Chapter 13

When a bimetallic strip is heated, it (a) does not bend at all (b) gets twisted in the form of an helix (c) bend in the form of an arc with the more expandable metal outside (d) bends in the form of an arc with the more expandable metal inside

The coefficient of apparent expansion of mercury in a glass vessel is \(153 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) and in a steel vessel is \(144 \times 10^{6} /{ }^{\circ} \mathrm{C}\). If \(\alpha\) for steel is \(12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), then that of glass is (a) \(9 \times 10^{-6} /^{-} \mathrm{C}\) (b) \(6 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) (c) \(36 \times 10^{-6} /{ }^{\prime} \mathrm{C}\) (d) \(27 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)

Solids expand on heating because (a) kinetic energy of the atoms increases (b) potential energy of the atoms increases (c) total energy of the atoms increases (d) the potential energy curve is asymmetric about the equilibrium distance between neighbouring atoms

Two rods of equal length and area of cross-section are kept parallel and lagged between temperatures \(20^{\circ} \mathrm{C}\) and \(80^{\circ} \mathrm{C}\). The ratio of the effective thermal conductivity to that of the first rod is \(\left[\right.\) the ratio \(\left.\left(\frac{K_{1}}{K_{2}}\right)=\frac{3}{4}\right]\) (a) \(7: 4\) (b) \(7: 6\) (c) \(4: 7\) (d) \(7: 8\)

An iron tyre is to be fitted on a wooden wheel \(1 \mathrm{~m}\) in diameter. The diameter of tyre is \(6 \mathrm{~mm}\) smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is \(3.6 \times 10^{-5} /{ }^{\circ} \mathrm{C}\) (a) \(167^{\circ} \mathrm{C}\) (b) \(334^{\circ} \mathrm{C}\) (c) \(500^{\circ} \mathrm{C}\) (d) \(1000^{\circ} \mathrm{C}\)

Two rods of same length and material transfer a given amount of heat in \(12 \mathrm{~s}\), when they are joined end to end (i.e., in series). But when they are joined in parallel, they will transfer same heat under same conditions in (a) 245 (b) \(3 \underline{5}\) (c) \(48 \mathrm{~s}\) (d) \(1.5 \mathrm{~s}\)

A glass flask of volume one litre at \(0^{\circ} \mathrm{C}\) is filled, level full of mercury at this temperature. The flask and mercury are now heated to \(100^{\circ} \mathrm{C}\). How much mercury will spill out, if coefficient of volume expansion of mercury is \(1.82 \times 10^{-4} /{ }^{\circ} \mathrm{C}\) and linear expansion of glass is \(0.1 \times 10^{-4} /{ }^{\circ} \mathrm{C}\) respectively? (a) \(21.2 \mathrm{cc}\) (b) \(15.2 \mathrm{cc}\) [c) \(1.52 \mathrm{cc}\) (d) \(2.12 \mathrm{cc} \mathrm{c}\)

A steel scale measures the length of a copper wire as \(80.0 \mathrm{~cm}\), when both are at \(20^{\circ} \mathrm{C}\) (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at \(40^{\circ} \mathrm{C}\) ? (Given \(\alpha_{\text {nteel }}=11 \times 10^{-6}\) per \(^{\circ} \mathrm{C}\) and \(\alpha_{\text {copper }}=17 \times 10^{-6}\) per \(^{\circ} \mathrm{C}\) ) (a) \(80.0096 \mathrm{~cm}\) (b) \(80.0272 \mathrm{~cm}\) (c) \(1 \mathrm{~cm}\) (d) \(25.2 \mathrm{~cm}\)

A steel scale measures the length of a copper wire as \(80.0 \mathrm{~cm}\), when both are at \(20^{\circ} \mathrm{C}\) (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at \(40^{\circ} \mathrm{C}\) ? (Given \(\alpha_{\text {nteel }}=11 \times 10^{-6}\) per \(^{\circ} \mathrm{C}\) and \(\alpha_{\text {copper }}=17 \times 10^{-6}\) per \(^{\circ} \mathrm{C}\) ) (a) \(80.0096 \mathrm{~cm}\) (b) \(80.0272 \mathrm{~cm}\) (c) \(1 \mathrm{~cm}\) (d) \(25.2 \mathrm{~cm}\)

Two metal strips that constitute a thermostat must necessarily differ in their (a) mass (b) length [c) resistivity (d) coefficient of linear expansion

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of \(0.1 \mathrm{~g}\) of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of the material of the second rod is \(1 / 4\) that of the first, the rate at which ice melts in \(\mathrm{gs}^{-1}\) will be (a) \(3.2\) (b) \(1.6\) (c) \(0.2\) (d) \(0.1\)

