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*Multiple options can be correct

QUESTION: 1

Which statement is incorrect?

Solution:

All reversible engines working for the same temperature of source and sink have same efficiencies. If the temperatures are different, the efficiency is different.

*Multiple options can be correct

QUESTION: 2

Heat given to a body which raises its temperature by 1°C is

Solution:

Heat required for raising the temperature of the whole body by 1ºC is called the thermal capacity of the body.

*Multiple options can be correct

QUESTION: 3

Infrared radiation is detected by

Solution:

Pyrometer is used to detect infra-red radiation.

*Multiple options can be correct

QUESTION: 4

Which of the following is more close to a black body?

Solution:

Black board paint is quite approximately equal to black bodies.

*Multiple options can be correct

QUESTION: 5

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

Solution:

Since pressure and volume are not changing, so temperature remains same.

*Multiple options can be correct

QUESTION: 6

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Solution:

When water is cooled to form ice, energy is released from water in the form of heat. As energy is equivalent to mass therefore when water is cooled to ice, its mass decreases.

*Multiple options can be correct

QUESTION: 7

At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

Solution:

*Multiple options can be correct

QUESTION: 8

Even Carnot engine cannot give 100% efficiency because we cannot

Solution:

The temperature of 0 K (absolute zero) can not be obtained .

*Multiple options can be correct

QUESTION: 9

1 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of g for the resulting mixture is

Solution:

For mixture of gases

*Multiple options can be correct

QUESTION: 10

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

Solution:

The energy radiated per second is given by

For same material e is same. σ is stefan's constant

*Multiple options can be correct

QUESTION: 11

“Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement or consequen ce of

Solution:

This is a statement of second law of thermodynamics

*Multiple options can be correct

QUESTION: 12

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature.

The ratio CP /CV for the gas is

Solution:

But for an adiabatic process, the pressure temperature relationship is given by

*Multiple options can be correct

QUESTION: 13

Which of the following parameters does not characterize the thermodynamic state of matter?

Solution:

Work is a path function. The remaining three parameters are state function.

*Multiple options can be correct

QUESTION: 14

A Carnot engine takes 3 *10 ^{6} cal. of heat from a reservoir at 627^{o} C , and gives it to a sink at 27^{ o} C . The work done by the engine is

Solution:

*Multiple options can be correct

QUESTION: 15

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Solution:

Wein’s law correctly explains the spectrum

*Multiple options can be correct

QUESTION: 16

According to Newton’s law of cooling, the rate of cooling of a body is proportional to ( Δθ)^{n} , wher e Δθ is the difference of the temperature of the body and the surroundings, and n is equal to

Solution:

*Multiple options can be correct

QUESTION: 17

One mole of ideal monatomic gas ( γ = 5 / 3) is mixed with one mole of diatomic gas (γ = 7 / 5) . What is g for the mixture? γ Denotes the ratio of specific heat at constant pressure, to that at constant volume

Solution:

*Multiple options can be correct

QUESTION: 18

If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be

Solution:

*Multiple options can be correct

QUESTION: 19

Which of the following statements is correct for any thermodynamic system ?

Solution:

Internal energy and entropy are state function, they do not depend upon path taken.

*Multiple options can be correct

QUESTION: 20

Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T_{1} ,T_{2} ), volume (V_{1 },V_{2}) and pressure ( P_{1} ,P_{2}) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Solution:

Here Q = 0 and W = 0. Therefore from first law of thermodynamics ΔU = Q + W = 0

∴ Internal energy of thesystem with partition = Internal energy of the system without partition.

*Multiple options can be correct

QUESTION: 21

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T_{2} and T_{1} (T_{2} >T_{1}) . The rate of heat transfer through the slab, in a steady state is with f equal to

Solution:

The thermal resistance

*Multiple options can be correct

QUESTION: 22

Which of the following is incorrect regarding the first law of thermodynamics?

Solution:

First law is applicable to a cyclic process. Concept of entropy is introduced by the second law.

