Chapter 13

Under which of the following conditions, the law \(p V=R T\) is not obeyed by a real gas? (a) High pressure and high temperature (b) Low pressure and low temperature (c) Low pressure and high temperature (d) High pressure and low temperature

A glass full of hot milk is poured on the table. It begins to cool gradually Which of the follwong is correct? (a) The rate of cooling is constant till milk attains the temperature of the surrounding (b) The temperature of milk falls off exponentially with time (c) While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surrounding and that is why it cools (d) All three phenomenon, conduction, convection and radiation are responsible for the loss of heat milk to the surroundings.

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 \(\lambda_{B}\) corresponding to maximum spectral radiancy in the radiation from \(B\) is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from \(A\), by \(1.00 \mu \mathrm{m}\). If the temperature of \(A\) is \(5802 \mathrm{~K}\) (a) The temperature of \(B\) is \(1934 \mathrm{~K}\) (b) \(\lambda_{B}=1.5 \mu \mathrm{m}\) (c) The temperature of \(B\) is \(11604 \mathrm{~K}\) (d) The temperature of \(B\) is \(2901 \mathrm{~K}\)

\(A B C D E F G H\) is hollow cube made of an insulator. Face \(A B C D\) has positive charge on it. Inside the cube, we have ionized hydrogen. The usual kinetic theory expression for pressure [NCERT Exemplar] (a) will be valid (b) will not be valid since the ions would experience forces orger than due to collisions with the walls (c) will not be valid since collisions with walls would not be elastic (d) will not be valid because isotropy is lost

An ice block of mass \(m\) at \(0^{\circ} \mathrm{C}\) is put in water of mass \(2 m\) at \(60^{\circ} \mathrm{C}\). The final temperature would be (a) \(60^{\circ} \mathrm{C}\) (b) \(0^{\circ} \mathrm{C}\) (c) \(30^{\circ} \mathrm{C}\) (d) \(13.3^{\circ} \mathrm{C}\) Passage II The latent heat of fusion of ice is \(80 \mathrm{calg}^{-1}\) and latent heat of steam is \(540 \mathrm{calg}^{-1}\). Change of state occurs only at melting point or boiling point of the substance. There is no change in temperature during the entire change of state. For rise in temperature \((\Delta T)\) heat required \(\Delta Q=m c \Delta T\), where \(c\) is specific heat of the substance.

Heat released when \(10 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) cools to water at \(100^{\circ} \mathrm{C}\) is (a) \(540 \mathrm{cal}\) (b) \(54 \mathrm{cal}\) (c) \(5400 \mathrm{cal}\) (d) \(54000 \mathrm{cal}\)

Heat released when \(10 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) cools to water at \(100^{\circ} \mathrm{C}\) is (a) \(540 \mathrm{cal}\) (b) \(54 \mathrm{cal}\) (c) \(5400 \mathrm{cal}\) (d) \(54000 \mathrm{cal}\)

Assertion The SI unit of Stefan's constant is \(\mathrm{Wm}^{-2} \mathrm{~K}^{-4}\). Reason This follows from Stefan's Law, \(\therefore\) $$ \begin{aligned} E &=\alpha T^{4} \\ \alpha &=\frac{E}{T^{4}}=\frac{\mathrm{Wm}^{-2}}{\mathrm{~K}^{4}} \end{aligned} $$

Assertion When temperature difference across the two sides of a wall is increased, its thermal conductivity increases. Reason Thermal conductivity depends on nature of material of the wall.

Assertion Cooking in a pressure cooker is faster. Reason Because steam does not leak out.

Assertion Two bodies at different temperature, if brought in thermal contact do not necessary settle to the mean temperature. Reason The two bodies may have different thermal capacities.

Assertion When temperature of a black body is halved, wavelength corresponding to which energy radiated is maximum becomes twice. Reason This is as per Wien's law.

