Thermodynamics IITJEE test series -2

Mulitiple Choice questions with Single answer

1. Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T₀, while Box B contains one mole of helium at temperature (7/3) T₀.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 finaltemperature of the gases, T, in terms of T₀ is
a)T=5/2T₀
b.T=3/7T₀
c.T=7/3T₀
d.T=3/2T₀

2.According to Newton’s law of cooling, the rate of cooling of a body is proportional to (`T)n, where `T is the difference of the temperature of the body and the surroundings, and n is equal to
(A) two
(B) three
(C) four
(D) one


3.The pressure of the gas in constant volume gas thermometer are 80 cm,90cm and 100cm of mercury at the ice point,the steam point and in a heated wax bath resp.Find the temperature of the wax bath
a)200° C
b)201° C
c)202° C
d) none of the above

4.The pressure P of one mole of gas varies with volume V as
P=4-3V²
Highest absolute temperature to gas can be heated is
a.16/9R
b.9/16R
c 1/16R
d None of the above

5.A sphere,a cube and a circular plate have the same mass and are made of same material.All of them are at the same temperatrure T.Which one will have maximum rate of cooling.
a. Sphere
b Cube
c. Circular plate
d. All will have same rate of cooling

Mulitiple Choice questions with More than one answer

6.For an ideal gas
a) Heat added or Heat taken is not null in adiabatic process
b) Internal energy does not change in the isothermal process
c) Change is internal energy is zero in the cyclic process
d. None of the above

7).In which of the following process,convection does takes place
a. sea and land breeze
b.boiling of the water
c.heating air around the furnace
d.warming of glass of bulb due to filament

8)if a gas has n degrees of freedom.Then the expression (C_p/C_p) +1 is equal to
a) 2(1/n +1)
b) 2(n + 1/2)
c) 2+n/2
d) none of the above

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

9. STATEMENT 1:The molar specfic heat capacity of the ideal gas in isothermal process is infinity
STATEMENT 2:Heat transfer is non zero in the Isothermal process

10.STATEMENT 1:Equation of state for a real gas is (P+a/V²)(V-b)=nRT

STATEMENT 2: Molecular attraction is not neglible and the size of molecules are not neglibile in comparison to average sepeartion between them

11.STATEMENT 1:Root mean square velocity of the gas does not change in a Isothermal process
STATEMENT 2:Isothermal process may be achieved by immersing the system in large reservior and performing the process slowly


Matrix Match type
12 Three identical cylinder A₁,A₂,A₃ contains equal moles of Helium,Nitrogen,Carbon dioxide at the same temperature

Match the column I to column II

A)Traslational Energy is maximun in the cylinder
B)Total energy is minimum in the cylinder
C)Root mean square velocity is maximum in the cylinder
D)Mean speed will be minimum in the cylinder

P) A₁
Q) A₂
R) A₃
S) No appropiate match given


Linked Comphrehension type

A box Of interior Volumme V₁ has a heavy airtight hinged lid of mass M and area A.The box contains n₁ moles of gas at Temperature T₀.The box is inside a chamber which also contains additional n₂ moles of the same gas at the same temperature..The gas in the chamber occupies the volume V₂.

13 find the pressure of the gas in the box
a)n₁RT₀/V₁
b)n₂RT₀/V₂
c)(n₁+n₂)RT/(V₁+V₂)
d) none of the above.

14 find the pressure of the gas in the chamber
a)n₁RT₀/V₁
b)n₂RT₀/V₂
c)(n₁+n₂)RT/(V₁+V₂)
d) none of the above.

15.Intailliy the hinged lid is closed.Then which of these expression is true
a.(n₁RT₀/V₁) -(n₂RT₀/V₂) <=Mg/A
b. (n₁RT₀/V₁) -(n₂RT₀/V₂) => Mg/A
c. (n₂RT₀/V₂) -(n₁RT₀/V₁) => Mg/A
d. (n₂RT₀/V₂) -(n₁RT₀/V₁) <= Mg/A

16.If the whole system is heated,at what temperature T will the gas pressure lift the hinged lid
a)T=Mg/RA(n₁/V₁ -n₂/V₂)
b)T=Mg/RA(n₂/V₂ -n₁/V₁)
c)T=Mg/RA(n₁/V₁ +n₂/V₂)
d) None of the above

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Mechanics Test Series -II

Multiple choice question with one or more answer
1. A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v²/2μg,v/μg
b. v²/μg,v/μg
c.v²/2Mg,v/μg
d none of the above


2.A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these


3.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.


