Chapter 16

A gas behaves more closely as an ideal gas at: (a) low pressure and low temperature (b) low pressure and high temperature (c) high pressure and low temperature (d) high pressure and high temperature

A vessel contains a mixture of nitrogen of mass \(7 \mathrm{~g}\) and carbon dioxide of mass \(11 \mathrm{~g}\) at temperature \(290 \mathrm{~K}\) and pressure \(1 \mathrm{~atm}\). The density of the mixture is : (a) \(1.1 \mathrm{~g} / \mathrm{L}\) (b) \(1.2 \mathrm{~g} / \mathrm{L}\) (c) \(1.515 \mathrm{~g} / \mathrm{L}\) (d) \(1.6 \mathrm{~g} / \mathrm{L}\)

Two chambers, one containing ' \(m_{1}^{\prime} \mathrm{g}\) of a gas at ' \(P_{1}\) ' pressure and other containing ' \(m_{2} \mathrm{~g}\) of a gas at \({ }^{\prime} P_{2}{\underline{\phantom{xx}}}^{\prime}\) pressure, are put in communication with each other. If temperature remains constant, the common pressure reached will be : (a) \(\frac{P_{1} P_{2}\left(m_{1}+m_{2}\right)}{P_{2} m_{1}+P_{1} m_{2}}\) (b) \(\frac{m_{1} m_{2}\left(P_{1}+P_{2}\right)}{\left(P_{2} m_{1}+P_{1} m_{2}\right)}\) (c) \(\frac{P_{1} P_{2} m_{1}}{P_{2} m_{1}+P_{1} m_{2}}\) (d) \(\frac{m_{1} m_{2} P_{2}}{\left(P_{2} m_{1}+m_{2} P_{1}\right)}\)

\(12 \mathrm{~g}\) of gas occupy a volume of \(4 \times 10^{-3} \mathrm{~m}^{3}\) at a temperature of \(7^{\circ} \mathrm{C}\). After the gas is heated at constant pressure, its density becomes \(6 \times 10^{-4} \mathrm{~g} / \mathrm{cm}^{3}\). What is the temperature to which the gas was heated? (a) \(1000 \mathrm{~K}\) (b) \(1400 \mathrm{~K}\) (c) \(1200 \mathrm{~K}\) (d) \(800 \mathrm{~K}\)

The pressure of a gas kept in an isothermal container is \(200 \mathrm{kPa}\). If half the gas is removed from it, the pressure will be: (a) \(100 \mathrm{kPa}\) (b) \(200 \mathrm{kPa}\) (c) \(400 \mathrm{kPa}\) (d) \(800 \mathrm{kPa}\)

How many cylinders of hydrogen at atmospheric pressure are required to fill a balloon whose volume is \(500 \mathrm{~m}^{3}\), if hydrogen is stored in cylinders of volume \(0.05 \mathrm{~m}^{3}\) at an absolute pressure of \(15 \times 10^{5} \mathrm{~Pa}\) ? (a) 700 (b) 675 (c) 605 (d) 710

Two identical containers \(A\) and \(B\) have frictionless pistons. Both contain same volume of ideal gas at same temperature. The gas in each cylinder is allowed to expand isothermally to double the initial volume. The mass of the gas in \(A\) is \(m_{A}\) and the mass of the gas in \(B\) is \(m_{B}\). The changes in the pressure in \(A\) and \(B\) are \(\Delta P\) and \(1.5 \Delta P\) respectively, then : (a) \(4 m_{A}=9 m_{B}\) (b) \(2 m_{A}=3 m_{B}\) (c) \(3 m_{A}=2 m_{B}\) (d) \(9 m_{A}=4 m_{B}\)

Two gases \(A\) and \(B\) are contained in the same vessel which is at temperature \(T\). The number of molecules of gas \(A\) is ' \(N^{\prime}\) and mass of each is ' \(m^{\prime}\). The number of molecules of gas ' \(B^{\prime}\) is \(2 N\), each of mass \((2 m)\). If mean square volocity of molecules of ' \(B\) ' is \(v^{2}\) and mean square velocity of \(x\) component of the velocity of ' \(A^{\prime}\) type is given by ' \(\omega^{2}\), then \(\omega^{2} / v^{2}\) is: (a) 2 (b) 1 (c) \(\frac{1}{3}\) (d) \(\frac{2}{3}\)