Assertion When speed of sound in a gas is \(c\), then $$ c_{\mathrm{rms}}=\sqrt{\frac{3}{\gamma}} \times c $$ Reason \(c=\sqrt{\frac{\gamma p}{\rho}}\)

Assertion The root mean speed (rms) of oxygen molecules at a certain absolute temperature \(T\) is \(c\).If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed would be \(2 \mathrm{c}\). Reason \(c \propto \sqrt{\frac{T}{M}}\)

Statement I The temperature dependence of resistance is usually given as \(R=R_{0}(1+\Delta t)\). The resistance of a wire changes from \(100 \Omega\) to \(150 \Omega\) when its temperature is increased from \(27^{\circ} \mathrm{C}\) to \(227^{\circ} \mathrm{C}\). This implies that \(\alpha=2.5 \times 10^{-3} \mathrm{C}^{-1}\). Statement II \(R=R_{0}(1+\alpha \Delta t)\) is valid only when the change in the temperature is small and \(\Delta R=\left(R-R_{0}\right) \ll

Statement I The temperature dependence of resistance is usually given as \(R=R_{0}(1+\Delta t)\). The resistance of a wire changes from \(100 \Omega\) to \(150 \Omega\) when its temperature is increased from \(27^{\circ} \mathrm{C}\) to \(227^{\circ} \mathrm{C}\). This implies that \(\alpha=2.5 \times 10^{-3} \mathrm{C}^{-1}\). Statement II \(R=R_{0}(1+\alpha \Delta t)\) is valid only when the change in the temperature is small and \(\Delta R=\left(R-R_{0}\right) \ll

\(1 \mathrm{~kg}\) of diatomic gas is at a pressure of \(8 \times 10^{4} \mathrm{Nm}^{-2}\). The density of the gas is \(4 \mathrm{~kg} \mathrm{~m}^{-3}\). What is the energy of the gas due to its thermal motion? [AIEEE 2009] (a) \(5 \times 10^{4} \mathrm{~J}\) (b) \(6 \times 10^{4} \mathrm{~J}\) \((\mathrm{c}) 7 \times 10^{4} \mathrm{~J}\) (d) \(3 \times 10^{4} \mathrm{~J}\)

Six molecules have speeds 2 unit, 5 unit, 3 unit, 6 unit, 3 unit and 5 unit. The rms speed is [WB JEE 2008] (a) 4 unit (b) \(1.7\) unit (c) \(4.2\) unit (d) 5 unit

What is an ideal gas? [a) One that consists of molecules (b) A gas satisfying the assumptions of kinetic theory [c) A gas having Maxwellian distribution of speed (d) A gas consisting of massless particles

A body cools from \(50^{\circ} \mathrm{C}\) to \(49^{\circ} \mathrm{C}\) in \(5 \mathrm{~s}\). How long will it take to cool from \(40^{\circ} \mathrm{C}\) to \(39^{\circ} \mathrm{C}\) ? Assume temperature of surroundings to be \(30^{\circ} \mathrm{C}\) and Newton's law of cooling is valid [BVP Engg- 2008] (a) \(2.5 \mathrm{~s}\) (b) \(10 \mathrm{~s}\) (c) \(20 \mathrm{~s}\) (d) \(5 \mathrm{~s}\)

A slab consists of two portions of different materials of same thickness and having the conductivities \(K_{1}\) and \(K_{2}\). The equivalent thermal conductivity of the slab is [Karnataka CET 2008] (a) \(K_{1}+K_{2}\) (b) \(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\) (c) \(\frac{2 K_{1} K_{2}}{K_{1}+K_{2}}\) (d) \(\sqrt{K_{1}+K_{2}}\)

A slab consists of two portions of different materials of same thickness and having the conductivities \(K_{1}\) and \(K_{2}\). The equivalent thermal conductivity of the slab is [Karnataka CET 2008] (a) \(K_{1}+K_{2}\) (b) \(\frac{K_{1} K_{2}}{K_{1}+K_{2}}\) (c) \(\frac{2 K_{1} K_{2}}{K_{1}+K_{2}}\) (d) \(\sqrt{K_{1}+K_{2}}\)

Two rigid boxes containing different ideal gases are placed on table. Box A contains one mole of nitrogen at temperature \(T_{0}\), while box \(B\) contains 1 mole of helium at temperature \((7 / 3) T_{0} .\) The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes) then, the final temperature of gases, \(T_{f}\), in terms of \(T_{0}\) is [Kerala CET 2008] (a) \(T_{f}=\frac{3}{7} T_{0}\) (b) \(T_{f}=\frac{7}{3} T_{0}\) (c) \(T_{f}=\frac{3}{2} T_{0}\) (d) \(T_{f}=\frac{5}{3} T_{0}\)

