Chapter 15

The temperature at which Centigrade thermometer and Kelvin thermometer gives the same reading, is: (a) \(4^{\circ}\) (b) \(273^{\circ}\) (c) not possible (d) \(0^{\circ}\)

What is the change in the temperature on Fahrenheit scale and on Kelvin scale, if a iron piece is heated from \(30^{\circ}\) to \(90^{\circ} \mathrm{C} ?\) (a) \(108^{\circ} \mathrm{F}, 60 \mathrm{~K}\) (b) \(100^{\circ} \mathrm{F}, 55 \mathrm{~K}\) (c) \(100^{\circ} \mathrm{F}, 65 \mathrm{~K}\) (d) \(60^{\circ} \mathrm{F}, 108 \mathrm{~K}\)

Which of the following carries anomalous expansion ? (a) Mercury (b) Water (c) Copper (d) Sodium

Two thermometers are constructed in such a way that one has a spherical bulb and the other has elongated cylindrical bulb. The bulbs are made of same material and thickness. Then: (a) spherical bulb will respond more quickly to temperature changes (b) cylindrical bulb will respond more quickly to temperature changes. (c) both bulbs will respond same to temperature changes (d) none of both bulbs respond to temperature changes

Mark correct option or options: (a) Sun temperature is measured by radiation pyrometer (b) Insect temperature is measured by thermocouple thermometer (c) Moon's temperature is measured by berthometer (d) All of the above

The temperature of a point in space is given by \(T=\left(x^{2}+y^{2}-z^{2}\right) .\) A mosquito located at \((1,1,2)\) desires to fly in such a direction that it will get heat as soon as possible. Then unit vector is : (b) \(-\frac{2}{3} \hat{1}-\frac{2}{3} \hat{j}+\frac{1}{3}\) (i) \(\frac{2}{3} \hat{i}-\frac{2}{3} \hat{j}-\frac{1}{3}\) (d) none of these

A bird is flying at a speed of \(5 \mathrm{~m} / \mathrm{s}\) in the direction of the vector \(4 \hat{i}+4 \hat{j}-2 \hat{k}\). The temperature of the region is given by \(T=x^{2}+y^{2}-z^{2}\) The rate of increase of temperature per unit time, at the instant it passes through the point \((1,1,2)\) is : (a) \(\frac{60}{3}{\underline{\phantom{xx}}}^{\circ} \mathrm{C} / \mathrm{s}\) (b) \(3^{\circ} \mathrm{C} / \mathrm{s}\) (c) \(18^{\circ} \mathrm{C} / \mathrm{s}\) (d) \(4^{\circ} \mathrm{C} / \mathrm{s}\)

At \(30^{\circ} \mathrm{C}\), the hole in a steel plate has diameter of \(0.99970\) \(\mathrm{cm}\). A cylinder of diameter exactly \(1 \mathrm{~cm}\) at \(30^{\circ} \mathrm{C}\) is to be slide into the hole. To what temperature the plate must be heated ? (Given : \(\alpha_{\text {steel }}=1.1 \times 10^{-5}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) ) (a) \(58^{\circ} \mathrm{C}\) (b) \(55^{\circ} \mathrm{C}\) (c) \(57.3^{\circ} \mathrm{C}\) (d) \(60^{\circ} \mathrm{C}\)

If same amount of heat is supplied to two identical spheres (one is hollow and other is solid), then: (a) the expansion in hollow is greater than the solid (b) the expansion in hollow is same as that in solid (c) the expansion in hollow is lesser than the solid (d) the temperature of both must be same to each other.

At \(20^{\circ} \mathrm{C}\), a steel ruler of \(20 \mathrm{~cm}\) long is graduated to give correct reading, but when it is used at a temperature of \(40^{\circ} \mathrm{C}\), what will be the actual length of the steel ruler? \(\left[\alpha_{\text {stèel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]\) (a) \(22.02 \mathrm{~cm}\) (b) \(19.6 \mathrm{~cm}\) (c) \(20.0048 \mathrm{~cm}\) (d) \(18.0002 \mathrm{~cm}\)

A second's pendulum clock having steel wire is calibrated at \(20^{\circ} \mathrm{C}\). When temperature is increased to \(30^{\circ} \mathrm{C}\), then how much time does the clock lose or gain in one week ? \(\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]\) (a) \(0.3628 \mathrm{~s}\) (b) \(3.626 \mathrm{~s}\) (c) \(362.8 \mathrm{~s}\) (d) \(36.28 \mathrm{~s}\)

