CBSE Questions for Class 11 Engineering Physics Kinetic Theory Quiz 14 - MCQExams.com

A closed hollow insulated cylinder is filled with gas at 0$$^{0}$$C and also contains an insulated piston of negligible weight and negligible thickness at the the middle point. The gas at one side of the piston is heated to 100$$^{0}$$C . If the piston moves 5cm, the length of the hollow cylinder is
  • 13.65 cm
  • 27.3 cm
  • 64.6 cm
  • 54.6 cm
An ideal monoatomic gas $$(C_{v}=1.5\ R)$$ initially at $$298$$ K and $$1.013$$ atm expands adiabatically irreversibly until it is in equilibrium with a constant external pressure of $$0.1013$$ atm. The final temperature (in Kelvin) of the gas is :
  • $$190.7$$
  • $$119.7$$
  • $$278$$
  • $$273$$
How many degrees of freedom have the gas molecules if at S.T.P the gas density is 1.3 kg/m$$^{3}$$ and the velocity of sound in the gas is 330 m/sec?
  • $$5$$
  • $$6$$
  • $$4$$
  • $$3$$
A motor draws some gas from an adiabatic container of volume 2 liters having a monatomic gas at a pressure 4 atm. After drawing the gas the pressure in the container reduces to 1 atm. If the motor converts 10% of the energy contained in the drawn gas and the output of the motor is 10p joule, then p is
( Use $$1atm=10^5 pascal)$$
  • 9
  • 4
  • 8
  • 6
Which of the following will have maximum total kinetic energy at temperature 300 K ?
  • $$1 kg, H_{2}$$
  • $$1 kg , He$$
  • $$\frac{1}{2}kg H_{2}+\frac{1}{2}kg He$$
  • $$\frac{1}{4}kg H_{2}+\frac{3}{4}kg He$$
A gas mixture consists of $$2$$ moles of oxygen and $$4$$ moles of argon at temperature $$T$$. Neglecting all vibrational modes, the total internal energy of the system is
  • $$4 RT$$
  • $$5 RT$$
  • $$15 RT$$
  • $$11 RT$$
2 moles of an ideal gas A ($$ {C}_{P} $$ $$= 4R$$) and 4 moles of an ideal gas B ($$ {C}_{V} $$ $$= \dfrac {3R}{2}$$) are taken together in a container and allowed to expand reversibly and adiabatically from 49L to 64L, starting from an initial temperature of $$ {47}^{0} $$C. The final temperature of the gas is :
  • $$4{}^{0}C$$
  • $$5{}^{0}C$$
  • $$7{}^{0}C$$
  • $$8{}^{0}C$$
The ratio of translational and rotational kinetic energies at 100 K temperature is 3 :Then the internal energy of one mole gas at that temperature is $$[R = 8.3 J/mol-K]$$
  • $$1175J$$
  • $$1037.5 J$$
  • $$2075 J$$
  • $$4150J$$
One mole of an ideal gas $$ [{C}_{v,m} = \frac {5}{2}R ] $$ at $$300$$ K and $$5$$ atm is expanded adiabatically to a final pressure of $$2$$ atm against a constant pressure of $$2$$ atm. The final temperature (in Kelvin) of the gas is:
  • $$270.2$$
  • $$273.0$$
  • $$248.5$$
  • $$200.5$$
Maxwell"s velocity distribution curve is given for the same quantity for two different temperatures. For the given curves then which of the folowing relation is true?


71856_23e8cbe6cfe04770bb993c56cbc34db8.jpg
  • $$T_{1}> T_{2}$$
  • $$T_{1}< T_{2}$$
  • $$T_{1}\leq T_{2}$$
  • $$T_{1}= T_{2}$$
During an experiment, an ideal gas is found to obey a condition $$\dfrac{P^{2}}{\rho }$$ $$= $$constant [$$\rho = $$density of the gas]. The gas is initially at temperature T, pressure P and density $$\rho$$. The gas expands such that density changes to $$\dfrac{\rho}{2}$$
  • The pressure of the gas changes to $$\sqrt{2}P$$
  • The temperature of the gas changes to $$\sqrt{2}T$$
  • The graph of the above process on the P-T diagram is parabola.
