PRACTICE SET THERMAL EXPANSION, CALORIMETRY & HEAT TRANSFER
1. PRACTICE SET-1
THERMAL EXPANSION \& CALORIMETRY
Q.1 Acentigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers \(140^{\circ}\). What is the fall in temperature as registered by the Centigrade thermometer
(1) \(30^{\circ}\)
(2) \(40^{\circ}\)
(3) \(60^{\circ}\)
(4) \(80^{\circ}\)
Q.2 At what temperature the centigrade (Celsius) and Fahrenheit, readings are the same
(1) \(-40^{\circ}\)
\((2)+40^{\circ}\)
(3) \(36.6^{\circ}\)
(4) \(-37^{\circ}\)
Q.3 Standardisation of thermometers is obtained with
(1) Jolly's thermometer
(2) Platinum resistance thermometer
(3)Thermocouple thermometer
(4) Gas thermometer
Q.4 The gas thermometers are more sensitive than liquid thermometers because
(1) Gases expand more than liquids
(2) Gases are easily obtained
(3) Gases are much lighter
(4) Gases do not easily change their states
Q.5 Mercury thermometers can be used to measure temperatures upto
(1) \(100^{\circ} \mathrm{C}\)
(2) \(212^{\circ} \mathrm{C}\)
(3) \(360^{\circ} \mathrm{C}\)
(4) \(500^{\circ} \mathrm{C}\)
Q.6 A constant volume gas thermometer shows pressure reading of \(50 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) of mercury at \(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) respectively. When the pressure reading is \(60 \mathrm{~cm}\) of mercury., the temperature is
(1) \(25^{\circ} \mathrm{C}\)
(2) \(40^{\circ} \mathrm{C}\)
(3) \(15^{\circ} \mathrm{C}\)
(4) \(12.5^{\circ} \mathrm{C}\)
Q.7 The relation that converts temperature in Celsius scale to temperature in Fahrenheit scale is
(1) \(\mathrm{t}^{\circ} \mathrm{F}=\frac{5}{9}\left(\mathrm{t}^{\circ} \mathrm{C}-32^{\circ}\right)\)
\((2) \mathrm{t}^{\circ} \mathrm{F}=\frac{5}{9} \mathrm{t}^{\circ} \mathrm{C}+32^{\circ}\)
(3) \(\mathrm{t}^{\circ} \mathrm{F}=\frac{9}{5} \mathrm{t}^{\circ} \mathrm{C}+32^{\circ}\)
(4) \(\mathrm{t}^{\circ} \mathrm{F}=\frac{9}{5}\left(\mathrm{t}^{\circ} \mathrm{C}+32^{\circ}\right)\)
Q.8 A temperature difference of \(5^{\circ} \mathrm{C}\) on Celsius scale corresponds to the following temperature difference in the Fahrenheit scale
(1) \(9^{\circ}\)
(2) \(41^{\circ}\)
(3) \(2.8^{\circ}\)
(4) \(15^{\circ}\)
Q.9 Mercury boils at \(367^{\circ} \mathrm{C}\). However, mercury thermometers are made such that they can measure temperature up to \(500^{\circ} \mathrm{C}\). This is done by
(1) Maintaining vacuum above mercury column in the stem of the thermometer
(2) Filling nitrogen gas at high pressure above the mercury column
(3) Filling nitrogen gas at low pressure above the mercury column
(4) Filling oxygen gas at high pressure above the mercury column
Q.10 At some temperature T, a bronze pin in a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when
(1) Only the block is heated
(3)Both block and pin are cooled together
(2) Both block and pin are heated together
(4) Only the pin is cooled
Q.11 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by
(1) \(0.5 \%\)
(2) \(2 \%\)
(3) \(1 \%\)
(4) \(4 \%\)
THERMAL EXPANSION, CALORIMETRY & HEAT TRANSFER
Q.12 A thin wire of length \(\mathrm{L}\) increases in length by \(1 \%\) when heated to a certain range of temperature. If a thin copper plate of area \(2 \mathrm{~L} \times \mathrm{L}\) is heated through same range the percentage increase in area will be
(1) \(3 \%\)
(2) \(2.5 \%\)
(3) \(1.5 \%\)
(4) \(2 \%\)
Q.13 Two rods of length \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) are made of materials of coefficients of linear expansions \(\alpha_{1}\) and \(\alpha_{2}\) respectively such that \(\mathrm{L}_{1} \alpha_{1}=\mathrm{L}_{2} \alpha_{2}\). The temperature of the rods is increased by \(\Delta\) T and correspondingly the change in their respective lengths be \(\Delta \mathrm{L}_{1}\) and \(\Delta \mathrm{L}_{2}\)
(1) \(\Delta \mathrm{L}_{1} \neq \Delta \mathrm{L}_{2}\)
(2) \(\Delta \mathrm{L}_{1}=\Delta \mathrm{L}_{2}\)
(3) Difference in length is a constant and is independent of rise of temperature
(4) Data is insufficient to arrive at a conclusion
Q.14 A rod of length \(40 \mathrm{~cm}\) has the coefficient of linear expansion \(\alpha_{1}=6 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). Another rod of length l has the coefficient of linear expansion \(\alpha_{2}=4 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). If the difference in length of the two rods always remain same at all temperatures, then the value of l is
(1) \(26 \mathrm{~cm}\)
(2) \(60 \mathrm{~cm}\)
(3) \(80 \mathrm{~cm}\)
