Chapter 13

Two absolute scales \(A\) and \(B\) have triple points of water defined to be \(200 A\) and \(350 B\). What is the relation between \(T_{A}\) and \(T_{B} ?\) [NCERT] (a) \(\frac{T_{A}}{T_{B}}=\frac{4}{7}\) (b) \(\frac{T_{A}}{T_{B}}=\frac{3}{7}\) (c) \(\frac{T_{A}}{T_{B}}=\frac{7}{3}\) (d) \(\frac{T_{A}}{T_{B}}=\frac{7}{4}\)

A faulty thermometer has its fixed points marked 5 and 95 . When this thermometer reads 68 , the correct temperature in celsius is (a) \(68^{\circ} \mathrm{C}\) (b) \(70^{\circ} \mathrm{C}\) (c) \(66^{\circ} \mathrm{C}\) (d) \(72^{\circ} \mathrm{C}\)

The triple point of neon and carbon dioxide are \(24.57 \mathrm{~K}\) and \(216.55 \mathrm{~K}\) respectively. These temperatures on the celsius and fahrenheit scales are respectively [NCERT] (a) \(-415.44^{\circ} \mathrm{F}\) and \(-69.88^{\circ} \mathrm{F}\) (b) \(415.44^{\circ} \mathrm{F}\) and \(69.88^{\circ} \mathrm{F}\) (c) \(-315.44^{\circ} \mathrm{F}\) and \(69.8 \mathrm{~F}^{\circ} \mathrm{F}\) (d) \(-69.88^{\circ} \mathrm{F}\) and \(415.44^{\circ} \mathrm{F}\)

The Fahrenheit and Kelvin scales of temperature will give the same reading at (a) \(-40\) (b) 313 (c) 574,25 (d) \(732.75\)

An amount of water of mass \(20 \mathrm{~g}\) at \(0^{\circ} \mathrm{C}\) is mixed with 40 \(\mathrm{g}\) of water at \(10^{\circ} \mathrm{C}\), final temperature of the mixture is (a) \(5^{\circ} \mathrm{C}\) (b) \(0^{\circ} \mathrm{C}\) (c) \(20^{\circ} \mathrm{C}\) (d) \(6.66^{\circ} \mathrm{C}\)

The rate of cooling at \(600 \mathrm{~K}\), if surrounding temperature is \(300 \mathrm{~K}\) is \(R\). The rate of cooling at \(900 \mathrm{~K}\) is (a) \(\frac{16}{3} R\) (b) \(2 \underline{R}\) (c) \(3 \underline{R}\) (d) \(\frac{2}{3} R\)

The temperature of a piece of metal is increased from \(27^{\circ} \mathrm{C}\) to \(84^{\circ} \mathrm{C}\). The rate at which energy is radiated is increased to (a) four times (b) two times (c) six times (d) eight times

One gram of ice is mixed with one gram of steam. At thermal equilibrium the temperature of mixture is (a) \(0^{\circ} \mathrm{C}\) (b) \(100^{\circ} \mathrm{C}\) (c) \(55^{\circ} \mathrm{C}\) (d) \(80^{\circ} \mathrm{C}\)

The temperature of a piece of metal is increased from \(27^{\circ} \mathrm{C}\) to \(84^{\circ} \mathrm{C}\). The rate at which energy is radiated is increased to (a) four times (b) two times (c) six times (d) eight times

If the ratio of densities of two substances is \(5: 6\) and that of the specific heats is \(3: 5\). Then, the ratio between heat capacities per unit volume is (a) \(1: 1\) (b) \(2: 1\) (c) \(1: 2\) (d) \(1: 3\)

Heat capacity of a substance is infinite. It means (a) heat is given out (b) heat is taken in (c) no change in temperature whether heat is taken in or given out (d) All of the above

Two cylindrical conductors \(A\) and \(B\) of same metallic material have their diameters in the ratio \(1: 2\) and lengths in the ratio \(2: 1\). If the temperature difference between their ends is same, the ratio of heat conducted respectively by \(A\) and \(B\) per second is (a) \(1: 2\) (b) \(1: 4\) (c) \(1: 16\) (d) \(1: 8\)