  • The graph of the above process on the P-T diagram is hyperbola.
A monoatomic ideal gas ($$ {C}_{V} = \dfrac {3}{2} R$$) is allowed to expand adiabatically and reversibly from initial volume of 8L at 300 K to a volume of $$ {V}_{2} $$ at 250 K. $$ {V}_{2} $$ is: 
(Given $${(4.8)}^{1/2}$$ = 2.2)
  • 10.5 L
  • 23 L
  • 8.5 L
  • 50.5 L
On heating 128 g of oxygen gas from 0$$^{\circ}$$C to 100$$^{\circ}$$C, $$C_V$$ and $$C_P$$ on an average are 5 and 7 cal mol$$^{-1}$$ degree$$^{-1}$$, the value of $$\Delta$$U and $$\Delta$$H are respectively :
  • 2800 cal, 2000 cal
  • 2000 cal, 2800 cal
  • 280 cal, 200 cal
  • none of the above
The heat capacity of a certain amount of a particular gas at constant pressure is greater than that at constant volume by 29.1 J/K. Match the items given in Column I with the items given in Column II.
List 1List 2
If the gas is monatomic, heat capacity at constant volume131 J/K
If the gas monatomic, heat capacity at constant pressure43.7 J/K
If the gas is rigid diatomic, heat capacity at constant pressure72.7 J/K
If the gas is vibrating diatomic, heat capacity at constant pressure102 J/K
  • A$$\rightarrow$$2, B$$\rightarrow$$3, C$$\rightarrow$$4, D$$\rightarrow$$1
  • B$$\rightarrow$$1, C$$\rightarrow$$3, D$$\rightarrow$$4, A$$\rightarrow$$1
  • C$$\rightarrow$$1, D$$\rightarrow$$3, A$$\rightarrow$$4, B$$\rightarrow$$1
  • D$$\rightarrow$$1, A$$\rightarrow$$3, B$$\rightarrow$$4, C$$\rightarrow$$1
$$S_1$$: At extermely high temperature degree of freedom of monatomic gas becomedue to activation of vibrational degree of freedom.
$$S_2$$: For a uniformly charged solid non-conducting sphere potential is maximum at it's centre.
$$S_3$$: Breaking stress of wire depends on its corss-sectional Area.
$$S_4$$: Only time varying magnetic field produces induced electric field which have lines of force.
  • FFFT
  • TTTF
  • FTFT
  • TFTF
At what temperature does the mean kinetic energy of hydrogen atoms increase to such an extent that they will escape out of the gravitational field of earth forever?
  • $$10075^o$$K
  • $$10000^o$$K
  • $$12075^o$$K
  • $$20000^o$$K
Consider a classroom of dimensions $$(5 \times 10 \times 3)\ $$m$$^3$$ at temperature $$20^{o}$$C and pressure $$1$$ atm. There are $$50$$ people in the room, each losing energy at the average of $$150$$ watts. Assuming that the walls, ceiling, floor, and furniture are perfectly insulated and none of them is absorbing heat. How much time will be needed for raising the temperature of air in the room to the body temperature (37$$^{o}C$$)? [For air $$C_p = \dfrac{7}{2} R$$ and neglect the loss of air to the outside as the temperature rises]
  • $$422$$ sec
  • $$411.3$$ sec
  • $$421.1$$ sec
  • $$413.1$$ sec
$$1$$ mole of an ideal gas $$A\ ({ C }_{ v,m }=3R)$$ and $$2$$ moles of an ideal gas $$B\ \left( { C }_{ v,m }=\cfrac { 3 }{ 2 } R \right)$$ are taken in a container and expanded reversibly and adiabatically from $$1$$ litre to $$4$$ litres starting from initial temperature of $$320K$$. $$\Delta E$$ or $$\Delta U$$ for the process is:
  • $$-240R$$
  • $$240R$$
  • $$480R$$
  • $$-960R$$
In a certain gas $$\displaystyle \frac{2}{5}$$th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. The average translation energy of one such molecule, when the temperature is $$27^{\circ}C$$ is given by $$x\times 10^{-23}\ J$$,then find $$x$$?
