CBSE Questions for Class 11 Engineering Physics Kinetic Theory Quiz 9 - MCQExams.com

The temperature (T) of one mole of an ideal gas varies with its volume (V) as $$T = -\alpha { V }^{ 3 }+\ \beta { V }^{ 2 }$$, where $$\alpha$$ and $$\beta$$ are positive constants. The maximum pressure of gas during this process is
  • $$\dfrac { \alpha \beta }{ 2R } $$
  • $$\dfrac { { \beta }^{ 2 }R }{ 4\alpha }$$
  • $$\dfrac { (\alpha +\beta )R }{ { 2\beta }^{ 2 } }$$
  • $$\dfrac { { \alpha }^{ 2 }R }{ { 2\beta } }$$
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increase the internal energy of gas is?
  • $$\frac{2}{5}$$
  • $$\frac{3}{5}$$
  • $$\frac{3}{7}$$
  • $$\frac{5}{7}$$
Two identical glass bulbs are interconnected by a thin glass tube at $$0^{\circ}C$$. A gas is filled at N.T.P. in these bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes $$1.5\ times$$. The temperature of hot bath will be
865956_5658c3edd3f248a29852cfa67c6da7f3.png
  • $$100^{\circ}$$
  • $$182^{\circ}C$$
  • $$256^{\circ}C$$
  • $$546^{\circ}C$$
A vessel of volume $$0.3 \ { { m }^{ 3 } }$$ contains Helium at $$20.0$$. The average kinetic energy per molecule for the gas is:
  • $$6.07\times { 10 }^{ -21 }J$$
  • $$7.3\times { 10 }^{ 3 }J$$
  • $$14.6\times { 10 }^{ 3 }J$$
  • $$12.14\times { 10 }^{ -21 }J$$
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:
  • $$1.5\ R$$
  • $$2.0\ R$$
  • $$2.5\ R$$
  • $$0$$
A monoatomic ideal gas, initially at temperature $$T_1$$. is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to temperature $$T_2$$ by releasing the piston suddenly. If $$L_1$$ and $$L_2$$ are the lengths of the gas column before and after expansion respectively, then $$\frac{T_1}{T_2}$$ is given by  
  • $$(\dfrac{L_1}{L_2})^{2/3}$$
  • $$\dfrac{L_1}{L_2}$$
  • $$\dfrac{L_2}{L_1}$$
  • $$(\dfrac{L_2}{L_1})^{2/3}$$
If for a gas $$\dfrac{R}{C_V}=0.67$$, this gas is made up of molecules which are.
  • Monatomic
  • Diatomic
  • Polyatomic
  • Mixture of diatomic and polyatomic molecules
One Kg of a diatomic gas is at a pressure of $$8\times 10^4$$N/ $$m^{2}$$. The density of the gas is $$4$$kg/ $$m^{3}$$. The energy of the gas due to its thermal motion will be
  • $$3\times 10^4$$J
  • $$5\times 10^4$$J
  • $$6\times 10^4$$J
  • $$7\times 10^4$$J
The internal energy of one gram of helium at $$100$$K and one atmospheric pressure is?
  • $$100$$J
  • $$1200$$J
  • $$300$$J
  • $$500$$J
Which one of the following is not an assumption of kinetic theory of gases?
  • The volume occupied by the molecules of the gas is negligible
  • The force of attraction between the molecules is negligible
  • The collision between the molecules are elastic
  • All molecules have same speed
A vessel of volume V contains a mixture of $$1$$mole of hydrogen and $$1$$ mole of oxygen(both considered as ideal). Let $$f_1(v)dv$$ denote the fraction of molecules with speed between v and $$(v+dv)$$ with $$f_2(v)dv$$, similarly for oxygen. then
  • $$f_1(v)+f_2(v)=f(v)$$ obeys the Maxwell's distribution law
  • $$f_1(v), f_2(v)$$ will obey the Maxwell's distribution law separately
  • Neither $$f_1(v)$$ nor $$f_2(v)$$ will obey the Maxwell's distribution law
  • $$f_2(v)$$ and $$f_1(v)$$ will be the same
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
  • $$9$$RT
  • $$11$$RT
  • $$15$$RT
If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature
  • Is doubled
  • Becomes one-fourth
  • Remains constant.
  • Become four times
The average kinetic energy of $$O_2$$ at a particular temperatures is $$0.768$$ eV. The average kinetic energy of $$N_2$$ molecules in eV at the same temperature is?
