Chapter 13

The reflectance and emittance of a perfectly black body are respectively (a) 0,1 (b) 1,0 (c) \(0.5,0.5\) (d) 0,0

The rate of emission of radiation of a black body at temperature \(27^{\circ} \mathrm{C}\) is \(E_{1}\). If its temperature is increased to \(327^{\circ} \mathrm{C}\), the rate of emission of radiation is \(E_{2} .\) The relation between \(E_{1}\) and \(E_{2}\) is (a) \(E_{1}=24 E_{1}\) (b) \(E_{2}=16 E_{1}\) (c) \(E_{2}=8 E_{1}\) (d) \(E_{2}=4 E_{1}\)

Two metallic spheres \(S_{1}\) and \(S_{2}\) are made of the same material and have identical surface finish. The mass of \(S_{1}\) is three times that of \(S_{2}\). Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of \(S_{1}\) to that of \(S_{2}\) is (a) \(1 / 3\) (b) \((1 / 3)^{1 / 3}\) (c) \(1 / \sqrt{3}\) (d) \(\sqrt{3} / 1\)

The rates of heat radiation from two patches of skin each of area \(A\), on a patient's chest differ by \(2 \%\). If the patch of the lower temperature is at \(300 \mathrm{~K}\) and emissivity of both the patches is assumed to be unity, the temperature of other patch would be (a) \(306 \mathrm{~K}\) (b) \(312 \mathrm{~K}\) (c) \(308.5 \mathrm{~K}\) (d) \(301.5 \mathrm{~K}\)

Three discs \(A, B\) and \(C\) having radii \(2 \mathrm{~m}, 4 \mathrm{~m}\) and \(6 \mathrm{~m}\) respectively are coated with carbon black on their other surfaces. The wavelengths corresponding to maximum intensity are \(300 \mathrm{~nm}, 400 \mathrm{~nm}\) and \(500 \mathrm{~nm}\) respectively. The power radiated by them are \(Q_{a}, Q_{b}\) and \(Q_{c}\) respectively (a) \(Q_{a}\) is maximum (b) \(Q_{b}\) is maximum (c) \(Q_{c}\) is maximum (d) \(Q_{a}=Q_{b}=Q_{c}\)

The rays of sun are focussed on a piece of ice through a lens of diameter \(5 \mathrm{~cm}\), as a result of which \(10 \mathrm{~g}\) ice melts in 10 min. The amount of heat received from sun, per unit area per min is (a) \(4 \mathrm{cal} \mathrm{cm}^{-2} \min ^{-1}\) (b) \(40 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~min}^{-1}\) [c) \(4 \mathrm{Jm}^{-2} \mathrm{~min}\) (d) \(400 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~min}^{-1}\)

The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase from \(20^{\circ} \mathrm{C}\) to \(20.5^{\circ} \mathrm{C}\). If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at \(20^{\circ} \mathrm{C}\), the temperature of water will be (a) \(21^{\circ} \mathrm{C}\) (b) \(22^{\circ} \mathrm{C}\) (c) \(24^{\circ} \mathrm{C}\) (d) \(28^{\circ} \mathrm{C}\)

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 (a) the hollow sphere will cool at a faster rate for all values of \(T\) (b) the solid sphere will cool at a faster rate for all values of \(T\) (c) both spheres will cool at the same rate for all values of \(T\) (d) both spheres will cool at the same rate only for small values of \(T\)

Solar radiation emitted by sun resembles that emitted by a black body at a temperature of \(6000 \mathrm{~K}\). Maximum intensity is emitted at a wavelength of about \(4800 \hat{A}\). If the sun were cooled down from \(6000 \mathrm{~K}\) to \(3000 \mathrm{~K}\), then the peak intensity would occur at a wavelength of (a) \(4800 \mathrm{~A}\) (b) \(9600 \mathrm{~A}\) (c) \(2400 \hat{A}\) (d) \(19200 \AA\)