  • 621
  • 623
  • 6.21
  • 62.1
One box containing $$1$$ mole of $$He$$ at $$7/3 T_0$$ and other box containing $$1$$ mole of a polyatomic gas $$(\gamma=1.33)$$ at $$T_0$$ are placed together to attain thermal equilibrium. The final temperature becomes $$T_f$$. Then :
  • $$T_f=\dfrac {9}{13}T_0$$
  • $$T_f=\dfrac {13}{9}T_0$$
  • $$T_f=\dfrac {5}{2}T_0$$
  • $$T_f=\dfrac {3}{2}T_0$$
Identify the type of gas filled in container A and B respectively
193596.jpg
  • Mono, mono
  • Dia, dia
  • Mono, dia
  • Dia, Mono
In a certain gas $$\displaystyle \frac{2}{5}$$th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by $$1^{\circ}C$$?
  • $$20.8 J$$
  • $$28.8 J$$
  • $$26.8 J$$
  • $$25.8 J$$
A rigid container of negligible heat capacity contains one mole of a gas. 10 calories of heat is required to increase the temperature by $$2^oC$$ in the Boyle's temperature range. The gas in container may be
  • He
  • $$H_2$$
  • $$O_2$$
  • Ar
A monoatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equal to unity. The molar heat capacity of gas is:
  • $$\frac {4R}{2}$$
  • $$\frac {3R}{2}$$
  • $$\frac {5R}{2}$$
  • zero
Which of the following statements is wrong about the gas?
  • The gas is monoatomic
  • The gas is $$He$$
  • The gas is a rare gas or inert gas
  • The number of molecules of gas is $$3.01 \times 10^{24}$$
Select the correct orders for gases represented with their characteristics:
  • Critical temperature < Boyle's temperature
  • van der Waal's constant 'a' : $$H_2O > NH_3 > N_2 > Ne$$
  • Heat capacity: $$NH_3 > CO_2 > O_2 = N_2 > Ar$$
  • Mean free path: $$He > H_2 > O_2 > N_2 > CO_2$$
Figure shows the variation of the internal energy $$U$$ with density $$\rho$$ of one mole of an ideal monatomic gas for thermodynamic cycle ABCA. Here process AB is a part of rectangular hyperbola

289897_b3a70d9e69fa4a638a2f5a310e3c219b.png
  • process AB is isothermal & net work in cycle is done on gas
  • process AB is isothermal & net work in cycle is done by the gas
  • process AB is isobaric & net work in cycle is done on the gas
  • process AB is adiabatic & net work in cycle is done by gas
Keeping the number of moles, volume and pressure the same, which of the following are the same for all ideal gas?
  • rms speed of a molecule
  • density
  • temperature
  • average of magnitude of momentum
A sample of a fluorocarbon was allowed to expand reversibly and adiabatically to twice its volume. In the expansion the temperature dropped from 298.15 to 248.44 K. Assume the gas behaves perfectly. Estimate the value of $$C_{V_1 m}$$.
  • $$C_{V_1m} = 31.6 Jk^{1} mol^{1}$$
  • $$C_{V_1m} = 3.16 Jk^{1} mol^{1}$$
  • $$C_{V_1m} = 316 Jk^{1} mol^{1}$$
  • None of these
One mole of an ideal gas $$\left (C_{v,m}\, =\, \displaystyle \frac {5}{2} R \right )$$ at $$300$$ K and $$5$$ atm is expanded adiabatically to a final pressure of $$2$$ atm against a constant pressure of $$2$$ atm. Final temperature of the gas is:
  • $$270$$ K
  • $$273$$ K
  • $$248.5$$ K
  • $$200$$ K
The quantity $$\dfrac {2U}{fkT}$$ represents (where $$U=$$ internal energy of gas)
  • mass of the gas
  • kinetic energy of the gas
  • number of moles of the gas
  • number of molecules in the gas
In the figure, an ideal gas is expanded from volume $$V_0$$ to $$2V_0$$ under three different processes. Process 1 is isobaric, process 2 is isothermal and process 3 is adiabatic. Let $$\Delta U_1, \Delta U_2$$ and $$\Delta U_3$$ be the change in the internal energy of the gas is these three processes, Then:

294459.png
  • $$\Delta U_1 > \Delta U_2 > \Delta U_3$$
  • $$\Delta U_1 < \Delta U_2 < \Delta U_3$$
  • $$\Delta U_2 < \Delta U_1 < \Delta U_3$$
  • $$\Delta U_2 < \Delta U_3 < \Delta U_1$$
Among the following, identify the substance in which molecules possess vibratory, rotatory and translatory motion, but their movements are not random.