A cylinder containing an ideal gas is in vertical position and has a piston of mass \(M\) that is able to move up or down without friction. If the temperature is increased. \(\quad\) |NCERT Exemplar] (a) both \(p\) and \(V\) of the gas will change (b) only \(p\) will increases according to Charles' law (c) \(V\) will change but not \(p\) (d) \(p\) will change but \(\operatorname{not} V\)

Water falls from a height of \(500 \mathrm{~m}\). What is the rise in temperature of water at the bottom if whole energy is used up in heating water ? (a) \(0.96^{\circ} \mathrm{C}\) (b) \(1.02^{\circ} \mathrm{C}\) (c) \(1.16^{\circ} \mathrm{C}\) (d) \(0.23^{*} \mathrm{C}\)

A lead bullet of \(10 \mathrm{~g}\) travelling at \(300 \mathrm{~ms}^{-1}\) strikes against a block of wood comes to rest. Assuming \(50 \%\) of heat is absorbed by the bullet, the increase in its temperature is (Specific heat of lead \(=150 \mathrm{JkgK}^{-1}\) ) (a) \(100^{\circ} \mathrm{C}\) (b) \(125^{\circ} \mathrm{C}\) (c) \(150^{\circ} \mathrm{C}\) (d) \(200^{\circ} \mathrm{C}\)

The ends of 2 different materials with their thermal conductivities, radii of cross-section and length all in the ratio of \(1: 2\) maintained at temperature difference. If the rate of the flow of heat in the longer rod is \(4 \mathrm{cals}^{-1}\), that in the shorter rod in cals \(^{-1}\) will be (a) (b) 2 (c) \(\underline{8}\) (d) 6

Which one of the following would raise the temperature of \(20 \mathrm{~g}\) of water at \(30^{\circ} \mathrm{C}\) most when mixed with it? (a) \(20 \mathrm{~g}\) of water at \(40^{\circ} \mathrm{C}\) (b) \(40 \mathrm{~g}\) of water at \(35^{\circ} \mathrm{C}\) (c) \(10 \mathrm{~g}\) of water at \(50^{\circ} \mathrm{C}\) (d) \(4 \mathrm{~g}\) of water at \(80^{\circ} \mathrm{C}\)

A sphere, a cube and a thin circular plate, all of same material and same mass are initialy heated to same high temperature, \(\quad\) [NCERT Exemplar] (a) Plate will cool fasted and cube the slowest (b) Sphere will cool fasted and cube the slowest (c) Plate will cool fasted and sphere the slowest (d) Cube will cool fastest and plate the slowest

A bimetallic strip consists of brass and iron when it is heated it bends into an arc with brass on the convex and iron on the concave side of the arc. This happens because (a) brass has a higher specific heat capacity than iron (b) density of brass is more than that of iron (c) it is easier to bend an iron strip than a brass strip of the same size (d) brass has a higher coefficient of linear expansion than iron

When the room temperature becomes equal to the dew point the relative humidity of the room is (a) \(100 \%\) (b) \(0^{96}\) (c) 7096 (d) \(85 \%\)

The efficiency of a Carnot engine is \(50 \%\) and temperature of sink is \(500 \mathrm{~K}\). If temperature of source is kept constant and its efficiency raised to \(60 \%\), then the required temperature of sink will be (a) \(100 \mathrm{~K}\) (b) \(600 \mathrm{~K}\) (c) \(400 \mathrm{~K}\) (d) \(500 \mathrm{~K}\)

The efficiency of a Carnot engine is \(50 \%\) and temperature of sink is \(500 \mathrm{~K}\). If temperature of source is kept constant and its efficiency raised to \(60 \%\), then the required temperature of sink will be (a) \(100 \mathrm{~K}\) (b) \(600 \mathrm{~K}\) (c) \(400 \mathrm{~K}\) (d) \(500 \mathrm{~K}\)

As the temperature is increased, the time period of a pendulum (a) increases as its effective length increases even though its centre of mass still remains at the centre of the bob (b) decreases as its effective length increases even though its centre of mass still remains at the centre of the bob (c) increases as its effective length increases due to shifting of centre of mass below the centre of the bob (d) decreases as its effective length increases remains same but the centre of mass shifts above the centre of the bob