A solid copper cube of edges \(1 \mathrm{~cm}\) is suspended in an evacuated enclosure. Its temperature is found to fall from \(100^{\circ} \mathrm{C}\) to \(99^{\circ} \mathrm{C}\) in \(100 \mathrm{~s}\). Another solid copper cube of edges \(2 \mathrm{~cm}\), with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from \(100^{\circ} \mathrm{C}\) to \(99^{\circ} \mathrm{C}\) will be approximately (a) \(25 \mathrm{~s}\) (b) \(50 \mathrm{~s}\) (c) \(200 \mathrm{~s}\) (d) \(400 \mathrm{~s}\)

When the temperature of a black body increases, it is observed that the wavelength corresponding of maximum energy changes from \(0.26 \mu \mathrm{m}\) to \(0.13 \mu \mathrm{m}\) to a body at the respective temperature. Then ratio of the emissivities \(\frac{E_{2}}{E_{1}}\) is (a) \(16 / 1\) (b) \(4 / 1\) (c) \(1 / 4\) (d) \(1 / 16\)

A black body at a temperature of \(327^{\circ} \mathrm{C}\) radiates \(4 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~s}^{-1}\), At a temperature of \(927^{\circ} \mathrm{C}\), the rate of heat radiated per unit area in cal \(\mathrm{cm}^{-2} \mathrm{~g}^{-1}\) will be (a) 16 (b) 32 (c) 64 (d) 128

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 (a) \(0^{\circ} \mathrm{C}\) (b) \(\frac{100}{l}{\underline{\phantom{xx}}}^{\circ} \mathrm{C} ;\) where \(l\) is the length of each rod (c) \(\frac{100}{2 l}^{*} \mathrm{C}\) (d) \(100^{\circ} \mathrm{C}\)

A solid cube and a solid sphere have equal surface areas. Both are at the same temperature of \(120^{\circ} \mathrm{C}\). Then (a) both of them will cool down at the same rate (b) the cube will cool down faster than the sphere (c) the sphere will cool down faster than the cube (d) whichever of the two is heavier will cool down faster

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 material of second rod is \(1 / 4\) that of first, the rate at which ice melts in \(\mathrm{g} / \mathrm{s}\) will be (a) \(3.2\) (b) \(1.6\) (c) \(0.2\) (d) \(0.1\)

A surface at temperature \(T_{0} \mathrm{~K}\) receives power \(P\) by radiation from a small sphere at temperature \(T>T_{0}\) and at a distance \(d\). If both \(T\) and \(d\) are doubled, the power received by the surface will become (a) \(\underline{P}\) (b) \(2 P\) (c) \(4 P\) (d) \(16 P\)

One end of a copper rod of length \(1.0 \mathrm{~m}\) and area of cross-section \(10^{-3} \mathrm{~m}^{2}\) is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is \(92 \mathrm{cal} / \mathrm{m}-\mathrm{s}-{ }^{\circ} \mathrm{C}\) and the latent heat of ice is \(8 \times 10^{4} \mathrm{cal} / \mathrm{kg}\), then the amount of ice which will melt in one min is (a) \(9.2 \times 10^{-3} \mathrm{~kg}\) (b) \(8 \times 10^{-3} \mathrm{~kg}\) (c) \(6.9 \times 10^{-3} \mathrm{~kg}\) (d) \(5.4 \times 10^{-1} \mathrm{~kg}\)

If a given mass of gas occupies a volume of \(100 \mathrm{cc}\) at 1 atm pressure and temperature of \(100^{\circ} \mathrm{C}(373.15 \mathrm{~K})\). What will be its volume at 4 atm pressure; the temperature being the same? (a) \(100 \mathrm{cc}\) (b) \(400 \mathrm{cc}\) [c) \(25 \mathrm{cc}\) (d) \(104 \mathrm{cc}\)