*Multiple options can be correct

QUESTION: 23

The figure shows a system of two concentric spheres of radii r_{1} and r_{2} are kept at temperatures T_{1} and T_{2}, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Solution:

Consider a shell of thickness (dr) and of radius (r) and the temperature of inner and outer surfaces of this shell be T, (T – dT)

*Multiple options can be correct

QUESTION: 24

A system goes from A to B via two processes I and II as shown in figure. If ΔU_{1} and ΔU_{2} are the changes in internal energies in the processes I and II respectively, then

Solution:

Change in internal energy do not depend upon the path followed by the process. It only depends on initial and final states i.e., ΔU_{1} = ΔU_{2}

*Multiple options can be correct

QUESTION: 25

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Solution:

*Multiple options can be correct

QUESTION: 26

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio C_{p}/C_{v } of the mixture is

Solution:

*Multiple options can be correct

QUESTION: 27

Assuming the Sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant powerd incident of Earth at a distance r from the Sun

where r_{0} is the radius of the Earth and σ is Stefan's constant.

Solution:

Total power radiated by Sun =

The intensity of power at earth's surface =

Total power received by Earth =

*Multiple options can be correct

QUESTION: 28

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_{0}, while Box contains one mole of helium at temperature . 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 final temperature of the gases, T_{f} in terms of T_{0} is

Solution:

Heat lost by He = Heat gained by N_{2}

_{}

*Multiple options can be correct

QUESTION: 29

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by 7°C. The gas is (R = 8.3 J mol^{–1} K^{–1})

Solution:

Hence the gas is diatomic.

*Multiple options can be correct

QUESTION: 30

When a system is taken from state i to state f along the path iaf, it is found that Q =50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is

Solution:

For path iaf,

For path ibf

*Multiple options can be correct

QUESTION: 31

A Carnot engine, having an efficiency of η= 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Solution:

The efficiency (η) of a Carnot engine and the coefficient of performance (β) of a refrigerator are related as

Also, Coefficient of performance (β) is given by Q_{2}/W

β= , where Q_{2} is the energy absorbed from the reservoir.

*Multiple options can be correct

QUESTION: 32

One end of a thermally insulated rod is kept at a temperature T_{1} and the other at T_{2}. The rod is composed of two sections of length l_{1} and l_{2} and thermal conductivities K_{1} and K_{2} respectively. The temperature at the interface of the two section is

Solution:

*Multiple options can be correct

QUESTION: 33

If C_{P} and C_{V} denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

Solution:

According to Mayer's relationship C_{P} – C_{V} = R

*Multiple options can be correct

QUESTION: 34

The speed of sound in oxygen (O_{2}) at a certain temperature is 460 ms^{–1}. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)

Solution:

The speed of sound in a gas is given by

*Multiple options can be correct

QUESTION: 35

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V_{1} and contains ideal gas at pressure P_{1} and temperature T_{1}. The other chamber has volume V, and contains ideal gas at pressure P_{2} and temperature T_{2}. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Solution:

Same as A . 20

*Multiple options can be correct

QUESTION: 36

A long metallic bar is carrying heat from one of its ends to the other end under steady–state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the following figures?

Solution:

The heat flow rate is given by

where θ1 is the temperature of hot end and v is temperature at a distance x from hot end.

The above equation can be graphically represented by option (a) .

*Multiple options can be correct

QUESTION: 37

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram.

Q.37. Assuming the gas to be ideal the work done on the gas in taking it from A to B is :

Solution:

A to B is an isobaric process. The work done

W = nR(T_{2}-T_{1}) = 2R(500 - 300)= 400R

*Multiple options can be correct

QUESTION: 38

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram.

The work done on the gas in taking it from D to A is :

Solution:

Work done by the system in the isothermal process

Therefore work done on the gas is + 414 R.

*Multiple options can be correct

QUESTION: 39

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram.

The net work done on the gas in the cycle ABCDA is :

Solution:

The net work in the cycle ABCDA is W = W_{AB} + W_{BC}+W_{CD}+W_{DA}

= 693.2 R – 414 R = 279.2 R

*Multiple options can be correct

QUESTION: 40

One kg of a diatomic gas is at a pressure of 8 × 10^{4}N/m^{2}. The density of the gas is 4kg/m^{3}. What is the energy of the gas due to its thermal motion?

Solution:

*Multiple options can be correct

QUESTION: 41

Statement 1 : The temperature dependence of resistance is usually given as R = R_{o} (1 + α Δt). The resistance of a wire changes from 100Ω to 150Ω when its temperature is increased from 27°C to 227°C. This implies that α = 2.5 × 10^{–3}/°C.

Statement 2 : R = R_{o} (1+ α Δt) is valid only when the change in the temperature ΔT is small and ΔR = (R – R_{0}) << R_{o}.