A uniform brass disc of radius \(a\) and mass \(m\) is set into spinning with angular speed \(\omega_{0}\) about an axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from \(\theta_{1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}\) to \(\theta_{2}^{\circ} \mathrm{C}\) without disturbing the disc, what will be its new angular speed ? (The coefficient of linear expansion of brass is \(\alpha\) ). (a) \(\omega_{0}\left[1+2 \alpha\left(\theta_{2}-\theta_{1}\right)\right]\) (b) \(\omega_{0}\left[1+\alpha\left(\theta_{2}-\theta_{1}\right)\right]\) (c) \(\frac{\omega_{0}}{\left[1+2 \alpha\left(\theta_{2}-\theta_{1}\right)\right]}\) (d) None of these

Calculate the compressional force required to prevent the metallic rod of length \(l \mathrm{~cm}\) and cross-sectional area \(A \mathrm{~cm}^{2}\) when heated through \(t^{\circ} \mathrm{C}\), from expanding along lengthwise. The Young's modulus of elasticity of the metal is \(E\) and mean coefficient of linear expansion is \(\alpha\) per degree celsius: (a) EA\alphat (b) \(\frac{E \text { A\alphat }}{(1+\alpha t)}\) (c) \(\frac{E A \alpha t}{(1-\alpha t)}\) (d) El\alphat

At temperature \(T_{0}\), two metal strips of length \(l_{0}\) and thickness \(d\), is bolted so that their ends coincide. The upper strip is made up of metal \(A\) and have coefficient of expansion \(\alpha_{A}\) and lower strip is made up of metal \(B\) with coefficient of expansion \(\alpha_{B} \cdot\left(\alpha_{A}>\alpha_{B}\right)\). When temperature of their blastic strip is in-seased from \(T_{0}\) to \(\left(T_{0}+\Delta T\right)\), on strip become longer than the other and blastic strip is bend in the form of a circle as shown in fig. Calculate the radius of furvature \(R\) of the strip: (a) \(R:=\frac{\left[2+\left(\alpha_{A}+\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T}\) (b) \(R=\frac{\left[2-\left(\alpha_{A}+\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T}\) (c) \(R=\frac{\left[2+\left(\alpha_{A}-\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T_{i}}\) (d) \(R=\frac{\left[2-\left(\alpha_{A}-\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta \mathcal{k}}\)

A copper rod of length \(l_{0}\) at \(0^{\circ} \mathrm{C}\) is placed on smooth surface. The rod is heated up to \(100^{\circ} \mathrm{C}\). The longitudinal strain developed is : \((\alpha=\) coefficient of linear expansion) (a) \(\frac{100 l_{0} \alpha}{l_{0}+100 l_{0} \alpha}\) (b) \(100 \alpha\) (c) zero (d) none of these

A steel rod of diameter \(1 \mathrm{~cm}\) is clamped firmly at each end when its temperature is \(25^{\circ} \mathrm{C}\) so that it cannot contract on cooling. The tension in the rod at \(0^{\circ} \mathrm{C}\) is : \(\left(\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)\) (a) \(4000 \mathrm{~N}\) (b) \(7000 \mathrm{~N}\) (c) \(7400 \mathrm{~N}\) (d) \(4700 \mathrm{~N}\)

What will be the stress at \(-20^{\circ} \mathrm{C}\), if a steel rod with a cross-sectional area of \(150 \mathrm{~mm}^{2}\) is stretched between two fixed points? The tensile load at \(20^{\circ} \mathrm{C}\) is \(5000 \mathrm{~N}:\) (Assume \(\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) and \(Y=200 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\) ) (a) \(12.7 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\) (b) \(1.27 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\) (c) \(127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\) (d) \(0.127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\)

Two steel rods and copper rod of equal length \(l_{0}\) and equal cross-sections are joined rigidly as shown. All the rods are in a state of zero tension at \(0^{\circ} \mathrm{C}\). The temperature of system increases upto \(30^{\circ} \mathrm{C}\), then : (a) tensile force on either steel plate is half of copper plate (b) the net expansion in copper plate is less than the thermal expansion of the copper plate (c) the expansion in either steel plates is larger than thermal expansion in steel plates (d) all of the above