(4) \(32 \mathrm{~cm}\)
Q.15 A liquid with coefficient of volume expansion \(\gamma\) is filled in a container of a material expansion \(\alpha\). If the liquid overflows on heating then
(1) \(\gamma=3 \alpha\)
(2) \(\gamma>3 \alpha\)
(3) \(\gamma<3 \alpha\)
(4) \(\gamma=\alpha^{3}\)
Q.16 Water does not freeze at the bottom of the lakes in winter because
(1)Ice is a good conductor of heat
(2) Ice reflects heat and light
(3) Of anomalous expansion of water between \(4^{\circ} \mathrm{C}\) to \(0^{\circ} \mathrm{C}\)
(4) Nothing can be said
Q.17 A one litre glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in this flask if coefficient of linear expansion of glass is \(9 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) while of volume expansion of mercury is \(1.8 \times 10^{-4} /{ }^{\circ} \mathrm{C}\)
(1) \(50 \mathrm{cc}\)
(2) \(100 \mathrm{cc}\)
(3) \(150 \mathrm{cc}\)
(4) \(200 \mathrm{cc}\)
Q.18 Two spheres of same size are made of the same material but one is solid and the other is hollow. They are heated to the same temperature
(1) Both spheres expand equally
(2) The solid sphere expands more
(3) The hollow sphere expands more
(4) Data is insufficient to arrive at a conclusion
Q.19 A bimetallic strip is made up of two metals with different \(\alpha\)
(1) On heating, it bends towards the metal with high \(\alpha\)
(2) On heating, it bends towards the metal with low \(\alpha\)
(3) On cooling, it bends towards the metal with high \(\alpha\)
(4) On cooling, it bends towards the metal with low \(\alpha\)
Q.20 A metal rod of length \(\mathrm{L}_{0}\), made of material of Young's modulus \(\mathrm{Y}\), area \(\mathrm{A}\) is fixed between two rigid supports. The coefficient of linear expansion of the rod is \(\alpha\). The rod is heated such that the tension in the \(\operatorname{rod}\) is \(\mathrm{T}\)
(1) \(\mathrm{T} \propto \mathrm{L}_{0}\)
(2) \(\mathrm{T} \propto \mathrm{A}_{0}^{0}\)
(3) \(\mathrm{T} \propto \mathrm{A}\)
(4) \(\mathrm{T} \propto \mathrm{L}_{0}^{0}\)
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.21 A triangular plate has two cavities, one square and one rectangular as shown. The plate is heated
(1) a increases, \(b\) decreases
(2) a and b both increase
(3) a and b increase, \(x\) and \(l\) decrease
(4) a, b, \(x\) and \(l\) all increase
Q.22 The coefficient of volume expansion of a solid is \(\mathrm{x}\) times the coefficient of linear expansion. Then \(\mathrm{x}\) is
(1) \(1.5\)
(2) 2
(3) \(2.5\)
(4) 3
Q.23 The metal of a pendulum clock has a coefficient of expansion as \(2 \times 10^{-5} / \mathrm{K}\). Its period is \(2 \mathrm{~s}\) at \(15^{\circ} \mathrm{C}\). If the temperature increases to \(25^{\circ} \mathrm{C}\), shall the clock
(1) Show correct time
(2) Lose time
(3) Gain time
(4) First lose and then gain time
Q.24 Amount of heat required to raise the temperature of a body through \(1 \mathrm{~K}\) is called its
(1) Water equivalent
(2) Thermal capacity
(3) Entropy
(4) Specific heat
Q.25 The specific heat of metals at low temperature is
(1) Proportional to \(T\)
(3) Proportional to \(T^{3}\)
(2) Proportional to \(\mathrm{T}^{2}\)
(4) Independent of T
Q.26 A body of mass \(m\) gram has specific heat c
(1) Heat capacity of the body is mc
(2) Water equivalent of the body is \(m\)
(3) Water equivalent of the body is mc
(4) Heat capacity of the body is c
Q.27 A metallic ball and 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
(1) Are the same for both
(2) Is greater for the ball
(3) Is greater for the spring
(4) For the two may or may not be the same depending upon the metal
Q.28 A mass of liquid with volume \(\mathrm{v}_{1}\) is completely changed into a gas of volume \(\mathrm{v}_{2}\) at a constant external pressure \(\mathrm{P}\) and temperature \(\mathrm{T}\). If the latent heat of evaporation for the given mass is \(\mathrm{L}\), then the increase in the internal energy of the system is
(1) Zero
(2) \(\mathrm{P}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)\)
(3) \(\mathrm{L}-\mathrm{P}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)\)
(4) \(\mathrm{L}\)
Q.29 During the melting of a slab of ice at \(273 \mathrm{~K}\) at atmospheric pressure
(1) Positive work is done by ice-water system on the atmosphere
(2) Positive work is done on the ice-water system by the atmosphere
(3) The internal energy of the ice-water system increases
(4) The internal energy of the ice-water system decreases
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.30 \(1 \mathrm{gm}\) steam at \(100^{\circ} \mathrm{C}\) can melt how much ice at \(0^{\circ} \mathrm{C}\)