When without change in temperature, a gas is forced in a smaller volume, its pressure increases because its molecules : (a) strike the unit area of the container wall more often (b) strike the unit area of the container wall at higher speed (c) strike the unit area of container wall with greater force id) have more energy

The pressure of an ideal gas is written as \(P=\frac{2 E}{3 V}\), here \(E\) refers to: (a) translational kinetic energy (b) rotational kinetic energy (c) vibrational kinetic energy (d) total kinetic energy

A gas is contained in a closed vessel at \(250 \mathrm{~K}\), then the percentage increase in pressure, if the gas is heated through \(1^{\circ} \mathrm{C}\), is : (a) \(0.4 \%\) (b) \(0.6 \%\) (c) \(0.8 \%\) (d) \(1.0 \%\)

A horizontal cylinder open from one end and closed from the other, is rotated with a constant angular velocity '\omega' about a vertical axis passing through its open end. If outside air pressure is \(P_{0}\), the temperature is \(T\), and the molar mass of air is \(m\), then find the air pressure as a function of the distance \(r^{\prime}\) from the rotational axis, : (Assume molar mass is independent of \(r\) ): (a) \(P=P_{0} e^{\left(w \omega^{2} r^{2} / 2 R T\right)}\) (b) \(P=P_{\alpha} e^{\left(m \omega^{2} r^{2} / R T\right)}\) (c) \(P=P_{0} e\) m \(\omega \mathrm{r}^{2} / \mathrm{RT} \quad\) (d) \(P=P_{0} e^{-m \omega^{2} r^{2} / 2 R T}\)

Mark correct option \(/ \mathrm{s}\) : (a) The root mean square speeds of the molecules of different ideal gases, maintained at the same temperature are the same (b) Electrons in a conductor have no motion in the absence of a potential difference across it (c) One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas The molar specific heat of the mixture at constant volume is \(2 R\) (d) The pressure exerted by an enclosed ideal gas depends on the shape of the container

Four molecules of a gas have speeds \(1,2,3\) and \(4 \mathrm{~km} / \mathrm{s}\). The value of the root-mean square speed of the gas molecules is : (a) \(\frac{1}{2} \sqrt{15} \mathrm{~km} / \mathrm{s}\) (b) \(\frac{1}{2} \sqrt{10} \mathrm{~km} / \mathrm{s}\) (c) \(2.5 \mathrm{~km} / \mathrm{s}\) (d) \(\sqrt{\frac{15}{2}} \mathrm{~km} / \mathrm{s}\)

The temperature of \(\mathrm{H}_{2}\) at which the rms velocity of its molecules is seven times the rms velocity of the molecules of nitrogen at \(300 \mathrm{~K}\), is (a) \(2100 \mathrm{~K}\) (b) \(1700 \mathrm{~K}\) (c) \(1350 \mathrm{~K}\) (d) \(1050 \mathrm{~K}\)

Choose the correct order of the root mean square velocity \(\left(v_{\mathrm{rms}}\right)\), the average velocity \(\left(v_{\mathrm{av}}\right)\) and the most probable velocity \(\left(v_{\mathrm{mp}}\right):\) (a) \(v_{\mathrm{mp}}>v_{\mathrm{av}}>v_{\mathrm{rms}}\) (b) \(v_{\mathrm{rms}}>v_{\mathrm{av}}>v_{\mathrm{mp}}\) (c) \(v_{\text {av }}>v_{\mathrm{mp}}>v_{\mathrm{rms}}\) (d) \(v_{\mathrm{m} p}>v_{\mathrm{rms}}>v_{\mathrm{av}}\)

Five gas molecules chosen at random are found to have speeds of \(500,600,700,800\) and \(900 \mathrm{~m} / \mathrm{s}\). Then : (a) the rms speed and the average speed are the same (b) the rms speed is \(14 \mathrm{~m} / \mathrm{s}\) higher than the average speed (c) the rms speed is \(14 \mathrm{~m} / \mathrm{s}\) lower than that the average speed (d) the rms speed is \(\sqrt{14} \mathrm{~m} / \mathrm{s}\) higher than that the average speed.