A flask of volume \(10^{3} \mathrm{cc}\) is completely filled with mercury at \(0^{\circ} \mathrm{C}\). The coefficient of cubical expansion of mercury is \(1.80 \times 10^{-6}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) and that of glass is \(1.4 \times 10^{-6} \mathrm{C}^{-1}\). If the flask is now placed in boiling water at \(100^{\circ} \mathrm{C}\), how much mercury will overflow? (a) \(7 \mathrm{cc}\) (b) \(1.4 \mathrm{cc}\) (c) \(21 \mathrm{cc}\) (d) \(28 \mathrm{cc}\)

What should be the lengths of a steel and copper rod at \(0^{\circ} \mathrm{C}\) so that the length of the steel rod is \(5 \mathrm{~cm}\) longer than the copper rod at any temperature? $$ \begin{aligned} &\alpha(\text { Steel })=1.1 \times 10^{-5}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1} \\ &\alpha(\text { Copper })=1.7 \times 10^{-5} \mathrm{C} \end{aligned} $$ (a) \(14.17 \mathrm{~cm} ; 9.17 \mathrm{~cm}\) (b) \(9.17 \mathrm{~cm}, 14.17 \mathrm{~cm}\) (c) \(28.34 \mathrm{~cm} ; 18.34 \mathrm{~cm}\) (d) \(14.17 \mathrm{~cm}, 18.34 \mathrm{~cm}\)

A flask of volume \(10^{3} \mathrm{cc}\) is completely filled with mercury at \(0^{\circ} \mathrm{C}\). The coefficient of cubical expansion of mercury is \(1.80 \times 10^{-6}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) and that of glass is \(1.4 \times 10^{-6} \mathrm{C}^{-1}\). If the flask is now placed in boiling water at \(100^{\circ} \mathrm{C}\), how much mercury will overflow? (a) \(7 \mathrm{cc}\) (b) \(1.4 \mathrm{cc}\) (c) \(21 \mathrm{cc}\) (d) \(28 \mathrm{cc}\)

When a liquid in a glass vessel is heated, its apparent expansion is \(10.30 \times 10^{-4} \mathrm{C}^{-1}\). When the same liquid is heated in a metal vessel, its apparent expansion is \(10.06 \times 10^{-4}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\). If the coefficient of linear expansion of glass \(=9 \times 10^{6}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\), what is the coefficient of linear expansion of metal? (a) \(51 \times 10^{-6} \circ \mathrm{c}^{-1}\) (b) \(17 \times 10^{-6}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) (c) \(25 \times 10^{-60} \mathrm{C}^{-1}\) (d) \(43 \times 10^{-6 \circ} \mathrm{C}^{-1}\)

Density of substance at \(0^{\circ} \mathrm{C}\) is \(10 \mathrm{~g} / \mathrm{cc}\) and at \(100^{\circ} \mathrm{C}\), its density is \(9.7 \mathrm{~g} / \mathrm{cc}\). The coefficient of linear expansion of the substance is (a) \(1.03 \times 10^{-4} \mathrm{C}^{-1}\) (b) \(3 \times 10^{-4}{\underline{\phantom{xx}}}^{-4} \mathrm{C}^{-1}\) (c) \(19.7 \times 10^{-3 *} \mathrm{C}^{-1}\) (d) \(10^{-3}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\)

A child running at a temperature of \(101^{\circ} \mathrm{F}\) is given an antipyrin (i.e., medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to \(98^{\circ} \mathrm{F}\) in \(20 \mathrm{~min}\), what is the average rate of extra evaporation caused by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of child is \(30 \mathrm{~kg}\). The specific heat of the human body is approximately the same as that of water and latent heat of evaporation of water at that temperature is about \(580 \mathrm{cal} / \mathrm{g}\). (a) \(4.31 \mathrm{~g} / \mathrm{min}\) (b) \(4.31 \mathrm{~g} / \mathrm{s}\) (c) \(2.31 \mathrm{~g} / \mathrm{min}\) (d) \(2.31 \mathrm{~g} / \mathrm{s}\)

A rectangular block is heated from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). The percentage increase in its length is \(0.2 \%\). What is the percentage increase in its volume? (a) \(0.696\) (b) \(0.1096\) (c) \(0.2 \%\) (d) \(0.496\)