(1) \(\frac{80}{540} \mathrm{gm}\)
(2) \(\frac{540}{80} \mathrm{gm}\)
(3) \(8 \mathrm{gm}\)
(4) \(8 \mathrm{~kg}\)
Q.31 The melting of solids under atmospheric pressure is
(1) An isometric change
(2) An isobaric change
(3) Both isobaric and isothermal change
(4) An adiabatic change
Q.32 \(3.2 \mathrm{~kg}\) of ice at \(-10^{\circ} \mathrm{C}\) just melts with a mass \(\mathrm{m}\) of steam
(1) \(\mathrm{m}=400 \mathrm{gm}\)
(2) \(\mathrm{m}=800 \mathrm{gm}\)
(3) \(\mathrm{m}=500 \mathrm{gm}\)
(4) \(\mathrm{m}=900 \mathrm{gm}\)
Q.33 A \(10 \mathrm{~kg}\) iron bar (specific heat \(0.11 \mathrm{cal} / \mathrm{gm}-{ }^{\circ} \mathrm{C}\) ) at \(80^{\circ} \mathrm{C}\) is placed on a block of ice. How much ice melts
(1) \(1.1 \mathrm{~kg}\)
(2) \(10 \mathrm{~kg}\)
(3) \(16 \mathrm{~kg}\)
(4) \(60 \mathrm{~kg}\)
Q.34 Water at \(0^{\circ} \mathrm{C}\) was boiled away over a burner supplying heat at a constant rate. If the time to raise the temperature from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\) is \(5 \mathrm{~min}\) and the time to boil away at \(100^{\circ} \mathrm{C}\) is \(28 \mathrm{~min}\), then the specific latent heat of steam in \(\mathrm{J} \mathrm{g}^{-1}\) is (take \(\mathrm{s}=1.0 \mathrm{cal} \mathrm{g}^{-1} \mathrm{~K}^{-1}\) )
(1) 540
(2) 2250
(3) 2352
(4) 2392
Q.35 \(100 \mathrm{~g}\) of ice is mixed with \(100 \mathrm{~g}\) of water at \(100^{\circ} \mathrm{C}\). What will be the final temperature of the mixture
(1) \(10^{\circ} \mathrm{C}\)
(2) \(20^{\circ} \mathrm{C}\)
(3) \(30^{\circ} \mathrm{C}\)
(4) \(40^{\circ} \mathrm{C}\)
Q.36 One kg of ice at \(0^{\circ} \mathrm{C}\) is mixed with \(1 \mathrm{~kg}\) of water at \(10^{\circ} \mathrm{C}\). The resulting temperature will be
(1) Between \(0^{\circ} \mathrm{C}\) and \(10^{\circ} \mathrm{C}\)
(2) Equal to \(0^{\circ} \mathrm{C}\)
(3) Less than \(0^{\circ} \mathrm{C}\)
(4) Greater than \(0^{\circ}\)
Q.37 \(1 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\) is mixed with \(1 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\). After thermal equilibrium is attained the temperature of the mixture is
(1) \(1^{\circ} \mathrm{C}\)
(2) \(50^{\circ} \mathrm{C}\)
(3) \(81^{\circ} \mathrm{C}\)
(4) \(100^{\circ} \mathrm{C}\)
Q.38 A 50 gm piece of iron at \(100^{\circ} \mathrm{C}\) is dropped into 100 gm water at \(20^{\circ} \mathrm{C}\). The temperature of mixture \(25.5^{\circ} \mathrm{C}\). The specific heat of iron in Calorie/gm \({ }^{\circ} \mathrm{C}\) will be
(1) \(0.341\)
(2) \(0.267\)
(3) \(0.082\)
(4) \(0.148\)
Q.39 A mass m of steam at \(100^{\circ} \mathrm{C}\) is to be passed into a vessel containing \(10 \mathrm{~g}\) of ice and \(100 \mathrm{~g}\) of water at \(0^{\circ} \mathrm{C}\) so that all the ice is melted and the temperature is raised to \(5^{\circ} \mathrm{C}\). Neglecting heat absorbed by the vessel, we get
(1) \(m=2.1 \mathrm{~g}\)
(2) \(m=4.2 \mathrm{~g}\)
(3) \(m=6.3 \mathrm{~g}\)
(4) \(m=8.4 \mathrm{~g}\)
Q.40 A ball of thermal capacity \(10 \mathrm{cal} /{ }^{\circ} \mathrm{C}\) is heated to the temperature of furnace. It is then transferred into a vessel containing water. The water equivalent of vessel and the contents is \(200 \mathrm{gm}\). The temperature of the vessel and its contents rises from \(10^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\). What is the temperature of furnace
(1) \(640^{\circ} \mathrm{C}\)
(2) \(64^{\circ} \mathrm{C}\)
(3) \(600^{\circ} \mathrm{C}\)
(4) \(100^{\circ} \mathrm{C}\)
HEAT TRANSFER
Q.41 Mud houses are cooler in summer and warmer in winter because
(1) Mud is superconductor of heat
(2) Mud is good conductor of heat
(3) Mud is bad conductor of heat
(4) None of these
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.42 Heat current is maximum in which of the following (rods are of identical dimension)
(1)Copper
(2)copper Steel
(3) Steel copper
(4)Steel
Q.43 Consider the following statements
Assertion (A) : Woolen clothes keep the body warm in winter
Reason (R) : Air is a bad conductor of heat Of these statements
(1) Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and the \(\mathrm{R}\) is a correct explanation of the \(\mathrm{A}\)
(2) Both \(A\) and \(R\) are true but the \(R\) is not a correct explanation of the \(A\)
(3) A is true but the \(\mathrm{R}\) is false
(4) Both A and \(R\) are false
(5) A is false but the \(\mathrm{R}\) is true