In case of molecules of an ideal gas, which of the following, average velocities cannot be zero? (a) \(\langle\bar{v}\rangle\) (b) \(\left.<\bar{v}^{3}\right\rangle\) (c) \(\left\langle\bar{v}^{4}\right\rangle\) (d) \(\left\langle\bar{v}^{5}\right\rangle\)

Choose the correct relation between the rms speed \(\left(v_{\mathrm{ms}}\right)\) of the gas molecules and the velocity of sound in that gas \(\left(v_{s}\right)\) in identical situations of pressure and temperature : (a) \(v_{\mathrm{rms}}=v_{\mathrm{s}}\) (b) \(v_{\mathrm{rms}}=\sqrt{\left(\frac{3}{\gamma}\right)} v_{\mathrm{s}}\) (c) \(v_{\mathrm{r} n \mathrm{n}}=\sqrt{\left(\frac{\gamma}{3}\right)} v_{\mathrm{c}}\) (d) \(\gamma v_{\mathrm{rms}}=3 v_{s}\)

At what temperature is the effective speed of gaseous hydrogen molecules equal to that of oxygen molecules at \(47^{\circ} \mathrm{C} ?\) (a) \(50 \mathrm{~K}\) (b) \(20 \mathrm{~K}\) (c) \(40 \mathrm{~K}\) (d) \(100 \mathrm{~K}\)

Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium? (a) Kinetic energy (b) Momentum (c) Density (d) Speed

On a fast moving train, a container is placed enclosing some gas at \(300 \mathrm{~K}\), while the train is in motion, the temperature of the gas (a) rises above \(300 \mathrm{~K}\) (b) falls below \(300 \mathrm{~K}\) (c) remains unchanged (d) becomes unsteady

The temperature at which average translational K.E. of molecule is equal to the K.E. of an electron accelerated from rest through a potential difference of \(1 \mathrm{~V}\), is : (a) \(T=7729 \mathrm{~K}\) (b) \(T=8879 \mathrm{~K}\) (c) \(T=7.72 \mathrm{~K}\) (d) \(T=772.9 \mathrm{~K}\)

The temperature of the mixture, if two perfectly monoatomic gases at absolute temperatures \(\overline{1}_{1}\) and \(T_{2}\) and number of moles in the gases \(n_{1}\) and \(n_{2}\), respectively are mixed, is: (Assume no loss of energy) (a) \(T=\frac{n_{1} T_{2}+n_{2} T_{1}}{n_{1}+n_{2}}\) (b) \(T=\frac{n_{1} T_{2}-n_{2} T_{1}}{n_{1}+n_{2}}\) (c) \(T=\frac{n_{1} T_{1}+n_{2} T_{2}}{n_{1}+n_{2}}\) (d) \(T=\frac{n_{1} T_{1}-n_{2} T_{2}}{n_{1}-n_{2}}\)

In a model of chlorine \(\left(\mathrm{Cl}_{2}\right)\), two \(\mathrm{Cl}\) atoms are rotated about their centre of mass as shown. Here the two 'Cl' atoms are \(2 \times 10^{-10} \mathrm{~m}\) apart and angular speed \(\omega=2 \times 10^{12} \mathrm{rad} / \mathrm{s}\). If the molar mass of chlorine is \(70 \mathrm{~g} / \mathrm{mol}\), then what is the rotational kineti \(_{2}\) energy of one \(\mathrm{Cl}_{2}\) molecule? (a) \(2.32 \times 10^{-20} \mathrm{~J}\) (b) \(2.32 \times 10^{-21} \mathrm{~J}\) (c) \(2.32 \times 10^{-i>}\) \\} (d) \(2.32 \times 10^{-22} \mathrm{~J}\)

If the temperature of 3 moles of helium gas is increased by \(2 \mathrm{~K}\), then the change in the internal energy of helium gas is: (a) \(70.0 \mathrm{~J}\) (b) \(68.2 \mathrm{~J}\) (c) \(74.8 \mathrm{~J}\) (d) \(78.2 \mathrm{~J}\)

Increase of pressure: (a) always increases the boiling point of a liquid (b) always increases the melting point of a solid (c) increases the melting point of solid which expand on melting (d) always decreases the melting point of solid

Unsaturated vapour obeys: (a) Ideal gas law (b) van der Waal's law (c) Boyle's law (d) Gay-Lussac law

In the case of saturated vapour: (a) pressure 'depends upon volume at constant temperature (b) pressure varies non-linearly with temperature at constant volume (c) pressure becomes less than one atmosphere at boiling point (d) pressure varies linearly with temperature at constant volume