A metal ball immersed in alcohol weighs \(w_{1}\) at \(0^{\circ} \mathrm{C} \quad \overline{5}\) and \(w_{2}\) at \(59^{\circ} \mathrm{C}\). The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol, it can be shown that (a) \(w_{1}>w_{2}\) (b) \(w_{1}=w_{2}\) (c) \(w_{1}

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of \(0.1 \mathrm{~g}\) of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of the material of the second rod is \(1 / 4\) that of the first, the rate at which ice melts in \(\mathrm{gs}^{-1}\) will be (a) \(3.2\) (b) \(1.6\) (c) \(0.2\) (d) \(0.1\)

A metal ball immersed in alcohol weighs \(w_{1}\) at \(0^{\circ} \mathrm{C} \quad \overline{5}\) and \(w_{2}\) at \(59^{\circ} \mathrm{C}\). The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol, it can be shown that (a) \(w_{1}>w_{2}\) (b) \(w_{1}=w_{2}\) (c) \(w_{1}

Two rods \(P\) and \(Q\) have equal lengths. Their thermal conductivities are \(K_{1}\) and \(K_{2}\) and cross-sectional areas are \(A_{1}\) and \(A_{2}\). When the temperature at ends of each rod are \(T_{1}\) and \(T_{2}\) respectively, the rate of flow of heat through \(P\) and \(Q\) will be equal, if (a) \(\frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}}\) (b) \(\frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}} \times \frac{T_{2}}{T_{1}}\) (c) \(\frac{A_{1}}{A_{2}}=\sqrt{\frac{K_{1}}{K_{2}}}\) (d) \(\frac{A_{1}}{A_{2}}=\left(\frac{K_{1}}{K_{1}}\right)^{2}\)

It is known that wax contracts on solidification. If molten wax is taken in a large vessel and it is allowed to cool slowly, then (a) it will start solidifying from the top to downward (b) it will starts solidifying from the bottom to upward (c) it will start solidifying from the middle, upward and downward at equal rates (d) the whole mass will solidify simultaneously

The amount of heat conducted out per second through a window, when inside temperature is \(10^{\circ} \mathrm{C}\) and outside temperature is \(-10^{\circ} \mathrm{C}\), is \(1000 \mathrm{~J} .\) Same heat will be conducted in through the window, when outside temperature is \(-23^{\circ} \mathrm{C}\) and inside temperature is (a) \(23^{\circ} \mathrm{C}\) (b) \(230 \mathrm{~K}\) (c) \(270 \mathrm{~K}\) (d) \(296 \mathrm{~K}\)

A substance of mass \(m \mathrm{~kg}\) requires a power input of \(P\) watts to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time \(t\) sec. What is the latent heat of fusion of the substance? (a) \(\frac{P m}{t}\) (b) \(\frac{P t}{m}\) (c) \(\frac{m}{P t}\) (d) \(\frac{t}{P m}\)

The ratio of thermal conductivity of two rods is \(5: 4\). The ratio of their cross-sectional areas is \(1: 1\) and they have the same thermal resistances. The ratio of their lengths, must will be (a) \(4: 5\) (b) \(9: 1\) (c) \(1: 9\) (d) \(5: 4\)

In heat transfer which method is based on gravitation (a) Natural convection (b) Conduction (c) Radiation (d) Stirrling of liquid

\(2 \mathrm{~kg}\) of ice at \(-20^{\circ} \mathrm{C}\) is mixed with \(5 \mathrm{~kg}\) of water at \(20^{\circ} \mathrm{C}\) in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are \(1 \mathrm{kcal} / \mathrm{kg}\) per \(^{\circ} \mathrm{C}\) and \(0.5 \mathrm{kcal} / \mathrm{kg} /{ }^{\circ} \mathrm{C}\) while the latent heat of fusion of ice is \(80 \mathrm{kcal} / \mathrm{kg}\). (a) \(7 \mathrm{~kg}_{1}\) (b) \(6 \mathrm{~kg}\) (c) \(4 \mathrm{~kg}\) (d) \(2 \mathrm{~kg}\)

If a liquid is heated in weightlessness the heat is transmitted through (a) conduction (b) convection (c) radiation (d) neither because the liquid cannot be heated in weightlessness