Q.44 The lengths and radii of two rods made of same material are in the ratios \(1: 2\) and \(2: 3\) respectively. If the temperature difference between the ends for the two rods be the same then in the steady state. The amount of heat flowing per second through them will be in the ratio
(1) \(1: 3\)
(2) \(4: 3\)
(3) \(8: 9\)
(4) \(3: 2\)
Q.45 Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 30 minutes. The ratio of their thermal conductivities will be
(1) \(1.5\)
(2) 1
(3) \(2 / 3\)
(4) 4
Q.46 If the coefficient of conductivity of aluminium is \(0.5 \mathrm{cal} / \mathrm{cm}-\mathrm{sec}-{ }^{\circ} \mathrm{C}\), then in order to conduct \(10 \mathrm{cal} / \mathrm{sec}-\mathrm{cm}^{2}\) in the steady state, the temperature gradient in aluminium must be
(1) \(5^{\circ} \mathrm{C} / \mathrm{cm}\)
(2) \(10^{\circ} \mathrm{C} / \mathrm{cm}\)
(3) \(20^{\circ} \mathrm{C} / \mathrm{cm}\)
(4) \(10.5^{\circ} \mathrm{C} / \mathrm{cm}\)
Q.47 The area of the glass of a window of a room is \(10 \mathrm{~m}^{2}\). and thickness \(2 \mathrm{~mm}\). The outer and inner temperature are \(40^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\) respectively. Thermal conductivity of glass in \(\mathrm{MKS}\) system is \(0.2\). The heat flowing in the room per second will be
(1) \(3 \times 10^{4}\) Joules
(2) \(2 \times 10^{4}\) Joules
(3) 30 Joules
(4) 45 Joules
Q.48 When two ends of a rod wrapped with cotton are maintained at different temperatures and after some time every point of the rod attains a constant temperature, then
(1) Conduction of heat at different points of the rod stops because the temperature is not increasing
(2) Rod is bad conductor of heat
(3) Heat is being radiated from each point of the rod
(4) Each point of the rod is giving heat to its neighbour at the same rate at which it is receiving heat
Q.49 In which case the thermal conductivity increases from left to right
(1) \(\mathrm{Al}, \mathrm{Cu}, \mathrm{Ag}\)
(2) \(\mathrm{Ag}, \mathrm{Cu}, \mathrm{Al}\)
(3) \(\mathrm{Cu}, \mathrm{Ag}, \mathrm{Al}\)
(4) \(\mathrm{Al}, \mathrm{Ag}, \mathrm{Cu}\)
Q.50 To a rough approximation, conductivities of metals are about
(1) 1000 times as those of liquids and 10,000 times of gases
(2) 10 times as those of liquids and 100 times of gases
(3) 100 times as those of liquids and 1000 times of gases
(4) 10,000 times as those of liquids and 1000 times of gases
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.51 A copper bar \(10 \mathrm{~cm}\) long has its ends pressed against copper tanks at \(0^{\circ} \mathrm{C}\) and \(100{ }^{\circ} \mathrm{C}\). The ends are separated by layers of dust \(0.1 \mathrm{~mm}\) thick. If conductivity of dust is \(0.001\) times that of copper, the temperatures of end \(\mathrm{P}\) and \(\mathrm{Q}\) of bar are [Take rate of flow of heat constant from \(\mathrm{P}\) to \(\mathrm{Q}\) ]
(1) \(33.3^{\circ} \mathrm{C}\) and \(66.7^{\circ} \mathrm{C}\)
(2) \(66.7^{\circ} \mathrm{C}\) and \(33.3^{\circ} \mathrm{C}\)
(3) \(75^{\circ} \mathrm{C}\) and \(25^{\circ} \mathrm{C}\)
(4) \(60^{\circ} \mathrm{C}\) and \(40^{\circ} \mathrm{C}\)
Q.52 Three rods of the same dimension have thermal conductivities \(3 \mathrm{~K}, 2 \mathrm{~K}\) and \(\mathrm{K}\). They are arranged as shown in figure given below, with their ends at \(100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\). The temperature of their junction is
(1) \(60^{\circ}\)
(2) \(70^{\circ}\)
(3) \(50^{\circ}\)
(4) \(35^{\circ}\)
Q.53 Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities \(\mathrm{K}_{1}\), \(\mathrm{K}_{2}, \mathrm{~K}_{3}, \mathrm{~K}_{4}\) and \(\mathrm{K}_{5}\). When points \(\mathrm{A}\) and \(\mathrm{B}\) are maintained at different temperatures, no heat flows through the central rod if
(1) \(\mathrm{K}_{1}=\mathrm{K}_{4}\) and \(\mathrm{K}_{2}=\mathrm{K}_{3}\)
(2) \(\mathrm{K}_{1} \mathrm{~K}_{4}=\mathrm{K}_{2} \mathrm{~K}_{3}\)
(3) \(\mathrm{K}_{1} \mathrm{~K}_{2}=\mathrm{K}_{3} \mathrm{~K}_{4}\)
(4) \(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{4}}=\frac{\mathrm{K}_{2}}{\mathrm{~K}_{3}}\)
Q.54 A wall has two layers A and B each made of different materials. The thickness of both the layers is the same. The thermal conductivity of \(\mathrm{A}, \mathrm{K}_{\mathrm{A}}=3 \mathrm{~K}_{\mathrm{B}}\). The temperature difference across the wall is \(20^{\circ} \mathrm{C}\) in thermal equilibrium
(1) The temperature difference across \(\mathrm{A}\) is \(15^{\circ} \mathrm{C}\)
(2) Rate of heat transfer across \(A\) is more than across \(B\)
(3) Rate of heat transfer across both is same
