\alpha_1+\alpha_2}\)
⇒ \(\frac{\ell_1 \alpha_1+\ell_2 \alpha_2}{\ell_1+\ell_2}\)
⇒ \(\frac{\left(\alpha_1+\alpha_2\right)}{2}\)
Answer: 3. \(\frac{\ell_1 \alpha_1+\ell_2 \alpha_2}{\ell_1+\ell_2}\)
Question 60. The volume thermal expansion coefficient of an ideal gas at constant pressure and temperature TK is
- T
- T2
- \(\frac{1}{\mathrm{~T}}\)
- \(\frac{1}{\mathrm{~T}^2}\)
Answer: 3. 1T
Question 61. A metallic ball and a highly stretched spring are made of the same material and have the same mass. They are heated so that they melt, the latent heat required
- Are the same for both
- Is greater for the ball
- Is greater for the spring
- The two may or may not be the same depending on the metal
Answer: 1. Are the same for both
Question 62. The coefficients of linear expansions of brass and steel are α1 and α2 respectively. When we take a brass rod of length l1 and a steel rod of length l2 at 0°C, then the difference in their lengths (l2– l1) will remain the same at all temperatures if :
- α1l1= α2l2
- α1l2= α2l1
- α12l2= α22l1
- α1l22 = α2 l12
Answer: 1. α1l1= α2l2
Question 63. If on heating liquid through 80ºC, the mass expelled is (1/100) th of mass still remaining, the coefficient of apparent expansion of liquid is:
- 1.25 × 10-4/ºC
- 12.5 × 10-4/ºC
- 1.25 × 10-5/ºC
- None of these
Answer: 1. 1.25 × 10-4/ºC
Question 64. An iron bar of length l and having a cross-section A is heated from 0 to 100ºC. If this bar is so held that it is not permitted to expand or bend, the force that is developed is:
- Inversely proportional to the cross-sectional area of the bar
- Independent of the length of the bar
- Inversely proportional to the length of the bar
- Directly proportional to the length of the bar
Answer: 2. Independent of the length of the bar
Question 65. If the sphere of iron is heated, then its
- Density increases
- Volume increases
- Radius decreases
- None of these
Answer: 2. Volume increases
Question 66. Two rods, one of aluminum of length l1 having a coefficient of linear expansion αaand the other of steel having a coefficient of linear expansion αs and length l2 are joined end to end. The expansion in both the rods is the same for the same variation of temperature. Then the value of \(\frac{\ell_1}{\ell_1+\ell_2}\)
Answer:
- \(\frac{\alpha_{\mathrm{s}}}{\alpha_{\mathrm{a}}}\)
- \(\frac{\alpha_{\mathrm{a}}}{\alpha_{\mathrm{s}}}\)
- \(\frac{\alpha_s}{\alpha_a+\alpha_s}\)
- \(\frac{\alpha_a}{\alpha_a+\alpha_s}\)
Answer: 3. \(\frac{\alpha_s}{\alpha_a+\alpha_s}\)
Question 67. A difference in temperature of 25º C is equivalent to a difference in franchise:
- 45º F
- 72º F
- 32º F
- 25º F
Answer: 1. 45º F
Question 68. What is the temperature at which we get the same reading on both the centigrade and Fahrenheit scales?
- – 40ºC or – 40ºF
- – 30ºC or – 30º F
- – 30ºC or – 40ºF
- – 10ºC or – 10ºF
Answer: 1. – 40ºC or – 40ºF
Question 69. Absolute temperature can be calculated by
- Mean square velocity of molecules
- Motion of the molecule
- Both (a) and (b)
- None of the above
Answer: 1. Mean square velocity of molecules
Question 70. The absolute zero is the temperature at which
- Water freezes
- All substances exist in a solid state
- Molecular motion ceases
- None of the above
Answer: 3. Molecular motion ceases
Question 71. Absolute zero (0K) is the temperature at which
- Matter ceases to exist
- Ice melts and water freezes
- The volume and pressure of a gas become zero
- None to these
Answer: 3. The Volume and pressure of gas become zero
Question 72. The temperature on the Celsius scale is 25°C. What is the corresponding temperature on the Fahrenheit scale
- 40°F
- 77°F
- 50°F
- 45°F
Answer: 2. 77°F
Question 73. Two thermometers are used to record the temperature of a room. If the bulb of one is wrapped in a wet hanky
- The temperature recorded by both will be the same
- The temperature recorded by the wet-bulb thermometer will be greater than that recorded by the other
- The temperature recorded by the dry-bulb thermometer will be greater than that recorded by the other
- None of the above
Answer: 3. The temperature recorded by dry-bulb thermometer will be greater than that recorded by the other
Question 74. A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 140°F. What is the fall in temperature as registered by the Centigrade thermometer
- 30°
- 40°
- 60°
- 80°
Answer: 2. 40°
Question 75. A 5°C rise in temperature is observed in a conductor by passing a current. When the current has doubled the rise in temperature will be approximately:
- 16°C
- 10°C
- 20°C
- 12°C
Answer: 3. 20°C
Question 76. Value of – 40ºC in Fahrenheit scale is:
- –40º F
- 32°F
- –32ºF
- 40ºC
Answer: 1. –40º F
Question 77. If temperature of an object is 140º F, then its temperature in centrigrade is :
- 105ºC
- 32ºC
- 140°C
- 60ºC
Answer: 4. 60ºC
Question 78. The color of a star indicates its :
- Temperature
- Distance
- Velocity
- Size
Answer: 1. Temperature
Question 79. The temperature of a body on a kelvin scale is found to be x K. When it is measured by Fahrenheit thermometer, it is found to be x°F, then the value of x is:
- 30
- 313
- 574.25
- 301.25
Answer: 3. 574.25
Question 80. A constant pressure thermometer when immersed in ice-cooled water gives a volume reading of 47.5 units and when immersed in boiling liquid, it gives a reading of 67 units. What is the boiling point of the liquid?