  • $$0.0015$$
  • $$0.0030$$
  • $$0.048$$
  • $$0.768$$
Molecular motion shows itself as.
  • Temperature
  • Internal energy
  • Friction
  • Viscosity
The kinetic energy of $$1$$g molecule of a gas, at normal temperature and pressure, is?
  • $$0.56\times 10^4$$J
  • $$2.7\times 10^2$$J
  • $$1.3\times 10^2$$J
  • $$3.4\times 10^3$$J
Pressure depends on distance as $$P = \dfrac{\alpha}{\beta} exp (- \dfrac{\alpha z}{k \theta})$$, where $$\alpha, \beta$$ are constants, z is distance, k is Boltzmann's constant, and $$\theta$$ is temperature. The dimensions of $$\beta$$ are
  • $$M^0L^0T^0$$
  • $$M^{-1}L^{-1}T^{-1}$$
  • $$M^0L^2T^0$$
  • $$M^{-1}L^{2}T^{2}$$
A vessel contains a mixture consisting of m$$_{1}$$ - 7 g of nitrogen (M$$_{1}$$ = 28) and m$$_{2}$$ = 11 g of carbon dioxide (M$$_{2}$$ = 44) at temperature T - 300 K and pressure P$$_{0}$$ = 1 atm. The density of the mixture is
  • $$1.46g\ per\ litre$$
  • $$2.567 g \ per \ litre$$
  • $$3.752 g \ per \ litre$$
  • $$4.572 g \ per \ litre$$
A gas performs Q work when it expand at constant pressure. During this process heat absorbed by the gas is 4Q. The average number of degrees of freedom for the gas is:
  • 5
  • 6
  • 4
  • 3.5
An ideal gas is initially at $$P_1$$, $$V_1$$ is expanded to $$P_2, V_2$$ and then compressed adiabatically to the same volume $$V_1$$ and pressure $$P_3$$. If W is the net work done by the gas in the complete process which of the following is true.
1010641_c06cf05d2f354282aba8dea5d8b9ad6b.png
  • $$W > 0; P_3 > P_1$$
  • $$W < 0; P_3 > P_1$$
  • $$W > 0; P_3 < P_1$$
  • $$W < 0; P_3 < P_1$$
A vessel contains a mixture consisting of $${m}_{1}=7kg$$ of nitrogen $$\left( { M }_{ 1 }=28 \right) $$ and $${m}_{2}=11g$$ of carbon dioixide $$\left( { M }_{ 2 }=44 \right) $$ at temeprature $$T=300K$$ and pressure $${ P }_{ 0 }=1\quad atm$$. The density of the mixture is:
  • $$1.446g$$ per litres
  • $$2.567g$$ per litre
  • $$3.752g$$ per litre
  • $$4.572g$$ per litre
The average degree of freedom per molecule for a gas isThe gas performs 25 J of work when it expands at constant pressure. The heat absorbed by the gas is
  • 75 J
  • 100 J
  • 150 J
  • 125 J
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is $$2.20\ times$$ the pressure measured at the triple point of water find the melting point of lead.
  • $$600K$$
  • $$420K$$
  • $$790K$$
  • $$510K$$
For a ideal gas.
  • The change in internal energy in a constant pressure process from temperature $$T_1$$ to $$T_2$$ is equal to $$NC_V(T_2-T_1)$$, where $$C_V$$ is the molar specific heat at constant volume and n is the number of moles of the gas
  • The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process
  • The internal energy does not change in an isothermal process
  • No heat is added or removed in an adiabatic process
Match List I with List II and select the correct answer using the codes given the lists.
List IList II
P. Boltzmann Constant$$1$$. $$[ML^2T^{-1}]$$
Q. Coefficient of viscosity$$2$$. $$[ML^{-1}T^{-1}]$$
R. Plank Constant$$3$$. $$[MLT^{-3}K^{-1}]$$
S. Thermal conducivity$$4$$. $$[ML^2T^{-2}K^{-1}]$$
  • P-$$3$$, Q-$$1$$, R-$$2$$, S-$$4$$
  • P-$$3$$, Q-$$2$$, R-$$1$$, S-$$4$$
  • P-$$4$$, Q-$$2$$, R-$$1$$, S-$$3$$
  • P-$$4$$, Q-$$1$$, R-$$2$$, S-$$3$$
An insulated box containing monatomic ideal gas of molar mass M is moving with a uniform speed v. The box suddenly stops and consequently the gas acquires a new temperature. Calculate the change in the temperature of the gas. Neglect heat absorbed by the box.