Water of volume \(2 \mathrm{~L}\) in a container is heated with a coil of \(1 \mathrm{~kW}\) at \(27^{\circ} \mathrm{C}\). The lid of the container is open and energy dissipates at rate of \(160 \mathrm{~J} / \mathrm{s}\). In how much time temperature will rise from \(27^{\circ} \mathrm{C}\) to \(77^{\circ} \mathrm{C}\) ? [Given specific heat of water is \(4.2 \mathrm{~kJ} / \mathrm{kg}\) ] (a) \(8 \min 20 \mathrm{~s}\) (b) \(6 \min 2 \mathrm{~s}\) (c) 7 min (d) \(14 \mathrm{~min}\)

A polished metal plate with a rough black spot on it is heated to about \(1400 \mathrm{~K}\) and quickly taken to a dark room. The spot will appear (a) darker than plate (b) brighter than plate (c) equally bright (d) equally dark

The temperature of equal masses of three different liquids \(A, B\) and \(C\) are \(12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C}\) and \(28^{\circ} \mathrm{C}\) respectively. The temperature when \(A\) and \(B\) are mixed is \(16^{\circ} \mathrm{C}\) and when \(B\) and \(C\) are mixed is \(23^{\circ} \mathrm{C}\). The temperature when \(A\) and \(C\) are mixed, is (a) \(18.2^{\circ} \mathrm{C}\) (b) \(22^{\circ} \mathrm{C}\) (c) \(20.2^{\circ} \mathrm{C}\) (d) \(25.2^{\circ} \mathrm{C}\)

The rate of radiation of a black body at \(0^{\circ} \mathrm{C}\) is \(E\) watt. The rate of radiation of this body at \(273^{\circ} \mathrm{C}\) will be (a) \(16 \bar{E}\) (b) \(8 E\) (c) \(4 \underline{E}\) (d) \(E\)

In an industrial process \(10 \mathrm{~kg}\) of water per hour is to be heated from \(20^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\). To do this steam at \(150^{\circ} \mathrm{C}\) is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at \(90^{\circ} \mathrm{C}\). How many kg of steam is required per hour? (Specific heat of steam \(=1\) calorie per \(\mathrm{g}^{\circ} \mathrm{C}\), Latent heat of vaporisation \(=540 \mathrm{cal} / \mathrm{g}\) ) (a) \(1 \mathrm{~g}\) (b) \(1 \mathrm{~kg}\) (c) \(10 \mathrm{~g}\) (d) \(10 \mathrm{~kg}\)

The temperature of a black body is increased by \(50 \%\), then the percentage of increase of radiation is approximately (a) \(100 \%\) (b) \(25 \%\) (c) \(400 \%\) (d) \(500 \%\)

The coefficient of linear expansion of crystal in one direction is \(a_{1}\) and that in every direction perpendicular to it is \(a_{2} .\) The coefficient of cubical expansion is (a) \(\alpha_{1}+\alpha_{2}\) (b) \(2 \alpha_{1}+\alpha_{2}\) (c) \(\alpha_{2}+2 \alpha_{2}\) (d) None of these

A body cools from \(80^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) in \(5 \mathrm{~min} .\) Calculate the time it takes to cool from \(60^{\circ} \mathrm{C}\) to \(30^{\circ} \mathrm{C}\). The temperature of the surroundings is \(20^{\circ} \mathrm{C}\). [NCERT] (a) \(9 \mathrm{~min}\) (b) \(7 \mathrm{~min}\) (c) \(8 \mathrm{~min}\) (d) \(10 \mathrm{~min}\)

Three rods of equal length \(l\) are joined to form an equilateral triangle \(P Q R . O\) is the mid point of \(P Q\). Distance \(O R\) remains same for small change in temperature. Coefficient of linear expansion for \(P R\) and \(R Q\) is same, i.e., \(\alpha_{2}\) but that for \(P Q\) is \(\alpha_{1}\). Then (a) \(\alpha_{2}=3 \alpha_{1}\) (b) \(\alpha_{2}=4 \alpha_{1}\) (c) \(\alpha_{1}=3 \alpha_{2}\) (d) \(\alpha_{1}=4 \alpha_{2}\)

If wavelength of maximum intensity of radiation emitted by sun and moon are \(0.5 \times 10^{-6} \mathrm{~m}\) and \(10^{-4} \mathrm{~m}\) respectively, the ratio of their temperatures is (a) \(1: 100\) (b) \(1: 200\) (c) \(200: 1\) (d) \(400: 1\)

A copper block of mass \(2.5 \mathrm{~kg}\) is heated in furnace to a temperature of \(500^{\circ} \mathrm{C}\) and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper \(=039 \mathrm{~J} / \mathrm{g}-\mathrm{K} ;\) heat of fusion of water \(=335 \mathrm{~J} / \mathrm{g}\) ) (a) \(25 \mathrm{~kg}\) (b) \(15 \mathrm{~kg}\) (c) \(9 \mathrm{~kg}\) (d) \(13 \mathrm{~kg}\)