- 135°C
- 125°C
- 112°C
- 100°C
Answer: 3. 112°C
Question 81. A beaker is completely filled with water at 4°C. The water will overflow if it is :
- Warmed to a temperature greater than 4°C
- Cooled to a temperature less than 4°C
- and both
- None of the above
Answer: 3. and both
Question 82. On a new scale of temperature (which is linear) called the W scale, the freezing and boiling points of water are 39°W and 239°W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale?
- 78°C
- 117°W
- 200°W
- 139°W
Answer: 2. 117°W
Question 83. A thermally isolated vessel contains 100 g of water at 0ºC. When air above the water is pumped out, some of the water freezes and some evaporates at 0ºC itself. Then the mass of the ice formed if no water is left in the vessel. Latent heat of vaporization of water at 0ºC = 2.10 × 106 J/kg and latent heat of fusion of ice = 3.36 × 105J/kg.
- 86.2 g
- 13.8 g
- 76.2 g
- 65.6 g
Answer: 1. 86.2 g
Question 84. 2 kg ice at – 20 ºC is mixed with 5 kg water at 20 ºC. The final amount of water in the mixture would be : Given: specific heat of ice = 0.5 cal/g ºC, specific heat of water = 1 cal/g ºC, latent heat of fusion of ice = 80 cal/gm ]
- 6 kg
- 7 kg
- 3.5 kg
- 5 kg
Answer: 1. 6 kg
Question 85. In an insulated vessel, 0.05 kg of steam at 373 K and 0.45 kg of ice at 253 K are mixed. Find the final temperature of the mixture (in Kelvin).
Given, Lfusion = 80 cal/gm = 336 J/gm, Lvaporization = 540 cal/gm = 2268 J/gm,
Sice = 2100 J/kg K = 0.5 cal/gm K and Swater = 4200 J/kg K = 1 cal/gmK
- 273 K.
- 373 K
- 300 K
- 253 K
Answer: 1. 273 K.
Question 86. The weight of a person is 60 kg. If he gets 105 calories heated through food and the efficiency of his body is 28%, then upto how much height he can climb when he user entire energy gained is climbing
- 100 m
- 200 m
- 400 m
- 1000 m
Answer: 2. 200 m
Question 87. When a block of iron floats in mercury at 0°C a fraction k1 of its volume is submerged, while at the temperature 60ºC, a fraction k2 is seen to be submerged. If the coefficient of volume expansion of iron is γFe, then the ratio \(\frac{k_1}{k_2}\)
- \(\frac{1+60 \gamma_{\mathrm{Fe}}}{1+60 \gamma_{\mathrm{Hg}}}\)
- \(\frac{1-60 \gamma_{\mathrm{Fe}}}{1+60 \gamma_{\mathrm{Hg}}}\)
- \(\frac{1+60 \gamma_{\mathrm{Fe}}}{1-60 \gamma_{\mathrm{Hg}}}\)
- \(\frac{1+60 \gamma_{\mathrm{Hg}}}{1+60 \gamma_{\mathrm{Fe}}}\)
Answer: 1. \(\frac{1+60 \gamma_{\mathrm{Fe}}}{1+60 \gamma_{\mathrm{Hg}}}\)
Question 88. A hot wire of copper is stretched at a temperature of 150ºC between two fixed walls. At what temperature will the wire break when it is cooled? The breaking stress of copper is 2.45 × 108 N/m2 Young’s modulus of copper = 11.8 × 1010 N/m2, coefficient of linear expansion of copper = 1.6 ×10-5/ºC.
