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IIT JAM Physics Mock Test - 7 - Physics MCQ


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30 Questions MCQ Test - IIT JAM Physics Mock Test - 7

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IIT JAM Physics Mock Test - 7 - Question 1

A vessel of volume V = 30l contains ideal gas at temperature 00C. After a portion of the gas has been let out. the pressure in the vessel decreases by ΔP = 0.78 atm. Find the mass of the released gas. The gas density under the normal conditions is ρ = 1 .3 g/l. .

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 1

Let m1 and m2 be the masses of the gas in the vessel before and after the gas is released. Hence mass of the gas released,   Δm = m1 -m2

Now from ideal gas equation

(where P0 = standard atmospheric pressure and T0 = 273 K)

From Eqs. (1) and (2) we get 

IIT JAM Physics Mock Test - 7 - Question 2

An ideal gas whose pressure varies with volume according to the following relation P = P0 - aV2. If we subject the gas to different pressures. What is the maximum temperature that the gas may attain?

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 2

PV = nRT
given that P : P = Po - aV2



 

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IIT JAM Physics Mock Test - 7 - Question 3

A box containing 2 moles of a diatomic ideal gas at temperature T0 is connected to another identical box containing 2 moles of a monoatomic ideal gas at temperature 5T0. There are no thermal losses and the heat capacity of the boxes and vibrational degree of freedom are negligible. Find the final temp, of the mixture

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 3

Heat gained = heat lost 
nCΔT=nCvΔT


IIT JAM Physics Mock Test - 7 - Question 4

One mole of an ideal gas whose adiabatic exponent equals R undergoes a process in which the gas pressure relates to the temperature as P = aTα. The work performed by the gas if its temperature gets an increment ΔT.

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 4

p = aTα


IIT JAM Physics Mock Test - 7 - Question 5

The efficiency of a cycle consisting of two isobaric and two adiabatic lines, if the pressure changes n times within the cycle. The working substance is an ideal gas whose adiabatic exponent is equal to γ.

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 5


IIT JAM Physics Mock Test - 7 - Question 6

The heat required to convert 1 gm of water into steam under standard atm pressure if the entropy of water at the boiling point is 0.31 and for 100% steam at the steam temperature is 1.74 is:-

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 6

ds = dQ/T
dQ = Tds 

IIT JAM Physics Mock Test - 7 - Question 7

If y = x cos x is a solution of an nth order linear differential equation

With real constant coefficients, then the least possible value of n is:-

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 7


y = x cos x
y 1 = - x sinx + cosx
yn = - sin x - x cos x - sin x
yn + y = - 2 sin x...(i)
yn1 + y1 = - 2cosx
y +yn = 2sinx...(ii)
(1)+(2) gives
y+ 2 yn + y = 0
so, ⇒ n = 4

IIT JAM Physics Mock Test - 7 - Question 8

The value of the integral

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 8




using definition of gamma function

Here n = 4

IIT JAM Physics Mock Test - 7 - Question 9

A monoatomic gas is described by the equation of state P(V - bn) = nRT Where b and R are constants and other quantities have their usual meanings. The maximum density (in makes per unit volume) to which this gas can be compressed is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 9

P (V- bn) = nRT
Differentiate equation with respect to V at constant T




for compression coefficient 

for maximum K,  

So. maximum density

IIT JAM Physics Mock Test - 7 - Question 10

Consider the surface corresponding to the equation 

A possible unit tangent to this surface at the point (1.2.-8) is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 10

The equation of surface is 
= 4x2 + y2 + z = 0 
So. gradient on the surface is 

But unit tangent on the surface is along z-direction

IIT JAM Physics Mock Test - 7 - Question 11

What are the eigen values of the given matrix:-

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 11





IIT JAM Physics Mock Test - 7 - Question 12

Which of the following matrices is Hermitian:-

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 12

For the matrix A to Be Hermitian 
A = ( A+)'



IIT JAM Physics Mock Test - 7 - Question 13

An system at temperature T has three energy states 0, ± ε. The entropy of the system in the low temperature (T→0) and high temperature (T → ∝) limits are respectively,

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 13

Using third law of thermodynamics entropy of closed system is moving toward to zero at zero tempS = KRf n zerature.
ST→0 = 0
We know partition function

Entropy S = KB, log z 
S = KBln z

IIT JAM Physics Mock Test - 7 - Question 14

One mole of an ideal gas undergoes the cycle ACBA shown in the pV diagram below one of the curved lines in the cycle represents an isothermal change at temperature T, while the other represents and adiabatic change, the net heat gained by gas in this cycle is _____

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 14

By the given conditions for the isothermal irreversible work 

for the isothermal reversible 'work
-W=Q
⇒ 
Total work = 
In isothermal process the net heat gain by the system used only for work. It is not contribute in internal e n erg y so the heat = 
 

IIT JAM Physics Mock Test - 7 - Question 15

An ideal gas at a temperature T is enclosed in a rigid container whose walls are initially at temperature T1, where T1 < T. The walls are covered on the outside with perfect thermal insulation and the system is allowed to come to equilibrium. The pressure exerted by the gas on the walls of the container.