  • $$\Delta T=2\dfrac{Mv^2}{3R}$$.
  • $$\Delta T=\dfrac{Mv^2}{3R}$$.
  • $$\Delta T=3\dfrac{Mv^2}{3R}$$.
  • $$\Delta T=4\dfrac{Mv^2}{3R}$$.
A gas molecule of mass $$M$$ at the surface of the earth has kinetic energy equivalent to $${0}^{o}C$$. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. ($${k}_{B}$$ is Boltzmann constant)
  • zero
  • $$\cfrac { 273{ k }_{ B } }{ 2Mg } $$
  • $$\cfrac { 546{ k }_{ B } }{ 3Mg } $$
  • $$\cfrac { 819{ k }_{ B } }{ 2Mg } \quad $$
An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes $$5.66$$V while its temperature falls to $$T/2$$. How many degrees of freedom do the gas molecules have?
  • 7
  • $$5$$.
  • 6
  • 8
$$m$$ grams of a gas of molecular weight $$M$$ is flowing in an insulated tube with velocity $$v$$. If the system is suddenly stopped then the rise in its temperature will be (γ= ratio of specific heats, R=universal gas constant, J=Mechanical equivalent of heat)
  • $$\dfrac {Mv^{2}(\gamma - 1)}{2RJ}$$
  • $$\dfrac {Mv^{2}\gamma}{2RJ}$$
  • $$\dfrac {v^{2}}{2Js}$$
  • $$\dfrac {Mv^{2}(\gamma - 1)}{2MRJ}$$
Two monatomic ideal gases $$1$$ and $$2$$ of molecular masses $$m_1$$ and $$m_2$$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas $$1$$ to that in gas $$2$$ is given by.
  • $$\sqrt{\dfrac{m_1}{m_2}}$$
  • $$\sqrt{\dfrac{m_2}{m_1}}$$
  • $$\dfrac{m_1}{m_2}$$
  • $$\dfrac{m_2}{m_1}$$
Two cylinders contain the same amount of ideal monatomic gas. The same amount of heat is given to two cylinders. If the temperature rise in cylinder A is $$T_0$$ then temperature rise in cylinder B will be :
1015215_39ae58532754477fabe5aef246c88c12.png
  • $$\dfrac{4}{3}T_0$$
  • $$2T_0$$
  • $$\dfrac{T_0}{2}$$
  • $$\dfrac{5}{3}T_0$$
One kg of a diatomic gas is at a pressure of $$8\times {10}^{4}N/{m}^{2}$$. The density of gas is $$4kg/{m}^{2}$$. What is the energy of the gas due to its thermal motion?
  • $$6\times {10}^{4}J$$
  • $$7\times {10}^{4}J$$
  • $$3\times {10}^{4}J$$
  • $$5\times {10}^{4}J$$
Ratio of $$C_P$$ and $$C_V$$ of gas '$$X$$' is 1.The number of atoms of the gas '$$X$$' present in $$11.2$$ litres of at NTP will be:
  • $$6.02\times 10^{23}$$
  • $$5.61\times 10^{23}$$
  • $$3.01\times 10^{23}$$
  • $$2.01\times 10^{23}$$
Valency of carbon is 44. From this, we understand that there are ____chemical bond/bonds between the carbon atom and one oxygen atom in the compound-carbon dioxide.
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If temperature of body increases by 10%, then increase in radiated energy of the body is :
  • 10 %
  • 40 %
  • 46 %
  • 1000 %
The average thermal energy of a oxygen atom at room temperature $$(27^{o}C)$$
  • $$4.5\times {10}^{-21}{J}$$
  • $$6.2 \times {10}^{-21}{J}$$
  • $$3.4 \times {10}^{-21}{J}$$
  • $$1.8 \times {10}^{-21}{J}$$
The amount of heat energy required to raise the temperature of $$1\ g$$ of helium in a container of volume $$10L$$, from $$T_{1}\ K$$ to  $$T_{2}\ K$$ is ($$N_{a} =$$ Avogadros number, $$k_{B}=$$ Boltzmann constant)
  • $$\dfrac { 3 }{ 2 } { N }_{ a }{ k }_{ B }\left( { T }_{ 2 }-{ T }_{ 1 } \right) $$
  • $$\dfrac { 3 }{ 7} { N }_{ a }{ k }_{ B }\left( { T }_{ 2 }-{ T }_{ 1 } \right) $$
  • $$\dfrac { 3 }{ 4 } { N }_{ a }{ k }_{ B }\left( { T }_{ 2 }-{ T }_{ 1 } \right) $$
  • $$\dfrac { 3 }{ 8 } { N }_{ a }{ k }_{ B }\left( { T }_{ 2 }-{ T }_{ 1 } \right) $$
The kinetic energy of $$ 1g $$ molecule of a gas at normal temperature and pressure is :
  • $$1.3$$ x $$10^2 J $$
  • $$2.7$$ x $$10^2 J $$
  • $$0.56$$ x $$10^4 J $$
  • $$3.4$$ x $$10^3 J $$

In an experiment, 1.35 mol of oxygen (O2) are heated at constant pressure starting at 11.0ºC. How much heat must be added to the gas to double its volume?