(4) Temperature difference across \(\mathrm{A}\) is \(5^{\circ} \mathrm{C}\)
Q.55 Two metal cubes A and B of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A and B are \(300 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}\) and \(200 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}\), respectively. After steady state is reached, the temperature \(t\) of the interface will be
(1) \(45^{\circ} \mathrm{C}\)
(2) \(90^{\circ} \mathrm{C}\)
(3) \(30^{\circ} \mathrm{C}\)
(4) \(60^{\circ} \mathrm{C}\)
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.56 Two cylinders \(\mathrm{P}\) and \(\mathrm{Q}\) have the same length and diameter and are made of different materials having thermal conductivities in the ratio \(2: 3\). These two cylinders are combined to make a cylinder. One end of \(\mathrm{P}\) is kept at \(100^{\circ} \mathrm{C}\) and another end of \(\mathrm{Q}\) at \(0^{\circ} \mathrm{C}\). The temperature at the interface of \(\mathrm{P}\) and \(\mathrm{Q}\) is
(1) \(30^{\circ} \mathrm{C}\)
(2) \(40^{\circ} \mathrm{C}\)
(3) \(50^{\circ} \mathrm{C}\)
(4) \(60^{\circ} \mathrm{C}\)
Q.57 Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of composite plate will be
(1) 5
(2) \(2.4\)
(3) \(1.5\)
(4) \(1.2\)
Q.58 Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is \(100^{\circ} \mathrm{C}\), then the temperature difference between the ends of other diagonal will be
(1) \(0^{\circ} \mathrm{C}\)
(2) \(\frac{100}{1}{ }^{\circ} \mathrm{C}\); where \(l\) is the length of each rod
(3) \(\frac{100}{21}{ }^{\circ} \mathrm{C}\)
(4) \(100^{\circ} \mathrm{C}\)
Q.59 Two identical rods of metal are welded end to end as shown in figure (a). 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in
(1) 1 minute
(2) 2 minutes
(3) 4 minutes
(4) 16 minutes
(a) \(0^{\circ} \mathrm{C}\)
(b) 
Q.60 Two bars of thermal conductivities \(\mathrm{k}\) and \(3 \mathrm{k}\) and lengths \(1 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is \(0^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) respectively, then the temperature \(\phi\) of the interface is
(1) \(50^{\circ} \mathrm{C}\)
(2) \(\frac{100}{3}{ }^{\circ} \mathrm{C}\)
(3) \(60^{\circ} \mathrm{C}\)
(4) \(\frac{200}{3}{ }^{\circ} \mathrm{C}\)
Q.61 Three rods A, B and C have the same dimensions. Their thermal conductivities are \(\mathrm{K}_{\mathrm{A}}, \mathrm{K}_{\mathrm{B}}\) and \(\mathrm{K}_{\mathrm{C}}\) respectively. A and \(B\) are placed end to end, with their free ends kept at a certain temperature difference. \(\mathrm{C}\) is placed separately, with its ends kept at the same temperature difference. The two arrangements conduct heat at the same rate. \(\mathrm{K}_{\mathrm{C}}\) must be equal to
(1) \(\mathrm{K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}\)
(2) \(\frac{K_{A} K_{B}}{K_{A}+K_{B}}\)
(3) \(\frac{1}{2}\left(\mathrm{~K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}\right)\)
(4) \(2 .\left(\frac{\mathrm{K}_{\mathrm{A}} \mathrm{K}_{\mathrm{B}}}{\mathrm{K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}}\right)\)
Q.62 The three rods described in the previous question are placed individually, with their ends kept at the same temperature difference. The rate of heat flow through \(\mathrm{C}\) is equal to the rate of combined heat flow through \(\mathrm{A}\) and \(\mathrm{B} . \mathrm{K}_{\mathrm{C}}\) must be equal to
(1) \(\mathrm{K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}\)
(2) \(\frac{K_{A} K_{B}}{K_{A}+K_{B}}\)
(3) \(\frac{1}{2}\left(\mathrm{~K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}\right)\)
(4) \(2 .\left(\frac{\mathrm{K}_{\mathrm{A}} \mathrm{K}_{\mathrm{B}}}{\mathrm{K}_{\mathrm{A}}+\mathrm{K}_{\mathrm{B}}}\right)\)
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.63 Three rods \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of the same length and cross-sectional area are joined in series as shown in the figure. Their thermal conductivities are in the ratio \(1: 2: 1.5\). If the open ends of \(\mathrm{A}\) and \(\mathrm{C}\) are at \(200^{\circ} \mathrm{C}\) and \(18^{\circ} \mathrm{C}\), respectively, the temperature at junction of \(A\) and \(B\) in equilibrium is
(1) \(74^{\circ} \mathrm{C}\)
(2) \(116^{\circ} \mathrm{C}\)
(3) \(156^{\circ} \mathrm{C}\)
(4) \(148^{\circ} \mathrm{C}\)
Q.64 There are two identical vessels filled with equal amounts of ice. The vessels are of different metals. If the ice melts in the two vessels in 20 and 35 minutes respectively the ratio of the coefficients of thermal conductivity of the two metals is