  • Bromine
  • Iodine
  • Ammonia
  • Silicon dioxide
Name $$A, B, C, D,E,$$ and $$F$$ in the following diagram showing change of state
512697.jpg
  • A $$=$$ Melting, B$$=$$ Vaporisation, C $$=$$ Condensation, D $$=$$ Solidification, E $$=$$ Sublimation, F $$=$$ Solidification of gaseous state
  • A $$=$$ Sublimation, B $$=$$ Vaporisation, C $$=$$ Condensation, D $$=$$ Solidification, E $$=$$ Melting, F $$=$$ Solidification of gaseous state
  • A $$=$$ Condensation, B $$=$$ Vaporisation, C $$=$$ Melting, D $$=$$ Solidification, E $$=$$ Sublimation, F $$=$$ Solidification of gaseous state
  • A $$=$$ Vaporisation, B $$=$$ Melting, C $$=$$ Condensation, D $$=$$ Solidification, E $$=$$ Sublimation, F $$=$$ Solidification of gaseous state
If one mole of a monoatomic gas $$\left (\gamma = \dfrac {5}{3}\right )$$ is mixed with one mole of diatomic gas $$\left (\gamma = \dfrac {7}{5}\right )$$, the value of $$\gamma$$ for the mixture is :
  • $$1.40$$
  • $$1.50$$
  • $$1.53$$
  • $$3.07$$
$$\displaystyle N_{2}$$ gas is assumed to behave ideally A given volume of $$\displaystyle N_{2}$$ originally at 373 k and 0.1013 M pa pressure is adiabatically compressed due to which its temperature rises to $$\displaystyle 673 \ K \left ( Cv=\frac{5}{2}R \right )$$

Which of the following statement(s) is/are correct?
  • The change in internal energy is 6235.5 J $$\displaystyle mole^{-1}$$
  • In this case the final internal pressure is equal to the external pressure
  • The final pressure of $$\displaystyle N_{2}$$ is approximately 0.38 MPa
  • The final pressure of $$\displaystyle N_{2}$$ is approximately 0.02 Mpa
According to the Kinetic Molecular Theory, temperature is directly proportional to:
  • average kinetic energy
  • lattice energy
  • ionization energy
  • free energy
  • average potential energy
A molecule of gas in a container hits one wall (1) normally and rebounds back. It suffers no collision and hits the opposite wall (2) which is at an angle of $$30^\circ$$ with wall 1. 
Assuming the collisions to be elastic and the small collision time to be the same for both the walls, the magnitude of average force by wall( $$F_2$$ ) provided to the molecule during collision satisfy :

335361_6852e6e5689d41a3a68d7eba3b379428.png
  • $$F_1\, >\, F_2$$
  • $$F_1\, <\, F_2$$
  • $$F_1\, =\,F_2$$, bothnon-zero
  • $$F_1\, =\, F_2\, =\, 0$$
A gaseous mixture enclosed in a vessel consists of one g mole of a gas A with $$\displaystyle \gamma =\left ( \frac{5}{3} \right ) $$ and some amount of gas B with $$\displaystyle \gamma = \frac{7}{5} $$ at a temperature The gasses A and B do not react with each other and are assumed to be ideal Find the number of g moles of the gas B if $$\displaystyle \gamma $$ for the gaseous mixture is $$\displaystyle \left ( \frac{19}{13} \right ) $$ 
  • 2
  • 5
  • 4
  • 3
One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is $$P_0$$. Choose the correct option(s) from the following.