  • $$1.12\times 10^4 J$$
  • $$1.40\times 10^4$$
  • $$2.12\times 10^4$$J 
  • $$3.12×10^4 J$$
By the ideal gas law, the pressure of $$0.60$$ moles $${NH}_{3}$$ gas in a $$3.00\ L$$ vessel at $${25}^{o}C$$ is, given that $$R=0.082\ L$$ atm $${mol}^{-1}{k}^{-1}$$:
  • $$48.9\ atm$$
  • $$4.89\ atm$$
  • $$0.489\ atm$$
  • $$489\ atm$$
Mean kinetic energy (or average energy) per gm. of a molecule of a monoatomic  gas is given by :
  • $$\dfrac{3RT}{2}$$
  • $$\dfrac{kT}{2}$$
  • $$\dfrac{RT}{3}$$
  • $$\dfrac{3kT}{2}$$
RMS velocity of an ideal gas at $$27^o C$$ is $$500{m/s}$$, Temperature is increased four times, RMS velocity will become.
  • $$1000{m/s}$$
  • $$560{m/s}$$
  • $$2000m/s$$
  • None of these
If the total number of $$H_2$$ molecules is double of the $$O_2$$ molecules then the ratio of total kinetic energies pf $$H_2$$ to that of $$O_2$$ at 300 K is :-
  • 1 : 1
  • 1 : 2
  • 2 : 1
  • 1 : 3
Ideal monoatomic gas is taken through a process $$dQ  =2dU$$. What is the molar heat capacity for the process? ( where dQ is heat  supplied and dU is change in internal energy)
  • 2R
  • 3R
  • 4R
  • 5R
The relation between the ratio of specific heats $$(\gamma)$$ of gas and degree of freedom  $$'f'$$ will be :
  • $$\gamma=f+2$$
  • $$\dfrac{1}{\gamma}=\dfrac{1}{f}+\dfrac{1}{2}$$
  • $$f=\dfrac{2}{\gamma-1}$$
  • $$f=2(\gamma-1)$$
Three particles are situated on a light and rigid rod along Y-axis as shown in the figure. If the system is rotating with angular velocity of $$2 rad/sec$$ about X axis, then the total kinetic energy of the system is :
  • $$92 J $$
  • $$184 J $$
  • $$ 276 J $$
  • $$46 J $$
The total kinetic energy of 1 mole of $${ N }_{ 2 }$$ at $$27^oC$$ will be approximately:
  • $$1500J$$
  • $$1500$$ calorie
  • $$1500$$ kilo calorie
  • $$1500$$ erg
The total Kinetic energy of $$1\ mole$$ of $${N}^{}_{2}$$ at $$27^{o}_{}{C}$$ will be approximately :-
  • $$1500\ J$$
  • $$15633\ cal$$
  • $$1500\ kcal$$
  • $$1500\ erg$$
$$3$$ mole of gas ''X"  and $$2$$ moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section , shown as
under 
The length of the cylinder is $$150cm$$. The gas "X" intermixes with gas "Y" at the point . If the molecular weight of the gases X and Y is $$20$$ and $$80$$ respectively, then what will be the distance of point A from Q?
  • $$75cm$$
  • $$50cm$$
  • $$37.5$$
  • $$90cm$$
How many degrees of freedom the gas molecules have if under STP the gas density $$\rho = 1.3 kg/m^3$$ and the velocity of sound propagation in it is $$330 ms^{-1}$$?
  • $$3$$
  • $$5$$
  • $$7$$
  • $$8$$
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