The value of \(\frac{p V}{T}\) for one mole of an ideal gas is nearly equal to \(\quad\) [BVP Engg. 2007] (a) \(2 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) (b) \(8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) (c) \(4.2 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) (d) \(2 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\)

The value of a metal sphere increase by \(0.24 \%\) when its temperature is raised by \(40^{\circ} \mathrm{C}\). The coefficient of linear expansion of the metal is... \({ }^{\circ} \mathrm{C}^{-1}\). [BVP Engg. 2007] (a) \(2 \times 10^{-5}\) (b) \(6 \times 10^{-5}\) (c) \(18 \times 10^{-5}\) (d) \(1.2 \times 10^{-5}\)

The temperature of the two outer surface of a composite slab, consisting of two materials having coefficients of thermal conductivity \(K\) and \(2 K\) and thickness \(x\) and \(4 x\), respectively are \(T_{2}\) and \(T_{1}\left(T_{2}>T_{1}\right)\). The rate of heat transfer through the slab, in a steady state is \(\left(\frac{A\left(T_{2}-T_{1}\right) K}{x}\right) f\), with \(f\) equal to \(\quad\) [UP SEE 2007] (a) 1 (b) \(\frac{1}{2}\) (c) \(\frac{2}{3}\) (d) \(\frac{1}{3}\)

On the basis of kinetic theory of gases, the mean kinetic energy of 1 mol per degree of freedom is [BVP Enge, 2006] (a) \(\frac{1}{2} k T\) (b) \(\frac{1}{2} R T\) (c) \(\frac{3}{2} k T\) (d) \(\frac{3}{2} R T\)

Thermal radiations are electromagnetic waves belonging to [BVP Engg 2006] (a) ultraviolet region (b) visible region [c) gamma region (d) infrared region

Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules? [UP SEE 2006] (a) Increase (b) Decrease (c) No change (d) Can't be determined

Two balloons are filled, one with pure helium gas and the other by air, respectively. If the pressure and temperature of these balloons are same then the number of molecules per unit volume is [UP SEE 2006] (a) more in the helium filled balloon (b) same in both balloons (c) more in air filled balloon (d) in the ratio of \(1: 4\)

When you make ice cubes, the entropy of water [UP SEE 2006] (a) does not change (b) increase (c) decreases (d) may either increase or decrease depending on the process used

The thermoelectric power for a thermocouple at the neutral temperature is [BVP Engs. 2005] (a) zero (b) maximum (c) negative (d) minimum hut mo

The thermoelectric power for a thermocouple at the neutral temperature is [BVP Engs. 2005] (a) zero (b) maximum (c) negative (d) minimum hut mo

A black body has maximum wavelength \(\lambda_{m}\) at \(2000 \mathrm{~K}\). Its corresponding wavelength at \(3000 \mathrm{~K}\) will be \(\quad\) [Kerala CET 2005] (a) \(\frac{3}{2} \lambda_{m}\) (b) \(\frac{2}{3} \lambda_{m}\) (c) \(\frac{16}{81} \lambda_{m}\) (d) \(\frac{81}{16} \lambda_{m}\)

A body with area \(A\) at maintained temperature \(T\) and emissivity \(e=0.6\) is kept inside a spherical black body. What will be the maximum energy radiated per second? (a) \(0.60 \sigma A T^{4}\) (b) \(0.80 \sigma A T^{4}\) (c) \(1.00 \sigma A T^{4}\) (d) \(0.40 \sigma A T^{4}\)

A body with area \(A\) at maintained temperature \(T\) and emissivity \(e=0.6\) is kept inside a spherical black body. What will be the maximum energy radiated per second? (a) \(0.60 \sigma A T^{4}\) (b) \(0.80 \sigma A T^{4}\) (c) \(1.00 \sigma A T^{4}\) (d) \(0.40 \sigma A T^{4}\)

In which of the following process, convection does not take place primarily? (a) Sea and land breeze (b) Boiling of water (c) Warming of glass of bulb due to filament (d) Heating air around a furnace

A liquid in a beaker has temperature \(\theta(t)\) at time \(t\) and \(\theta_{0}\) is temperature of surroundings, then according to Newton's law of cooling the correct graph between \(\log _{e}\left(\theta-\theta_{0}\right)\) and \(t\) is \(\quad\) IAIEEE 2012! (a) (b) (d) (c)