A wheel is \(80.3 \mathrm{~cm}\) in circumference. An iron tyre measures \(80.0 \mathrm{~cm}\) around its inner face. If the coefficient of linear expansion for iron is \(1.2 \times 0^{-5}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\), the temperature of the tyre must be raised by (a) \(105^{\circ} \mathrm{C}\) (b) \(417^{\circ} \mathrm{C}\) (c) \(312^{+} \mathrm{C}\) (d) \(223^{\circ} \mathrm{C}\)

A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \(500 \mathrm{~ms}^{-1}\) in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground [NCERT Exemplar]

The temperature gradient in the earth's crust is \(32^{\circ} \mathrm{C} \mathrm{km}^{-1}\) and the mean conductivity of earth is \(0.008 \mathrm{cals}^{-1} \mathrm{~cm}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\). Considering earth to be a sphere of radius \(6000 \mathrm{~km}\) loss of heat by earth everyday is about (a) \(10^{30} \mathrm{cal}\) (b) \(10^{40} \mathrm{cal}\) (c) \(10^{20} \mathrm{cal}\) (d) \(10^{18} \mathrm{cal}\)

A metal rod having linear expansion coefficient \(2 \times 10^{-5}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) has a length of \(1 \mathrm{~m}\) at \(20^{\circ} \mathrm{C}\). The temperature at which it is shortened by \(1 \mathrm{~mm}\) is (a) \(-20^{\circ} \mathrm{C}\) (b) \(-15^{\circ} \mathrm{C}\) (c) \(-30^{\circ} \mathrm{C}\) (d) \(-25^{\circ} \mathrm{C}\)

A bimetallic strip is made of aluminium and steel \(\left(\alpha_{\mathrm{N}}>\alpha_{\text {ateel }}\right) .\) On heating, the strip will [NCERT Exemplar] (a) remain straight (b) get twisted (c) will bend with aluminium on concave side (d) will bend with steel on concave side

A metal ball immersed in water weighs \(w_{1}\) at \(0^{\circ} \mathrm{C}\) and \(w_{2}\) at \(50^{\circ} \mathrm{C}\). The coefficient of cubical expansion of metal is less than that of water. Then (a) \(w_{1}w_{2}\) (c) \(w_{1}=w_{2}\) (d) data is not sufficient

A bimetallic is made of two strips \(A\) and \(B\) having coefficients of linear expansion \(\alpha_{A}\) and \(\alpha_{B}\). If \(\alpha_{A}<\alpha_{B}\), then on heating, the strip will (a) bend with \(A\) on outer side (b) bend with \(B\) on outer side (c) not bend at all (d) None of the above

A cylinder of radius \(r\) and thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of linear radius \(r\) and outer radius \(2 r\), whose thermal conductivity is \(K_{2}\). There is no loss of heat across cylindrical surfaces, when the ends of the combined system are maintained at temperatures \(T_{1}\) and \(T_{2}\). The effective thermal conductivity of the system, in the steady state is (a) \(\frac{K_{1} K_{1}}{K_{1}+K_{2}}\) (b) \(K_{1}+K_{2}\) (c) \(\frac{K_{1}+3 K_{2}}{4}\) (d) \(\frac{3 K_{1}+K_{2}}{4}\)

A cylinder of radius \(r\) and thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of linear radius \(r\) and outer radius \(2 r\), whose thermal conductivity is \(K_{2}\). There is no loss of heat across cylindrical surfaces, when the ends of the combined system are maintained at temperatures \(T_{1}\) and \(T_{2}\). The effective thermal conductivity of the system, in the steady state is (a) \(\frac{K_{1} K_{1}}{K_{1}+K_{2}}\) (b) \(K_{1}+K_{2}\) (c) \(\frac{K_{1}+3 K_{2}}{4}\) (d) \(\frac{3 K_{1}+K_{2}}{4}\)

A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly (a) its speed of rotation increases (b) its speed of rotation decreases (c) its speed of rotation remains same (d) its speed increases because its moment of inertia increases

The power radiated by a black body is \(P\), and it radiates maximum energy around the wavelength \(\lambda_{0}\). If the temperature of black body is now changed so that it radiates maximum energy around a wavelength \(\lambda_{0} / 4\), the power radiated by it will increase by a factor of (a) \(\frac{4}{3}\) (b) \(\frac{16}{9}\) (c) \(\frac{64}{27}\) (d) \(\frac{256}{81}\)