An ice box used for keeping eatable cold has a total wall area of \(1 \mathrm{~m}^{2}\) and a wall thickness of \(5.0 \mathrm{~cm}\). The thermal conductivity of the ice box is \(K=0.01\) joule/metre- \({ }^{\circ} \mathrm{C}\). It is filled with ice at \(0^{\circ} \mathrm{C}\) along with eatables on a day when the temperature is \(30^{\circ} \mathrm{C}\). The latent heat of fusion of ice is \(334 \times 10^{3}\) joule \(/ \mathrm{kg}\). The amount of ice melted in one day is \((1\) day \(=86.400 \mathrm{~s})\) (a) \(776 \mathrm{~g}\) (b) \(7760 \mathrm{~g}\) (c) \(11520 \mathrm{~g}\) (d) \(1552 \mathrm{~g}\)

If a given mass of gas occupies a volume of \(100 \mathrm{cc}\) at 1 atm pressure and temperature of \(100^{\circ} \mathrm{C}(373.15 \mathrm{~K})\). What will be its volume at 4 atm pressure; the temperature being the same? (a) \(100 \mathrm{cc}\) (b) \(400 \mathrm{cc}\) [c) \(25 \mathrm{cc}\) (d) \(104 \mathrm{cc}\)

1 mole of \(\mathrm{H}_{2}\) gas is contained in a box of volume \(V=1.00 \mathrm{~m}^{3}\) at \(T=300 \mathrm{~K}\). The gas is heated to a temperature of \(T=3000 \mathrm{~K}\) and the gas gets converted to a gas of hydrogen atoms The final pressure would be (considering all gases to be ideal) [NCERT Exemplar] (a) same as the pressure initially (b) 2 times the pressure initially (c) 10 times the pressure initially (d) 20 times the pressure initially

When a gas filled in a closed vessel is heated through \(1^{\circ} \mathrm{C}\), its pressure increases by \(0.4 \%\). The initial temperature of the gas was (a) \(250 \mathrm{~K}\) (b) \(2500 \mathrm{~K}\) (c) \(250^{\circ} \mathrm{C}\) (d) \(25^{\circ} \mathrm{C}\)

When a gas filled in a closed vessel is heated through \(1^{\circ} \mathrm{C}\), its pressure increases by \(0.4 \%\). The initial temperature of the gas was (a) \(250 \mathrm{~K}\) (b) \(2500 \mathrm{~K}\) (c) \(250^{\circ} \mathrm{C}\) (d) \(25^{\circ} \mathrm{C}\)

A metal \(\operatorname{rod} A B\) of length \(10 x\) has its one end \(A\) in ice at \(0^{\circ} \mathrm{C}\) and the other end \(B\) in water at \(100^{\circ} \mathrm{C}\). If a point \(P\) on the rod is maintained at \(400^{\circ} \mathrm{C}\), then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporationof water is \(540 \mathrm{cal} / \mathrm{g}\) and latent heat of melting of ice is \(80 \mathrm{cal} / \mathrm{g}\). If the point \(P\) is at a distance of \(\lambda x\) from the ice end \(A\), find the value of \(\lambda\). (Neglect any heat loss to the surroundings). (a) 9 (b) 2 (c) 6 (d) 1

An inflated rubber balloon contains one mole of an ideal gas, has a pressure \(p\), volume \(V\) and temperature \(T\). If the temperature rises to \(1.1 T\), and the volume is increased to \(1.05 \mathrm{~V}\). the final pressure will be (a) \(1.1 p\) (b) \(p\) (c) less than \(p\) (d) between \(p\) and \(1.1 p\)

A sphere and a cube of same material and same volume. One heated upto same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiation emitted will be (a) \(1: 1\) (b) \(\frac{4 \pi}{3}: 1\) (c) \(\left(\frac{\pi}{6}\right)^{1 / 3}: 1\) (d) \(\frac{1}{2}\left(\frac{4 \pi}{3}\right)^{2 / 3}: 1\)

Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points are \(T\) and \(\sqrt{2} T\) respectively in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points? (a) \(\frac{\sqrt{2}+1}{2} T\) (b) \(\frac{2}{\sqrt{2}+1} T\) (c) 0 (d) None of these