An equilateral triangle \(A B C\) is formed by joining three rods of equal length and \(D\) is the mid-point of \(A B\). The coefficient of linear expansion for \(A B\) is \(\alpha_{1}\) and for \(A C\) and \(B C\) is \(\alpha_{2}\). Find the relation between \(\alpha_{1}\) and \(\alpha_{2}\), if distance \(D C\) remains constant for small changes in temperature (a) \(\alpha_{1}=\alpha_{2}\) (b) \(\alpha_{1}=4 \alpha_{2}\) (c) \(\alpha_{2}=4 \alpha_{1}\) (d) \(\alpha_{1}=\frac{1}{2} \alpha_{2}\)

In an anisotropic medium, the coefficients of linear expansion of a solid are \(\alpha_{1}, \alpha_{2}\) and \(\alpha_{3}\) in three mutually perpendicular directions. The coefficient of volume expansion for the solid is (a) \(\alpha_{1}-\alpha_{2}+\alpha_{3}\) (b) \(\frac{\alpha_{1}+\alpha_{2}+\alpha_{3}}{3}\) (c) \(\alpha_{1}+\alpha_{2}+\alpha_{3}\) (d) none of these

The bulk modulus of water is \(2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\). The pressure required to increase the density of water by \(0.1 \%\) is : (a) \(2.1 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}\) (b) \(2.1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\) (c) \(2.1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) (d) \(2.1 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}\)

At a temperature \(t^{\circ} \mathrm{C}\), a liquid is completely filled in a spherical shell of copper. If \(\Delta T\) increases temperature of the liquid and the shell, then the outward pressure \(d P\) on the shell resulted from increase in temperature is given by: (Given, \(K=\) Bulk modulus of the liquids, \(\gamma=\) coefficient of volume expansion, \(\alpha=\) coefficient of linear expansion of the material of the shell) (a) \(\frac{K}{2}(\gamma-3 \alpha) \Delta T\) (b) \(K(3 \alpha-\gamma) \Delta T\) (c) \(3 \alpha(K-\gamma) \Delta T\) (d) \(\gamma(3 \alpha-K) \Delta T\)

Using the following, data, at what temperature will the wood just sink in benzene? Density of wood at \(0^{\circ} \mathrm{C}=8.8 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}\) Density of benzene at \(0^{\circ} \mathrm{C}=9 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}\) Cubical expansivity of wood \(=1.5 \times 10^{-4} \mathrm{~K}^{-1}\) Cubical expansivity of benzene \(=1.2 \times 10^{-3} \mathrm{~K}^{-1}\) (a) \(27^{\circ} \mathrm{C}\) (b) \(21.7^{\circ} \mathrm{C}\) (c) \(31^{\circ} \mathrm{C}\) (d) \(31.7^{\circ} \mathrm{C}\)

In a U-tube, a liquid is poured to a height \(h^{\prime}\) in each arm. When left and right arms of the tube is heated to temperature \(T_{1}\) and \(T_{2}\) respectively, the height in each arm changes to \(h_{1}\) and \(h_{2}\) respectively. What is the relation between coefficients of volume expansion of liquid and heights, \(h_{1}\) and \(h_{2}\) ? (a) \(\gamma=\frac{h_{1}-h_{2}}{T_{1} h_{2}-T_{2} h_{1}}\) (b) \(\gamma=\frac{h_{1}+h_{2}}{T_{1} h_{2}-T_{2} h_{1}}\) (c) \(\gamma=\frac{h_{1}+h_{2}}{T_{1} h_{2}+T_{2} h_{1}}\) (d) \(\gamma=\frac{h_{1}-h_{2}}{T_{1} h_{1}-T_{2} h_{2}}\)

The ratio of thermal capacities of two spheres \(A\) and \(B\), if their diameters are in the ratio \(1: 2\), densities in the ratio \(2: 1\), and the specific heat in the ratio of \(1: 3\), will be: (a) \(1: 6\) (b) \(1: 12\) (c) \(1: 3\) (d) \(1: 4\)

In similar calorimeters, equal volumes of water and alcohol, when poured, take \(100 \mathrm{~s}\). and 74 s respectively to cool from \(50^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\). If the thermal capacity of each calorimeter is numerically equal to volume of either liquid, then the specific heat capacity of alcohol is : (Given: the relative density of alcohol as \(0.8\) and specific heat capacity of water as \(1 \mathrm{cal} / \mathrm{g} /{ }^{\circ} \mathrm{C}\) ) (a) \(0.8 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\) (b) \(0.6 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\) (c) \(0.9 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\) (d) \(1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\)