(1) \(4: 7\)
(2) \(7: 4\)
(3) \(16: 49\)
(4) \(49: 16\)
Q.65 Temperature at the surface of lake is \(-20^{\circ} \mathrm{C}\). Then temperature of water just below the lower surface of ice layer is
(1) \(-4^{\circ} \mathrm{C}\)
(2) \(0^{\circ} \mathrm{C}\)
(3) \(4^{\circ} \mathrm{C}\)
\((4)-20{ }^{\circ} \mathrm{C}\)
Q.66 Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at temperature of boiling water, the length upto which wax melts are \(8.4 \mathrm{~cm}\) and \(4.2 \mathrm{~cm}\) respectively. If thermal conductivity of copper is \(0.92\), then thermal conductivity of iron is
(1) \(0.23\)
(2) \(0.46\)
(3) \(0.115\)
(4) \(0.69\)
Q.67 During severe winter in the low temperature zones of the world, the superficial parts of the lakes are frozen, leaving water below. The freezing at the bottom is prevented because
(1) The conductivity of ice is low
(2) The water has large specific heat
(3) The water has large latent heat of fusion
(4) The temperature of the earth at the bottom of the lake is high
Q.68 If the steady thickness of ice layer is \(100 \mathrm{~cm}\) and that of water is \(4.20 \mathrm{~m}\) in a lake of a cold country where temperature of air is \(-5.0^{\circ} \mathrm{C}\) and temperature of water at the bottom is \(4^{\circ} \mathrm{C}\). The ratio of the thermal conductivity of water to that of ice is
(1) \(4: 3\)
(2) \(4.25: 1\)
(3) \(3: 1\)
(4) \(5.25: 1\)
Q.69 A \(10 \mathrm{~cm}\) layer of ice has been formed over a pond of water. The temperature of air above is \(-5^{\circ} \mathrm{C}\). How long will it take the layer to become \(10.1 \mathrm{~cm}\) thick? (Given \(\mathrm{K}_{\mathrm{ice}}=0.008\) CGS units, density of ice \(=1 \mathrm{gm} / \mathrm{cc}\) and \(\left.\mathrm{L}_{\text {ice }}=80 \mathrm{cal} / \mathrm{gm}\right)\)
(1) \(2005 \mathrm{sec}\)
(2) \(1705 \mathrm{sec}\)
(3) \(1405 \mathrm{sec}\)
(4) \(705 \mathrm{sec}\)
Q.70 One feels hotter at the top of a flame than the sides because of
(1) Conduction
(2) Convection
(3) Radiations
(4) Both ' 1 ' and ' 3 '
Q.71 Mode of transmission of heat, in which heat is carried by the moving particles, is
(1) Radiation
(2) Conduction
(3) Convection
(4) Wave motion
Q.72 While measuring the thermal conductivity of a liquid, we keep the upper part hot and lower part cool, so that
(1) Convection may be stopped
(2) Radiation may be stopped
(3) Heat conduction is easier downwards
(4) It is easier and more convenient to do so
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.73 The layers of atmosphere are heated through
(1) Convection
(2) Conduction
(3) Radiation
(4) (2) and (3) both
Q.74 The rate of loss of heat from a body cooling under conditions of forced convection is proportional to its (A) heat capacity (B) surface area (C) absolute temperature (D) excess of temperature over that of surrounding state if
(1) A, B, C are correct
(2) Only A and \(\mathrm{C}\) are correct
(3) Only B and D are correct
(4) Only D is correct
Q.75 Heat travels through vacuum by
(1) Conduction
(2) Convection
(3) Radiation
(4) Both (1) and (2)
Q.76 For a perfectly black body, its absorptive power is
(1) 1
(2) \(0.5\)
(3) 0
(4) Infinity
Q.77 Which of the following is the example of ideal black body
(1) Kajal
(2) Black board
(3) A pin hole in a box
(4) None of these
Q.78 Which of the following is the best example of an ideal black body
(1) Lamp black
(2) Platinum black
(3) Highly heated charcoal lamp
(4) Cavity maintained at constant temperature
Q.79 The spectrum from a black body radiation is a
(1) Line spectrum
(2) Band spectrum
(3) Continuous spectrum
(4) Line and band spectrum both
Q.80 In summer one feels cold on entering an air conditioned room. This can be explained by
(1) Newton's law of cooling
(2) Stefan's law
(3) Kirchoff's law
(4) Prevost's theory of heat exchange
Q.81 Out of the radiations falling on surface of a body, \(30 \%\) radiations are absorbed and \(30 \%\) are transmitted then its reflection coefficient will be
(1) \(0.3\)
(2) \(0.6\)
(3) \(0.4\)
(4) Zero
Q.82 There is a black spot on a body. If the body is heated and carried in dark room then it glows more. This can be explained on the basis of
(1) Newton's law of cooling
(2) Wien's law
(3) Kirchoff's law
(4) Stefan's
Q.83 If between wavelength \(\lambda\) and \(\lambda+\mathrm{d} \lambda, \mathrm{e}_{\lambda}\) and \(\mathrm{a}_{\lambda}\) be the emissive and absorptive powers of a body and \(E_{\lambda}\) be the emissive power of a perfectly black body, then according to Kirchoff's law, which is true