1010959_2f71b2dccec543e4abb5609f8f3fb9cd.png
  • Internal energies at A and B are the same
  • Work done by the gas in process AB is $$P_oV_o$$ ln $$4$$
  • Pressure at C is $$\dfrac{P_o}{4}$$
  • Temperature at C is $$\dfrac{T_o}{4}$$
If the radii of two copper spheres are in the ratio $$1 : 3$$ and increase in their temperatures are in the ratio $$9 : 1$$ then the ratio of the increase in their internal energy will be
  • $$1 : 4$$
  • $$2 : 1$$
  • $$4 : 1$$
  • $$1 : 3$$
Relation between pressure ($$P$$) and energy density ($$E$$) of an ideal gas is-
  • $$P=2/3E$$
  • $$P=3/2E$$
  • $$P=3/5E$$
  • $$P=E$$
An insulated container is divided into two equal portions. One portion contains an ideal monoatomic gas at pressure $$P$$ and temperature $$T$$, while the other portion is a perfect vacuum. If a hole is opened between the two portions, the change in internal energy of the gas is
  • Zero
  • Equal to work done by the gas
  • Equal to work done on the gas
  • $$3RT/2$$
Let $$\overline {v}, v_{rms}$$ and $$v_{p}$$, respectively, denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monatiomc gas at absolute temperature $$T$$. The mass of a molecules is $$m$$. Then
  • No molecule can have a speed greater than $$\sqrt {2} v_{rms}$$
  • No molecule can have speed less than $$v_p/\sqrt {2}$$
  • $$v_{p} < \overline {v} < v_{rms}$$
  • The average kinetic energy of a molecule is $$\dfrac {3}{4}mv^{2}_{P}$$
An ideal gas is taken from the state A(pressure $$P_0$$, volume $$V_0$$) to the state B (pressure $$P_0/2$$, volume $$2V_0$$) along a straight line path in the P-V diagram. Select the correct statement(s) from the following.
  • The work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm
  • In the T-V diagram, the path AB becomes a part of the parabola
  • In the P-T diagram, the path AB becomes a part of hyperbola
  • In going from A to B, the temperature T of the gas first increases to maximum value and then decreases
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between $$P_1$$ and $$P_2$$?
939333_baf40843a0bc4a409ab0c65b38e61c2b.png
  • $$P_1 > P_2$$
  • $$P_1 = P_2$$
  • $$P_1 < P_2$$
  • Data is insufficient
The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be
  • $$PV=\Big(\dfrac{5}{32}\Big)RT$$
  • $$PV = 5 RT$$
  • $$PV = \Big(\dfrac{5}{2}\Big)RT$$
  • $$PV = \Big(\dfrac{5}{16}\Big)RT$$
The maximum high temperature molar heat capacity at constant volume to be expected for acetylene which is linear molecule is:
  • 9 cal/deg-mol
  • 12 cal/deg-mol
  • 19 cal/deg-mol
  • 14 cal/deg-mol
In the given figure conainer $$A$$ holds an ideal gas at a pressure of $$5.0 \times 10^{5}\ Pa$$ and a temperature of $$300\ K.$$ It is connected by the tin tube (and a closed valve) to container $$B$$, with four times the volume of $$A$$. Container $$B$$ hold same ideal gas at a pressure of $$1.0\ \times 10^{5}\ Pa$$ and a temperature of $$400\ K$$. The valve is opened to allow the pressure to equalize, but the temperature of each container kept constant at its initial value. The final pressure in the two containers will be close to :
1031287_7b5d344b2bc749a593ae2280f3b7272b.png
  • $$2.0 \times 10^{5}\ Pa$$
  • $$2.5 \times 10^{5}\ Pa$$
  • $$3.0 \times 10^{5}\ Pa$$
  • $$3.5 \times 10^{5}\ Pa$$
Liquid is filled in a vessel which is kept in a room with temperature $$20^\circ C$$. When the temperature of the liquid is $$80^\circ C$$, then it losses heat at the rate of 60 cal/sec.What will be the rate of loss of heat when the temperature of the liquid is $$40^\circ C$$.
  • 180 cal/sec
  • 40 cal/sec
  • 30 cal/sec
  • 20 cal/sec
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