\(22 \mathrm{~g}\) of carbon dioxide at \(27^{\circ} \mathrm{C}\) is mixed in a closed container with \(16 \mathrm{~g}\) of oxygen at \(37^{\circ} \mathrm{C}\). If both gases are considered as ideal gases, then the temperature of the mixture is (a) \(24.2^{\circ} \mathrm{C}\) (b) \(28.5^{\circ} \mathrm{C}\) (c) \(31.5^{\circ} \mathrm{C}\) (d) \(33.5^{\circ} \mathrm{C}\)

A bar of iron is \(10 \mathrm{~cm}\) at \(20^{\circ} \mathrm{C}\). At \(19^{\circ} \mathrm{C}\) it will be \((\alpha\) of iron \(\left.=11 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) (a) \(11 \times 10^{-6} \mathrm{~cm}\) longer (b) \(11 \times 10^{-6} \mathrm{~cm}\) shorter (c) \(11 \times 10^{-5} \mathrm{~cm}\) shorter (d) \(11 \times 10^{-5} \mathrm{~cm}\) longer

A bar of iron is \(10 \mathrm{~cm}\) at \(20^{\circ} \mathrm{C}\). At \(19^{\circ} \mathrm{C}\) it will be \((\alpha\) of iron \(\left.=11 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) (a) \(11 \times 10^{-6} \mathrm{~cm}\) longer (b) \(11 \times 10^{-6} \mathrm{~cm}\) shorter (c) \(11 \times 10^{-5} \mathrm{~cm}\) shorter (d) \(11 \times 10^{-5} \mathrm{~cm}\) longer

The volume of a metal sphere increases by \(0.24 \%\) when its temperature is raised by \(40^{\circ} \mathrm{C}\). The coefficient of linear expansion of the metal is ... \({ }^{\circ} \mathrm{C}\). (a) \(2 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\) (b) \(6 \times 10^{-5}\) per \(^{\circ} \mathrm{C}\) (c) \(2.1 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\) (d) \(1.2 \times 10^{-5} \mathrm{per}^{\circ} \mathrm{C}\)

\(8 \mathrm{~g}\) of \(\mathrm{O}_{2}, 14 \mathrm{~g}\) of \(\mathrm{N}_{2}\) and \(22 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) is mixed in a container of \(10 \mathrm{~L}\) capacity at \(27^{\circ} \mathrm{C}\). The pressure exerted by the mixture in terms of atmospheric pressure is \(\left(R=0.082 \mathrm{~L}\right.\) atm \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) ) (a) \(1.4 \mathrm{~atm}\) (b) \(2.5 \mathrm{~atm}\) (c) \(3.7 \mathrm{~atm}\) (d) \(8.7 \mathrm{~atm}\)

A wall has two layers \(A\) and \(B\), made of two different materials. The thermal conductivity of material \(A\) is twice that of \(B\). If the two layers have same thickness and under thermal equilibrium, the temperature difference across the wall is \(48^{\circ} \mathrm{C}\), the temperature difference across layer \(B\) is (a) \(40^{\circ} \mathrm{C}\) (b) \(32^{\circ} \mathrm{C}\) (c) \(16^{\circ} \mathrm{C}\) (d) \(24^{\circ} \mathrm{C}\)

Inside a cylinder closed at both ends is a movable piston. On one side of the piston is a mass \(m\) of a gas, and on the other side a mass \(2 m\) of the same gas. What fraction of the volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? The temperature is the same throughout. (a) \(\frac{2}{3}\) (b) \(\frac{1}{3}\) (c) \(\frac{1}{2}\) (d) \(\frac{1}{4}\)

Inside a cylinder closed at both ends is a movable piston. On one side of the piston is a mass \(m\) of a gas, and on the other side a mass \(2 m\) of the same gas. What fraction of the volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? The temperature is the same throughout. (a) \(\frac{2}{3}\) (b) \(\frac{1}{3}\) (c) \(\frac{1}{2}\) (d) \(\frac{1}{4}\)

Two moles of monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of the mixture at constant volume is (a) \(1.55 R\) (b) \(2.10 R\) (c) \(1.63 R\) (d) \(2.20 R\)