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 15

We know that PV = nRT 
P ∝ T 
P1 ∝ T1

PT1 = P1T

It means P > P1
The pressure exerted by the gas on the walls of container is higher at the initial stage than at the final stage.

IIT JAM Physics Mock Test - 7 - Question 16

Consider the CO molecule as a system of two point particles which has both translational and rotational degrees of freedom. Using classical statistical mechanics. the molar specific heat Cv of CO gas is given in form of the Boltzmann constant KB by

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 16

Translation degree of freedom = 3 
Rotational degree of freedom = 2

IIT JAM Physics Mock Test - 7 - Question 17

The vector  is perpendicular to  is perpendicular to  Then the angle between 

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 17


..(i)

 ...(ii)
Subtracting  



IIT JAM Physics Mock Test - 7 - Question 18

In the temperature range 100 - 1000 C. the molar specific heat of a metal varies with temperature T (measured in degrees Celsius) according to the formula  If 0.2 kg of the metal at 600 C is brought in thermal  contact with 0.1 kg of the same metal at 300 c, the final equilibrium temperature in deg c, will be

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 18



We know that at the thermal equilibrium 
Heat absorbed = Heat released


IIT JAM Physics Mock Test - 7 - Question 19

A monoatomic gas undergoes a process given by 2 du + 3dω = 0 Then the process is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 19




VT = constat

IIT JAM Physics Mock Test - 7 - Question 20

An ideal gas in a Cylinder is Compressed adiabatic ally to one - third of its initial Volume. During this process 20 J work is done on the gas by compressing agent. Which of the following Statements is true for this case?

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 20

dw = -20J 
for adiabatic process 
dO = du + dw = 0 
du = - dw 
du = 20J

IIT JAM Physics Mock Test - 7 - Question 21

The ratio y = CP / Cof H2, gas is 7/5 at room temperature, and 5/3 at low temperatures (around 50 K). The reason for this change is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 21


We know at low temperature rotational motion of molecules is not consider so, total energy is due to the translatory or vibrational motion.




But at room temperature rotational motion is consider so

But at room temperature rotational motion is consider so



IIT JAM Physics Mock Test - 7 - Question 22

Calculate the variation of Cp with pressure at constant temperature of a substance for which the equation of state is given the relation

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 22






...(ii)
By the equation (1) and (2)

IIT JAM Physics Mock Test - 7 - Question 23

f(x) is a periodic function of x with a period of 2π. In the interval -π<x<π,  f(x) is given by

In the expansion of f(x) as a Fourier series of sine and cosine functions, the coefficient of cos 2x is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 23


     ( COS X = t )
 

IIT JAM Physics Mock Test - 7 - Question 24

The volume of the portion of the cylinder x2 + y2 = 4 in the first octant between the lanes z = 0 and 3x - z = 0 is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 24


IIT JAM Physics Mock Test - 7 - Question 25

For in isolated thermodynamical system, most probable, and root mean square values respectively of the molecular speeds of a gas room temperature being Maxwellian velocity distribution, then

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 25

According to maxwell velocity distribution law

IIT JAM Physics Mock Test - 7 - Question 26

For an isolated thermodynamical system P, V, T, U, S. and F represent the pressure. volume, temperature, internal energy, and free energy respectively. Then the following relation is true

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 26

F = U - TS
dF = dl) - TdS - SdT 
= (TdS - PdV) - TdS - SdT 
= - PdV - SdT

IIT JAM Physics Mock Test - 7 - Question 27

If z1 and z2 are two complex numbers then

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 27


IIT JAM Physics Mock Test - 7 - Question 28

The sublimation curve of solid ammonia is given by ln p = 23 - 3750/T and the vaporization curve of the liquid ammonia is given by In p = 19.5 -3050/T. where p is in mm of Hg and T is in K. The temperature of the triple point of ammonia is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 28

For sublimation of NH3
...(i)
Fori vaporization of NH3

At triple point    
T = Tr

IIT JAM Physics Mock Test - 7 - Question 29

The eigen values of the matrix  are given by  Which one of the following statement is NOT true?

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 29




So, λ have following values




and two eigen values are complex. Ans. (C)

IIT JAM Physics Mock Test - 7 - Question 30

Let  is a solution of the Laplace equation then the vector field  is

Detailed Solution for IIT JAM Physics Mock Test - 7 - Question 30



So,   is not solenoidal but irrotational.

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