- 20.2ºC
- 43.2ºC
- 64.9ºC
- 70.2ºC
Answer: 1. 20.2ºC
Question 89. Liquid oxygen at 50K is heated to 300 K at a constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?
Answer: 1.
Question 90. Steam at 1000C is passed into 20g of water at 100C. When water acquires a temperature of 800C, the mass of water present will be:
[Take specific heat of water = 1 cal g-1 °C-1 and latent heat of steam = 540 cal g-1]
- 24 g
- 31.5 g
- 42.5 g
- 22.5 g
Answer: 4. 22.5 g
Question 91. The value of the coefficient of volume expansion of glycerin is 5 × 10-4 K-1. The fractional change in the density of glycerin for a rise of 40°C in its temperature, is:
- 0.020
- 0.025
- 0.010
- 0.015
Answer: 1. 0.020
Question 92. a piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted in to heat during its fall. The value of h is :
[Latent heat of ice is 3.4 × 105 J/Kg and g = 10 N/kg]
- 68 km
- 34 km
- 544 km
- 136 km
Answer: 4. 136 km
Question 93. A sample of 0.1 g of water at 100ºC and normal pressure (1.013 × 105 Nm-2) requires 54 cal of heat energy to convert to stream at 100ºC. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample is:
- 104.3 J
- 84.5 J
- 42.2 J
- 208.7 J
Answer: 4. 208.7 J
Question 94. A metal rod of Young’s modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by tºC, the linear stress developed in its is:
- \(\frac{Y}{\alpha t}\)
- \(Y \alpha t\)
- \(\frac{1}{(Y \alpha t)}\)
- \(\frac{\alpha t}{Y}\)
Answer: 2. \(Y \alpha t\)
Question 95. An aluminum sphere of 20 cm diameter is heated from 0ºC to 100ºC. Its volume changes by (given that coefficient of linear expansion for aluminum αAl = 23 × 10-6/ºC)
- 2.89 cc
- 9.28 cc
- 49.8 cc
- 28.9 cc
Answer: 4. 28.9 cc
Question 96. A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area S and length L. L is slightly less than 30 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to the surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Young’s modulus is Y, the force that one part of the wheel applies on the other part is:
- 2πSYαΔT
- SYαΔT
- π SYαΔT
- 2SYαΔT
Answer: 4. 2SYαΔT
Question 97. A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°C. The temperature at which the clock will show the correct time, and the coefficient of linear expansion (α) of the metal of the pendulum shaft are respectively:
- 60°C ; α = 1.85 × 10-4/°C
- 30°C ; α = 1.85 × 10-3/°C
- 55°C ; α = 1.85 × 10-2/°C
- 25°C ; α = 1.85 × 10-5/°C
Answer: 4. 25°C ; α = 1.85 × 10-4/°C
Question 98. A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, and filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75º C. T is given by : (Given: room temperature = 30ºC, specific heat of copper = 0.1 cal/gmºC)
- 825º C
- 800ºC
- 885ºC
- 1250ºC
Answer: 3. 885ºC
Question 99. An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating it. The temperature should be raised by:
- \(3 P K \alpha\)
- \(\frac{\mathrm{P}}{3 \alpha \mathrm{K}}\)
- \(\frac{\mathrm{P}}{\alpha \mathrm{K}}\)
- \(\frac{3 \alpha}{\mathrm{PK}}\)
Answer: 2. \(\frac{\mathrm{P}}{3 \alpha \mathrm{K}}\)
Question 100. An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4°C. Calculate the specific heat of the unknown metal if the water temperature stabilizes at 21.5°C. (Specific heat of brass is 394 J kg-1 K-1)
- 916 J kg-1 K-1
- 458 J kg-1 K-1
- 1232 J kg-1 K-1
- 654 J kg-1 K-1
Answer: 1. 916 J kg-1 K-1
Question 101. A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK-1 containing 0.5 kg water. The initial temperature of the water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg-1K-1 and 400Jkg-1K-1]
- 30%
- 25%
- 15%
- 20%
Answer: 4. 20%
Question 102. Two rods A and B of identical dimensions are at a temperature of 30°C. If A is heated upto 180°C and B upto T°C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is :
- 270°C
- 200°C
- 230°C
- 250°C
Answer: 3. 230°C
Question 103. Ice at -20°C is added to 50 g of water at 40 °C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/°C Specific heat of Ice = 2.1 J/g/°C. Heat of fusion of water at 0°C = 334 J/g
- 100 g
- 40 g
- C60 g
- 50 g
Answer: 2. 40 g