(1) \(e_{\lambda}=a_{\lambda}=E_{\lambda}\)
(2) \(e_{\lambda} E_{\lambda}=a_{\lambda}\)
(3) \(e_{\lambda}=a_{\lambda} E_{\lambda}\)
(4) \(\mathrm{e}_{\lambda} \mathrm{a}_{\lambda} \mathrm{E}_{\lambda}=\) constant
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.84 The figure shows two similar sheets of tin plate, one polished and the other painted dull black. A piece of cork is attached on the reverse side of each plate by means of melted paraffin wax. What will happen when an electric bulb placed exactly midway between them is switched on
(1) The cork on the polished plate falls off first
(2) The cork on the dull black plate falls off first
(3) Both corks fall off at the same time
(4) Neither cork falls off
Q.85 During total solar eclipse Fraunhoffer's lines appear bright because
(1) Moon totally covers both parts of sun photo sphere and chromosphere
(2) Sun light is scattered by moon
(3) Moon blocks the radiations emitted by chromosphere
(4) Moon blocks the radiations emitted by photosphere and radiations emitted by chromosphere reach the earth
Q.86 A black body radiates energy at the rate of \(\mathrm{E}\) watt \(/ \mathrm{m}^{2}\) at a high temperature \(\mathrm{T} \mathrm{K}\). When the temperature is reduced to \(\frac{\mathrm{T}}{2} \mathrm{~K}\), the radiant energy will be
(1) \(\frac{E}{16}\)
(2) \(\frac{E}{4}\)
(3) \(4 \mathrm{E}\)
(4) \(16 \mathrm{E}\)
Q.87 At temperature \(\mathrm{T}\), the power radiated by a body is \(\mathrm{Q}\) watts. At the temperature 3 the power radiated by it will be
(1) \(3 Q\)
(2) \(9 Q\)
(3) \(27 \mathrm{Q}\)
(4) \(81 \mathrm{Q}\)
Q.88 A black metal foil is warmed by radiation from a small sphere at temperature \(\mathrm{T}\) and at a distance \(\mathrm{d}\). It is found that the power received by the foil is ' \(\mathrm{P}\) '. If both the temperature and the distance are doubled, the power received by the foil will be
(1) \(16 \mathrm{P}\)
(2) \(4 \mathrm{P}\)
(3) \(2 \mathrm{P}\)
(4) \(\mathrm{P}\)
Q.89 A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is T, then
(1) The hollow sphere will cool at a faster rate for all values of T
(2) The solid sphere will cool at a faster rate for all values of T
(3) Both spheres will cool at the same rate for all values of T
(4) Both spheres will cool at the same rate only for small values of T
Q.90 Two bodies A and B have thermal emissivities of \(0.01\) and \(0.81\) respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength \(\lambda_{\mathrm{B}}\) corresponding to maximum spectral radiancy in the radiation from \(\mathrm{B}\) is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from \(\mathrm{A}\), by \(1.00 \mu \mathrm{m}\). If the temperature of \(\mathrm{A}\) is \(5802 \mathrm{~K}\)
(1) The temperature of \(\mathrm{B}\) is \(1934 \mathrm{~K}\)
(2) \(\lambda_{\mathrm{B}}=1.5 \mu \mathrm{m}\)
(3) The temperature of \(\mathrm{B}\) is \(11604 \mathrm{~K}\)
(4) The temperature of B is \(2901 \mathrm{~K}\)
THERMAL EXPANSION, CALORIMETRY \& HEAT TRANSFER
Q.91 The temperature of a piece of iron is \(27^{\circ} \mathrm{C}\) and it is radiating energy at the rate of \(\mathrm{Q} \mathrm{kW} \mathrm{m}^{-2}\). If its temperature is raised to \(151^{\circ} \mathrm{C}\), the rate of radiation of energy will become approximately
(1) \(2 \mathrm{Q} \mathrm{kW} \mathrm{m}{ }^{-2}\)
(2) \(4 \mathrm{Q} \mathrm{kW} \mathrm{m}{ }^{-2}\)
(3) \(6 \mathrm{Q} \mathrm{kW} \mathrm{m}{ }^{-2}\)
(4) \(8 \mathrm{Q} \mathrm{kW} \mathrm{m}{ }^{-2}\)
Q.92 If \(\mathrm{E}\) is the total energy emitted by a body at a temperature \(\mathrm{T} \mathrm{K}\) and \(\mathrm{E}_{\max }\) is the maximum energy emitted by it at the same temperature, then
(1) \(\mathrm{E} \propto \mathrm{T}^{4} ; \mathrm{E}_{\max } \propto \mathrm{T}^{5}\)
(2) \(\mathrm{E} \propto \mathrm{T}^{4} ; \mathrm{E}_{\max } \propto \mathrm{T}^{-5}\)
(3) \(\mathrm{E} \propto \mathrm{T}^{-4} ; \mathrm{E}_{\max } \propto \mathrm{T}^{4}\)
(4) \(\mathrm{E} \propto \mathrm{T}^{5} ; \mathrm{E}_{\max } \propto \mathrm{T}^{4}\)
Q.93 A metal ball of surface area \(200 \mathrm{~cm}^{2}\) and temperature \(527^{\circ} \mathrm{C}\) is surrounded by a vessel at \(27^{\circ} \mathrm{C}\). If the emissivity of the metal is \(0.4\), then the rate of loss of heat from the ball is \(\left(\sigma=5.67 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{2}-\mathrm{s}-\mathrm{K}^{4}\right)\)
(1) 108 Joules approx.
(2) 168 Joules approx
(3) 182 Joules approx
(4) 192 Joules approx.