Three very large plates of some area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates aremaintained at temperatures \(2 T\) and \(3 T\) respectively. The temperature of the middle (i.e., second) plate under steady state condition is \(\quad\) [IIT JEE 2012] (a) \(\left(\frac{65}{2}\right)^{1 / 4} T\) (b) \(\left(\frac{97}{4}\right)^{1 / 4} T\) (c) \(\left(\frac{97}{2}\right)^{1 / 4} T\) (d) \((97)^{1 / 4} T\)

Assuming the sun to be a spherical body of radius \(R\) at a temperature of \(T \mathrm{~K}\) evaluate the total radiant power incident on the earth at a distance \(r\) from the sun. [AIEEE 2006] (a) \(\pi r_{0}^{2} R^{2} \sigma T^{4} / r^{2}\) (b) \(r_{0}^{2} R^{2} \sigma T^{4} / 4 \pi r^{2}\) (c) \(R^{2} \sigma T^{4} / r^{2}\) (d) \(4 \pi r_{0}^{2} R^{2} \sigma T^{4} / r^{2}\)

Two rigid boxes containing different ideal gases are placed on a table box \(A\) contains one mole of nitrogen at temperature \(T_{0}\) while box \(B\) contains one mole of helium at temperature \(\left(\frac{7}{3}\right) T_{0}\). The boxes are then put into thermal contact with 0each other and heat flows between them untill the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases in terms of \(T_{0}\) is [AIEEE 2006] (a) \(T_{f}=\frac{7}{3} T_{0}\) (b) \(T_{r}=\frac{3}{2} T_{0}\) (c) \(T_{r}=\frac{5}{2} T_{0}\) (d) \(T_{f}=\frac{3}{7} T_{0}\)

Two rigid boxes containing different ideal gases are placed on a table box \(A\) contains one mole of nitrogen at temperature \(T_{0}\) while box \(B\) contains one mole of helium at temperature \(\left(\frac{7}{3}\right) T_{0}\). The boxes are then put into thermal contact with 0each other and heat flows between them untill the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases in terms of \(T_{0}\) is [AIEEE 2006] (a) \(T_{f}=\frac{7}{3} T_{0}\) (b) \(T_{r}=\frac{3}{2} T_{0}\) (c) \(T_{r}=\frac{5}{2} T_{0}\) (d) \(T_{f}=\frac{3}{7} T_{0}\)

Three perfect gases at absolute temperature \(T_{1}, T_{2}\) and \(T_{3}\) are mixed. The masses of molecules are \(m_{1}, m_{2}\) and \(m_{3}\) and the number of molecules are \(n_{1}, n_{2}\) and \(n_{3}\) respectively. Assuming no loss of energy the final \mathrm{\\{} t e m p e r a t u r e ~ o f ~ t h e ~ m i x t u r e ~ i s ~ (a) \(\frac{\left(T_{1}+T_{2}+T_{j}\right)}{3}\) (b) \(\frac{n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}}{\left(n_{1}+n_{2}+n_{3}\right)}\) (c) \(\frac{n_{1} T_{1}^{2}+n_{2} T_{2}^{2}+n_{1} T_{3}^{2}}{n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}}\) (d) \(\frac{n_{1}^{2} T_{1}^{2}+m^{2} T_{2}^{2}+n_{3}^{2} T_{3}^{2}}{\left(n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}\right)}\)

Two thermally insulated vessels 1 and 2 are filled with air at temperatures \(\left(T_{1}, T_{2}\right)\) volumes \(\left(V_{1}, V_{2}\right)\) and pressures ( \(p_{1}, p_{2}\) ) respectively of the value joining the two vessels is opened the temperature inside the vessel at equilibrium will be \(\quad\) [AIEEE 2008, 04] (a) \(T_{1}+T_{2}\) (b) \(\left(T_{1}+T_{2}\right) / 2\) (c) \(\frac{T_{1} T_{2}\left(p_{1} V_{1}+p_{2} V_{2}\right)}{p_{1} V_{1} T_{2}+p_{2} V_{2} T_{1}}\) (d) \(\frac{T_{1} T_{2}\left(p_{1} V_{1}+p_{2} V_{2}\right)}{p_{1} V_{1} T_{1}+p_{2} V_{2} T_{2}}\)