The maximum energy in the thermal radiation from a hot source occurs at \(\lambda=11 \times 10^{-5} \mathrm{~cm}\). If temperature of another source is n times, for which wavelength of maximum energy is \(5.5 \times 10^{-5} \mathrm{~cm}\), then \(n\) is (a) 2 (b) 4 (c) \(\frac{1}{2}\) (d) 1

A black body radiates at two temperatures \(T_{1}\) and \(T_{2}\), such that \(T_{1}

Steam is passed into \(22 \mathrm{~g}\) of water at \(20^{\circ} \mathrm{C}\). The mass of water that will be present when the water acquires a temperature of \(90^{\circ} \mathrm{C}\) (Latent heat of steam is \(540 \mathrm{cal} / \mathrm{g}\) ) is (a) \(24.8 \mathrm{~g}\) (b) \(24 \mathrm{~g}\) (c) \(36.6 \mathrm{~g}\) (d) \(30 \mathrm{~g}_{1}\)

An object is cooled from \(75^{\circ} \mathrm{C}\) to \(65^{\circ} \mathrm{C}\) in 2 min in a room at \(30^{\circ} \mathrm{C}\). The time taken to cool another identical object from \(55^{\circ} \mathrm{C}\) to \(45^{\circ} \mathrm{C}\) in the same room, in minutes is (a) 4 (b) 5 (c) 6 (d) 7

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then, the pressure in the compartment is (a) same everywhere (b) lower in front side (c) lower in rear side (d) lower in upper side

A black body at \(1373^{\circ} \mathrm{C}\) emits maximum energy corresponding to a wavelength of \(1.78\) micron. The temperature of moon for which \(\lambda_{m}=14\) micron would be (a) \(62.6^{\circ} \mathrm{C}\) (b) \(-58.9^{\circ} \mathrm{C}\) (c) \(63.7^{\circ} \mathrm{C}\) (d) \(64.2^{\circ} \mathrm{C}\)

A room is maintained at \(20^{\circ} \mathrm{C}\) by a heater of resistance \(20 \Omega\) connected to \(200 \mathrm{~V}\) mains. The temperature is uniform throughout the room and heat is transmitted through a glass window of area \(1 \mathrm{~m}^{2}\) and thickness \(0.2 \mathrm{~cm}\). What will be the temperature outside? Given that thermal conductivity \(K\) for glass is \(0.2 \mathrm{cal} / \mathrm{m} /{ }^{\circ} \mathrm{C}\) sec and \(J=4.2 \mathrm{~J} / \mathrm{cal}\) (a) \(15.24^{\circ} \mathrm{C}\) (b) \(15.00^{\circ} \mathrm{C}\) (c) \(24.15^{\circ} \mathrm{C}\) (d) None of these

There is formation of layer of snow \(x \mathrm{~cm}\) thick on water, when the temperature of air is \(-\theta^{\circ} \mathrm{C}\) (less than freezing point). The thickness of layer increases from \(x\) to \(y\) in the time \(t\), then the value of \(t\) is given by (a) \(\frac{(x+y)(x-y) \rho L}{2 k \theta}\) (b) \(\frac{(x-y) \rho L}{2 k \theta}\) (c) \(\frac{(x+y)(x-y) \rho L}{k \theta}\) (d) \(\frac{(x-y) \rho L k}{2 \theta}\)

The rectangular surface of area \(8 \mathrm{~cm} \times 4 \mathrm{~cm}\) of a black body at a temperature of \(127^{\circ} \mathrm{C}\) emits energy at the rate of \(E\) per second. If the length and breadth of the surface are each reduced to half of its initial value, and the temperature is raised to \(327^{\circ} \mathrm{C}\), the rate of emission of energy will become (a) \(\frac{3}{8} E_{1}\) (b) \(\frac{81}{16} E\) (c) \(\frac{9}{16} E\) (d) \(\frac{81}{64} E\)

The rectangular surface of area \(8 \mathrm{~cm} \times 4 \mathrm{~cm}\) of a black body at a temperature of \(127^{\circ} \mathrm{C}\) emits energy at the rate of \(E\) per second. If the length and breadth of the surface are each reduced to half of its initial value, and the temperature is raised to \(327^{\circ} \mathrm{C}\), the rate of emission of energy will become (a) \(\frac{3}{8} E_{1}\) (b) \(\frac{81}{16} E\) (c) \(\frac{9}{16} E\) (d) \(\frac{81}{64} E\)