An ideal gas is found to obey an additional law \(p V^{2}=\) constant. The gas is initially at temperature \(T\) and volume \(V\), Then it expands to a volume \(2 \mathrm{~V}\), the temperature becomes (a) \(T / \sqrt{2}\) (b) \(2 \mathrm{~T}\) (c) \(2 T / 2\) (d) \(4 \underline{T}\)

The rms velocity of gas molecules is \(300 \mathrm{~ms}^{-1}\). The rms velocity of molecules of gas with twice the molecular weight and half the absolute temperature is (a) \(300 \mathrm{~ms}^{-1}\) (b) \(600 \mathrm{~ms}^{-1}\) (c) \(75 \mathrm{~ms}^{-1}\) (d) \(150 \mathrm{~ms}^{-1}\)

\(N\) molecules, each of mass \(m\), of gas \(A\) and \(2 \mathrm{~N}\) molecules, each of mass \(2 m\), of gas \(B\) are contained in the same vessel which is maintained at a temperature \(T\). The mean square velocity of molecules of \(B\) type is denoted by \(V_{2}\) and the mean square velocity of \(A\) type is denoted by \(V_{1}\), then \(\frac{V_{1}}{V_{2}}\) is (a) 2 (b) (c) \(1 / 3\) (d) \(2 / 3\)

Calculate the rms speed of smoke particles each of mass \(5 \times 10^{-17} \mathrm{~kg}\) in their Brownian motion in air at \(\mathrm{NTP}\left(k=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)\) (a) \(1.5 \mathrm{~mm} \mathrm{~s}^{-1}\) (b) \(1.5 \mathrm{~ms}^{-1}\) (c) \(1.5 \mathrm{cms}^{-1}\) (d) \(1.5 \mathrm{kms}^{-1}\)

If a graph is plotted taking the temperature in Fahrenheit along \(Y\)-axis and the corresponding temperature in celsius along the \(X\)-axis, it will be straight line (a) having a +ve intercept on \(Y\)-axis (b) having a tve intercept on \(X\)-axis (c) passing through the origin (d) having a -ve intercepts on both the axis

At a certain temperature, the ratio of the rms velocity of \(\mathrm{H}_{2}\) molecules to \(\mathrm{O}_{2}\) molecule is (a) \(1: 1\) (b) \(1: 4\) (c) \(4: 1\) (d) \(16: 1\)

An oxygen cylinder of volume \(30 \mathrm{~L}\) has an initial gauge pressure of \(15 \mathrm{~atm}\) and a temperature of \(27^{\circ} \mathrm{C}\). After some oxygen is withdrawn from the cylinder the gauge pressure drops to 11 atm and its temperature drops to \(17^{\circ} \mathrm{C} .\) The mass of oxygen taken out of the cylinder \(\left(R=8.31 . \mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)\). molecular mas of \(\mathrm{O}_{2}=32 \mathrm{u}\) ) is [NCERT] (a) \(0.14 \mathrm{~g}\) (b) \(0.02 \mathrm{~g}\) (c) \(0.14 \mathrm{~kg}\) (d) \(0.014 \mathrm{~kg}\)

The root mean square velocity of the molecules in a sample of helium is \(5 / 7\) th that of the molecules in a sample of hydrogen. If the temperature of the hydrogen as is \(0^{\circ} \mathrm{C}\), that of helium sample is about (a) \(0^{\circ} \mathrm{C}\) (b) \(4 \mathrm{~K}\) (c) \(273^{*} \mathrm{C}\) (d) \(100^{\circ} \mathrm{C}\)