4.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these

5.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cottanθ/A
d. Atantanθ

6.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above

7.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e²/64mπε₀a²
b. zero
c. e²/16mπε₀a²
d. none of the above

8.The potential energy of a certain particle is given by
U=20x²+35z³.Find the vector force on it
a. -40xi-105z²k
b. 40xi-105z²k
c.-10xi-105z²k
d 40xi+105z²k

Matrix Match type

9.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force

Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero

Mechanics Test Series -II

Multiple choice question with one or more answer
1. A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v²/2μg,v/μg
b. v²/μg,v/μg
c.v²/2Mg,v/μg
d none of the above


2.A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these


3.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.


4.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these

5.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cotθ/A
d. A tanθ

6.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above

7.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e²/64mπε₀a²
b. zero
c. e²/16mπε₀a²
d. none of the above

8.The potential energy of a certain particle is given by
U=20x²+35z³.Find the vector force on it
a. -40xi-105z²k
b. 40xi-105z²k
c.-10xi-105z²k
d 40xi+105z²k

Matrix Match type

9.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force

Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero

Momentum and Center of Mass

Linear Momentum is defined as
p=mv

where v is the velocity of the particle

-Momentum is a velocity vector
-Momentum of system of particles is the vector sum of individaul momentum of the particle
p_total=∑v_iM_i



Center Of Mass: R_cm=∑r_iM_i/∑M_i

In co -ordinates system
x_cm=∑x_iM_i/∑M_i

y_cm=∑y_iM_i/∑M_i
z_cm=∑z_iM_i/∑M_i

Velocity of CM=∑v_iM_i/∑M_i

Acceleration of CM=∑F_ext/∑M_i


Law Of conservation of Momentum:
if ∑F_ext=0

then ∑v_iM_i=constant

Work And Energy

Work:- Work done by the force is defined as dot product of force and displacement vector
- For constant Force
W=F.s

where F is the force vector and s is displacement Vector
-For variable Force

dW=F.ds

or W=∫F.ds

-It is a scalar quantity

Conservative And Non Conservative Forces
-If the workdone by the force in a closed path is zero,Then it is called conservative Force
-If the workdone by the force in a closed path is not zero,Then it is called non conservative Force
-Conservative Forces are gravtitional ,electrical force
-Non Conservative Forces are friction

Kinetic Energy:-It is the energy possesed by the body in motion
-it is defined as
K.E=(1/2)mv²
- Networkdone by the external force is equal to the change in the kinetic energy of the system
W=K_f-K_i


Potential Energy:
-It is the kind of energy possesed due to configuration of the system
-It is due to conservative force
-it is defined as

dU=-F.dr
U_f-U_i=-∫F.dr
Where F is the conservative force

F=-(∂U/∂x)i-(∂U/∂y)j-(∂U/∂z)k

For gravtitional Force
Change in Potential Energy =mgh

where h is the height between the two points


Mechanical Energy is defined as
=K.E+P.E

Law Of conservation of Energy

In absence of external forces,intenal forces being conservative ,total energy of the system remains constant.
K.E₁+P.E₁=K.E₂+P.E₂

Uniform Circular Motion,Friction And Frame Of refrence

Uniform Circular Motion
-A body moving with constant speed on the circle
-Acceleration is Directed towards centre
a=v²/r

Where v is the speed and r is the radius of the circle

-Centrepetal force is required to move the body in the circle
F=mv²/r




Friction:

Frictional force acts between the bodies whenever there is a relative motion between them.
When bodies do the slip ,frictional force is called static frictional force and when the bodies does not slip ,it is called kinetic frictional force.

Kinetic Frictional force:-When bodies slip over each other

f=μ_kN


Where N is the normal contact force between the surface
And μ_k is the coefficent of kinetic Friction

Direction of frictional force is such that relative slipping is opposed by the friction

Static Frictional force:

-Frictional force can also act even if there is no relative motion.Such force is called static Frictional force
-Maximum Statix friction that a body can exert on other body in contact with it is called limiting Friction.
f_max=μ_sN

Where
N is the normal contact force between the surface
And μ_s is the coefficent of static Friction
f_max is the maximum possible force of static Friction


Some Imp points
1. μ_s > μ_k
2 Angle of friction tanλ=μ_s


Frame Of refrence:

Inertial Frame Of refrence:

-Inertial frame of refrences are objects which are at rest or moving at constant Velocity
-Exmaple:A person standing in a train moving at constant velocity
-Newtons law are valid


Non Inertial Frame Of refrence:-Inertial frame of refrences are objects which are accelerated
-Exmaple: A person standing in a train moving with increasing speed.
-Newtons law are not valid.

To apply newtons law ,pseudo force has to be introduced in the equation whose value will be
F=-ma

where a is the accelration of the non inertial frame of refrence