A composite metal bar of uniform section is made up of length \(25 \mathrm{~cm}\) of copper, \(10 \mathrm{~cm}\) of nickel and \(15 \mathrm{~cm}\) of aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at \(100^{\circ} \mathrm{C}\) and the aluminium end at \(0^{\circ} \mathrm{C}\). The whole rod is covered with belt so that no heat loss occurs at the side. If \(K_{\mathrm{Cu}}=2 K_{\mathrm{Al}}\) and \(K_{\mathrm{Al}}=3 K_{\mathrm{Ni}}\), then what will be the temperatures of \(\quad\) Cu-Ni and Ni-Al junctions repectively \begin{tabular}{|c|c|c|} \hline \(\mathrm{Cu}\) & \(\mathrm{Ni}\) & \(\mathrm{Al}\) \\ \hline \(100^{\circ} \mathrm{C}\) & & \(0^{\circ} \mathrm{C}\) \end{tabular} (a) \(23.33^{\circ} \mathrm{C}\) and \(78.8^{\circ} \mathrm{C}\) (b) \(83.33^{\circ} \mathrm{C}\) and \(\underline{20^{\circ} \mathrm{C}}\) (c) \(50^{\circ} \mathrm{C}\) and \(30^{\circ} \mathrm{C}\) (d) \(30^{\circ} \mathrm{C}\) and \(50^{\circ} \mathrm{C}\)

The only possibility of heat flow in a themros flask is through its cork which is \(75 \mathrm{~cm}^{2}\) in area and \(5 \mathrm{~cm}\) thick its thermal conductivity is \(0.075 \mathrm{cal} / \mathrm{cm} \sec ^{\circ} \mathrm{C}\). The outside temperatue is \(40^{\circ} \mathrm{C}\) and latent heat of ice is \(80 \mathrm{cal} \mathrm{g}^{-1}\). Time taken by \(500 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\) in the flask to melt into water at \(0^{\circ} \mathrm{C}\) is (a) \(2.47 \mathrm{~h}\) (b) \(4.27 \mathrm{~h}\) (c) \(7.42 \mathrm{~h}\) (d) \(4.82 \mathrm{~h}\)

Two identical conducting rods are first connected independently to two vessels, one containing water at \(100^{\circ} \mathrm{C}\) and the other containing ice at \(0^{\circ} \mathrm{C}\). In the second case, the rods are joined end to end and connected to the same vessels. Let \(q_{1}\) and \(q_{2} \mathrm{~g} / \mathrm{s}\) be the rate of melting of ice in two cases respectively. The ratio of \(q_{1} / q_{2}\) is (a) \(1 / 2\) (b) \(2 / 1\) (c) \(4 / 1\) (d) \(1 / 4\)

A liquid is filled in a container which is kept in a room whose temperature is \(20^{\circ} \mathrm{C}\). When temperature of liquid is \(80^{\circ} \mathrm{C}\), it emits heat at the rate of \(45 \mathrm{cals}^{-1}\), When temperature of liquid falls to \(40^{\circ} \mathrm{C}\), its rate of heat loss will be (a) \(15 \mathrm{cals}^{-1}\) (b) \(30 \mathrm{cals}^{-1}\) (c) \(45 \mathrm{cal} \mathrm{s}^{-1}\) (d) \(60 \mathrm{cal}^{-1}\)

A black body is at a temperature of \(2880 \mathrm{~K}\). The energy of radiation emitted by this object with wavelength between \(499 \mathrm{~nm}\) and \(500 \mathrm{~nm}\) is \(U_{1}\), between 999 and \(1000 \mathrm{~nm}\) is \(U_{2}\) and between \(1499 \mathrm{~nm}\) and \(1500 \mathrm{~nm}\) is \(U_{3}\). The Wien's constant \(b=2.88 \times 10^{6} \mathrm{nmK}\). Then (a) \(U_{1}=0\) (b) \(U_{3}=0\) (c) \(U_{1}>U_{2}\) (d) \(U_{2}>U_{1}\)

Two bodies \(A\) and \(B\) are placed in an evacuated vessel maintained at a temperature of \(27^{\circ} \mathrm{C}\). The temperature of \(A\) is \(327^{\circ} \mathrm{C}\) and that of \(B\) is \(227^{\circ} \mathrm{C}\). The ratio of heat loss from \(A\) and \(B\) is about (a) \(2: 1\) (b) \(4: 1\) (c) \(1: 2\) (d) \(1: 4\)

A black metal foil is warmed by radiation from a small sphere at temperature \(T\) and at a distance \(d\). It is found that the power received by the foil is \(P\). If both the temperature and distance are doubled, the power received by the foil will be (a) \(16 P\) (b) \(4 P\) (c) \(2 P\) (d) \(\underline{P}\)