The average translatory energy and rms speed of molecules in a sample of oxygen gas at \(300 \mathrm{~K}\) are \(5.21 \times 10^{-21} \mathrm{~J}\) and \(484 \mathrm{~ms}^{-1}\) respectively. The sorresponding values at \(600 \mathrm{~K}\) are nearly (assuming deal gas behaviour) (a) \(\left.12.42 \times 10^{-21}\right\rfloor, 968 \mathrm{~ms}^{-1}\) (b) \(7.78 \times 10^{-21} \mathrm{~J}, 684 \mathrm{~ms}^{-1}\) (c) \(6.21 \times 10^{-21} \mathrm{~J}, 968 \mathrm{~ms}^{-1}\) (d) \(12.42 \times 10^{-21} \mathrm{~J}, 684 \mathrm{~ms}^{-1}\)

The average energy and the rms speed of molecules in a sample of oxygen gas at \(400 \mathrm{~K}\) are \(7.21 \times 10^{-21} \mathrm{~J}\) and \(524 \mathrm{~ms}^{-1}\) respectively. The corresponding values at \(800 \mathrm{~K}\) are nearly (a) \(14.42 \times 10^{-21} 3,1048 \mathrm{~ms}^{-1}\) (b) \(10.18 \times 10^{-21} J, 741 \mathrm{~ms}^{-1}\) (c) \(7.21 \times 10^{-21} \mathrm{~J}, 1048 \mathrm{~ms}^{-1}\) (d) \(14.42 \times 10^{-21} \mathrm{~J}, 741 \mathrm{~ms}^{-1}\)

The average energy and the rms speed of molecules in a sample of oxygen gas at \(400 \mathrm{~K}\) are \(7.21 \times 10^{-21} \mathrm{~J}\) and \(524 \mathrm{~ms}^{-1}\) respectively. The corresponding values at \(800 \mathrm{~K}\) are nearly (a) \(14.42 \times 10^{-21} 3,1048 \mathrm{~ms}^{-1}\) (b) \(10.18 \times 10^{-21} J, 741 \mathrm{~ms}^{-1}\) (c) \(7.21 \times 10^{-21} \mathrm{~J}, 1048 \mathrm{~ms}^{-1}\) (d) \(14.42 \times 10^{-21} \mathrm{~J}, 741 \mathrm{~ms}^{-1}\)

The average kinetic energy of a gas molecule at \(27^{\circ} \mathrm{C}\) is \(6.21 \times 10^{-21} \mathrm{~J} .\) Its average kinetic energy at \(127^{\circ} \mathrm{C}\) will be (a) \(12.2 \times 10^{-21} \mathrm{~J}\) (b) \(8.28 \times 10^{-21} \mathrm{~J}\) (c) \(10.35 \times 10^{-21} \mathrm{~J}\) (d) \(11.35 \times 10^{-21} \mathrm{~J}\)

A solid material is supplied with heat at constant rate and the temperature of the material changes as shown. From the graph, the false conclusion drawn is (a) \(A B\) and \(C D\) of the graph represent phase changes (b) \(A B\) represents the change of state from solid to liquid (c) Latent heat of fusion is twice the latent heat of vaporization (d) \(C D\) represents change of state from liquid to vapour [e) Latent heat of vaporization is twice the latent heat of fusion

The value of molar specific heat at constant volume for 1 mole of polyatomic gas having \(n\) number of degrees of freedom at temperature \(T \mathrm{~K}\) is \((R=\) universal gas constant) (a) \(\frac{n R}{2 T}\) (b) \(\frac{n R}{2}\) (c) \(\frac{n R T}{2}\) (d) \(2 n R T\)

The value of \(\gamma\) for gas \(X\) is \(1.33\), the \(X\) is (a) \(\mathrm{Ne}\) (b) \(0_{3}\) (c) \(\mathrm{N}_{2}\) (d) \(\mathrm{NH}_{3}\)

The thermal radiation from a hot body travels with a velocity of (a) \(330 \mathrm{~ms}^{-1}\) (b) \(2 \times 10^{8} \mathrm{~ms}^{-1}\) (c) \(3 \times 10^{8} \mathrm{~ms}^{-1}\) (d) \(230 \times 10^{8} \mathrm{~ms}^{-1}\)