The molar heat capacity of rock salt at low temperatures varies with temperature according to Debye's \(T^{3}\) law". Thus, \(C=k \frac{T^{3}}{\theta^{3}}\) where, \(k=1940 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \theta=281 \mathrm{~K}\). How much heat is required to raise the temperature of 2 moles of rock salt from \(10 \mathrm{~K}\) to \(50 \mathrm{~K}\) ? (a) \(800 \mathrm{~J}\) (b) \(373 \mathrm{~J}\) (c) \(273 \mathrm{~J}\) (d) None of these

A drilling machine of \(10 \mathrm{~kW}\) power is used to drill a bore in a small aluminium block of mass \(8 \mathrm{~kg}\). If \(50 \%\) of power is used up in heating the machine itself or lost to the surroundings then how much is the rise in temperature of the block in \(2.5\) minutes? (Given: specific heat of aluminium \(=0.91 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}\) ) (a) \(103^{\circ} \mathrm{C}\) (b) \(130^{\circ} \mathrm{C}\) (c) \(105^{\circ} \mathrm{C}\) (d) \(30^{\circ} \mathrm{C}\)

The temperature at which phase transition occurs, depends on: (a) pressure (b) volume (c) density (d) mass

Under some conditions, a material can be heated above or cooled below the normal phase change temperature without a phase change occurring. The resulting state : (a) may be stable (b) may be unstable (c) must be stable (d) must be unstable

It takes 20 minutes to melt \(10 \mathrm{~g}\) of ice, when rays from the 'sun are focussed by a lens of diameter \(5 \mathrm{~cm}\) on to a block of ice. The heat received from the sun on \(1 \mathrm{~cm}^{2}\) per minute is : (Given: \(L=80 \mathrm{k} \mathrm{cal} / \mathrm{kg}\) ) (a) \(R=2.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}\) (b) \(R=3.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}\) (c) \(R=0.204 \mathrm{cal} / \mathrm{cm}^{2}-\min\) (d) \(R=204 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}\)

If in \(1.1 \mathrm{~kg}\) of water which is contained in a calorimeter of water equivalent \(0.02 \mathrm{~kg}\) at \(15^{\circ} \mathrm{C}\), steam at \(100^{\circ} \mathrm{C}\) is passed, till the temperature of calorimeter and its contents rises to \(80^{\circ} \mathrm{C}\). The mass of steam condensed in kilogram is: (a) \(0.131\) (b) \(0.065\) (c) \(0.260\) (d) \(0.135\)

\(5 \mathrm{~g}\) of water at \(30^{\circ} \mathrm{C}\) and \(5 \mathrm{~g}\) of ice at \(-20^{\circ} \mathrm{C}\) are mixed together in a calorimeter. The water equivalent of calorimeter is negligible and specific heat and latent heat of ice are \(0.5 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\) and \(80 \mathrm{cal} / \mathrm{g}\) respectively. The final temperature of the mixure is: (a) \(0^{\circ} \mathrm{C}\) (b) \(-8^{\circ} \mathrm{C}\) (c) \(-4^{\circ} \mathrm{C}\) (d) \(2^{\circ} \mathrm{C}\)

In an energy recycling process, \(X g\) of steam at \(100^{\circ} \mathrm{C}\) becomes water at \(100^{\circ} \mathrm{C}\) which converts \(Y \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\) into water at \(100^{\circ} \mathrm{C}\). The ratio of \(X / Y\) will be : (a) \(\frac{1}{3}\) (b) \(\frac{2}{3}\) (c) 3 (d) 2

At \(30^{\circ} \mathrm{C}\), a lead bullet of \(50 \mathrm{~g}\), is fired vertically upwards with a speed of \(840 \mathrm{~m} / \mathrm{s}\). The specific heat of lead is \(0.02 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\). On returning to the starting level, it strikes to a cake of ice at \(0^{\circ} \mathrm{C}\). The amount of ice melted is: (Assume all the energy is spent in melting only) (a) \(62.7 \mathrm{~g}\) (b) \(55 \mathrm{~g}\) (c) \(52.875 \mathrm{~kg}\) (d) \(52.875 \mathrm{~g}\)