Q.94 If the rates of cooling of two bodies are same then for which body the rate of fall of temperature will be more? For the body whose thermal capacity is
(1) More
(2) Less
(3) Infinity
(4) Any value
Q.95 According to Newton's law of cooling, the rate of cooling of a body is proportional to \((\Delta \theta)^{\mathrm{n}}\), where \(\Delta \theta\) is the difference of the temperature of the body and the surroundings and \(n\) is equal to
(1) One
(2) Two
(3) Three
(4) Four
Q.96 Newton's law of cooling is used in laboratory for the determination of the
(1) Specific heat of the gases
(2) The latent heat of gases
(3) Specific heat of liquids
(4) Latent heat of liquids
Q.97 Liquid is filled in a vessel which is kept in a room with temperature \(20^{\circ} \mathrm{C}\). When the temperature of the liquid is \(80^{\circ} \mathrm{C}\), then it loses heat at the rate of \(60 \mathrm{cal} / \mathrm{sec}\). What will be the rate of loss of heat when the temperature of the liquid is \(40^{\circ} \mathrm{C}\)
(1) \(180 \mathrm{cal} / \mathrm{sec}\)
(2) \(40 \mathrm{cal} / \mathrm{sec}\)
(3) \(30 \mathrm{cal} / \mathrm{sec}\)
(4) \(20 \mathrm{cal} / \mathrm{sec}\)
Q.98 A bucket full of hot water is placed in a room. Water takes \(\mathrm{t}_{1}\) seconds to cool from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\), \(\mathrm{t}_{2}\) seconds to cool from \(80^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\) and \(\mathrm{t}_{3}\) seconds to cool from \(70^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) then
(1) \(\mathrm{t}_{3}>\mathrm{t}_{2}>\mathrm{t}_{1}\)
(2) \(\mathrm{t}_{1}=\mathrm{t}_{2}=\mathrm{t}_{3}\)
(3) \(\mathrm{t}_{1}>\mathrm{t}_{2}>\mathrm{t}_{3}\)
(4) \(\mathrm{t}_{1}>\mathrm{t}_{2}>\mathrm{t}_{3}\)
Q.99 A calorimeter of negligible water equivalent contains 430 gm of water and it cools at the rate of \(0.24^{\circ} \mathrm{C}\) per minute in the surroundings at \(30^{\circ} \mathrm{C}\). If at any moment the temperature of water is \(34^{\circ} \mathrm{C}\) then at what rate the heat should be supplied to it to keep its temperature constant
(1) \(0.24 \mathrm{Cal} / \mathrm{minute}\)
(2) \(100 \mathrm{Cal} /\) minute
(3) \(103.2 \mathrm{Cal} /\) minute
(4) None of the above
Q.100 A black body has maximum wave length \(\lambda_{\mathrm{m}}\) at temperature \(2000 \mathrm{~K}\). Its corresponding wavelength at temperature \(3000 \mathrm{~K}\) will be
(1) \(\frac{3}{2} \lambda_{m}\)
(2) \(\frac{2}{3} \lambda_{m}\)
(3) \(\frac{4}{9} \lambda_{m}\)
(4) \(\frac{9}{4} \lambda_{m}\) Q.101 Consider the following statements
Assertion (A) : When temperature increases, the colour of a star shifts towards smaller wavelength, i.e., towards violet colour
Reason (R) : Red colour has maximum wavelength Of these statements
(1) Both A and \(R\) are true and the \(R\) is a correct explanation of the \(A\)
(2) Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but the \(\mathrm{R}\) is not a correct explanation of the \(\mathrm{A}\)
(3) A is true but the \(R\) is false
(4) Both A and R are false
(5) \(\mathrm{A}\) is false but the \(\mathrm{R}\) is true
Q.102 The wavelength of radiation emitted by a body depends upon
(1) The nature of its surface
(2) The area of its surface
(3) The temperature of its surface
(4) All the above factors
Q.103 On investigation of light from three different stars \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\), it was found that in the spectrum of A the intensity of red colour is maximum, in \(\mathrm{B}\) the intensity of blue colour is maximum and in \(\mathrm{C}\) the intensity of yellow colour is maximum. From these observations it can be concluded that
(1) The temperature of \(\mathrm{A}\) is maximum, \(\mathrm{B}\) is minimum and \(\mathrm{C}\) is intermediate
(2) The temperature of \(\mathrm{A}\) is maximum, \(\mathrm{C}\) is minimum and \(\mathrm{B}\) is intermediate
(3) The temperature of \(\mathrm{B}\) is maximum, \(\mathrm{A}\) is minimum and \(\mathrm{C}\) is intermediate
(4) The temperature of \(\mathrm{C}\) is maximum, \(\mathrm{B}\) is minimum and \(\mathrm{A}\) is intermediate
Q.104 If black wire of platinum is heated, then its colour first appear red, then yellow and finally white. It can be understood on the basis of
(1) Wien's displacement law
(3) Newton's law of cooling
(2) Prevost theory of heat exchange
(4) None of the above
Q.105 Shown below are the black body radiation curves at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right)\). Which of the following plots is correct
(1) 
(2) 
(3) 
(4) 
Q.106 The spectrum of a black body at two temperatures \(27^{\circ} \mathrm{C}\) and \(327^{\circ} \mathrm{C}\) is shown in the figure. Let \(\mathrm{A}_{1}\) and \(\mathrm{A}_{2}\) be the areas under the two curves respectively. The value of \(\frac{A_{2}}{A_{1}}\) is
(1) \(1: 16\)
(3) \(2: 1\)
(2) \(4: 1\)
(4) \(16: 1\)