A brass boiler has a base area \(0.15 \mathrm{~m}^{2}\) and thickness \(1.0 \mathrm{~cm}\). It boils water at the rate of \(6.0 \mathrm{~kg} / \mathrm{min}\) when placed on a gas stove. The temperature of the part of the flame in contact with the boiler will be. (Thermal conductivity of brass \(=109 \mathrm{~J} / \mathrm{s}-\mathrm{m}-\mathrm{K}\), Heat of vapourization of water \(=2256 \times 10^{3} \mathrm{~J} / \mathrm{kg}\) ) [NCERT] (a) \(158^{\circ} \mathrm{C}\) (b) \(208^{\circ} \mathrm{C}\) (c) \(238^{\circ} \mathrm{C}\) (d) \(264^{\circ} \mathrm{C}\)

The thermal radiation from a hot body travels with a velocity of (a) \(330 \mathrm{~ms}^{-1}\) (b) \(2 \times 10^{8} \mathrm{~ms}^{-1}\) (c) \(3 \times 10^{8} \mathrm{~ms}^{-1}\) (d) \(230 \times 10^{8} \mathrm{~ms}^{-1}\)

A body cools in a surrounding which is at a constant temperature of \(\theta_{0}\). Assume that it obeys Newton's law of cooling. Its temperature \(\theta\) is plotted against time \(t\). Tangents are drawn to the curve at the points \(P\left(\theta=\theta_{2}\right)\) and \(Q\left(\theta=\theta_{1}\right) .\) These tangents meet the time axis at angles of \(\phi_{2}\) and \(\phi_{1}\), as shown(a) \(\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{0}}{\theta_{2}-\theta_{0}}\) (b) \(\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{0}}{\theta_{1}-\theta_{0}}\) (c) \(\frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{1}}{\theta_{2}}\) (d) \(\frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{2}}{\theta_{1}}\)

A brass boiler has a base area \(0.15 \mathrm{~m}^{2}\) and thickness \(1.0 \mathrm{~cm} .\) It boils water at the rate of \(6.0 \mathrm{~kg} / \mathrm{min}\) when placed on a gas stove. The temperature of the part of the flame in contact with the boiler will be. (Thermal conductivity of brass \(=109 \mathrm{~J} / \mathrm{s}-\mathrm{m}-\mathrm{K}\), Heat of vapourization of water \(=2256 \times 10^{3} \mathrm{~J} / \mathrm{kg}\) ) [NCERT] (a) \(158^{\circ} \mathrm{C}\) (b) \(208^{\circ} \mathrm{C}\) (c) \(238^{\circ} \mathrm{C}\) (d) \(264^{*} \mathrm{C}\)

Assuming the sun to have a spherical outer surface of radius \(r\) radiating like a black body at temperature \(t^{\circ} \mathrm{C}\), the power received by a unit surface (normal to the incident rays) at a distance \(R\) from the centre of the sun is ( \(\sigma\) is stefan's constant) (a) \(4 \pi r^{2} \sigma t^{4}\) (b) \(\frac{r^{2} \sigma(t+273)^{4}}{4 \pi R^{2}}\) (c) \(\frac{16 \pi^{2} r^{2} \sigma t^{4}}{R^{2}}\) (d) \(\frac{r^{2} \sigma(1+273)^{4}}{R^{2}}\)

Two spheres made of same material have radii in the ratio \(1: 2 .\) Both are at same temperature. Ratio of heat radiation energy emitted per second by them is (a) \(1: 2\) (b) \(1: 4\) (c) \(1: 8\) (d) \(1: 16\)

Mark the correct options \(\quad\) [NCERT Exemplar) (a) A system \(X\) is in thermal equilibrium with \(Y\) but not with Z. System \(Y\) and \(Z\) may be in thermal equilibrium with each other. (b) A system \(X\) is in thermal equilibrium with \(Y\) but not with Z. System \(Y\) and \(Z\) are not in thermal equilibrium with each other. (c) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) must be in thermal equilibrium with each other. (d) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The system \(Y\) and \(Z\) may be in thermal equilibrium with each other.