Solution:

(The relation R = R_{0} (1 +α Δt) is valid for small values of Δt and R_{0} is resistance at 0°C and also (R – R_{0}) should be much smaller than R_{0}. So, statement (1) is wrong but statement (2) is correct.

*Multiple options can be correct

QUESTION: 42

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is

Solution:

*Multiple options can be correct

QUESTION: 43

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

Solution:

Here, work done is zero.

So, loss in kinetic energy = change in internal energy of gas

*Multiple options can be correct

QUESTION: 44

Three perfect gases at absolute temperatures T_{1}, T_{2} and T_{3} are mixed. The masses of molecules are m_{1}, m_{2} and m_{3} and the number of molecules are n_{1}, n_{2} and n_{3} respectively. Assuming no loss of energy, the final temperature of the mixture is :

Solution:

Number of moles of first gas = n_{1}/N_{A}

Number of moles of second gas =n_{2}/N_{A}

Number of moles of third gas =n_{3}/N_{A}

If there is no loss of energy then

*Multiple options can be correct

QUESTION: 45

A Carnot engine operating between temperatures T_{1 }and T_{2} has efficiency 1/6. When T_{2} is lowered by 62 K its efficiency increases to 1/3. Then T_{1} and T_{2 }are, respectively:

Solution:

Efficiency of engine

*Multiple options can be correct

QUESTION: 46

100g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K):

Solution:

*Multiple options can be correct

QUESTION: 47

A wooden wheel of radius R is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Young's modulus is Y, the force that one part of the wheel applies on the other part is :

Solution:

∴ The ring is pressing the wheel from both sides,

*Multiple options can be correct

QUESTION: 48

Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

Solution:

Heat given to system =

*Multiple options can be correct

QUESTION: 49

A liquid in a beaker has temperature θ(t) at time t and θ_{0} is temperature of surroundings, then according to Newton's law of cooling the correct graph between log_{e} (θ-θ_{0}) and t is :

Solution:

Newton's law of cooling

Integrating

Which represents an equation of straight line.

Thus the option (a) is correct.

*Multiple options can be correct

QUESTION: 50

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :

Solution:

on solving we get T_{2} = 750 K

*Multiple options can be correct

QUESTION: 51

The above p-v diagram represents the thermodynamic cycle of an engine, operatingwith an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Solution:

Same as in A -51

*Multiple options can be correct

QUESTION: 52

If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ_{0}, the graph between the temperature T of the metal and time t will be closest to

Solution:

According to Newton’s law of cooling, the temperature goes on decreasing with time non-linearly.

*Multiple options can be correct

QUESTION: 53

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100ºC is: (For steel Young’s modulus is 2*10^{11}Nm^{-2} and coefficient of thermal expansion is 1.1*10-^{5 }K^{-1 })

Solution:

Young's modulus Y = stress/strain stress = Y ´ strain

Stress in steel wire = Applied pressure Pressure = stress = Y × strain

= 2.2 × 10^{8} Pa

*Multiple options can be correct

QUESTION: 54

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2 }are filled in the tube.Each liquid subtends 90º angle at centre. Radius joining their interface makes an angle a with vertical. Ratio d_{1}/d_{2} is:

Solution:

Pressure at interface A must be same from both the sides to be in equilibrium.

*Multiple options can be correct

QUESTION: 55

Three rods of Copper, Brass and Steel are welded together to form a Y shaped structure. Area of cross - section of each rod = 4cm ^{2} . End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C. Lengths of the copper,, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:

Solution:

Rate of heat flow is given by,

Where, K = coefficient of thermal conductivity l = length of rod and A = Area of cross-section of rod

If the junction temperature is T, then

*Multiple options can be correct

QUESTION: 56

One mole of a diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

Solution:

In cyclic process, change in total internal energy is zero.

Where, C_{v} = molar specific heat at constant volume.

*Multiple options can be correct

QUESTION: 57

A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways :

(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.

(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.

In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is :

Solution:

The entropy change of the body in the two cases is same as entropy is a state function.

*Multiple options can be correct

QUESTION: 58

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = U/V∝T^{4}

and pressure p=1/3 (U/V). If the shell now undergoes an adiabatic expansion the relation between T and R is :

Solution:

*Multiple options can be correct

QUESTION: 59

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is

Solution:

*Multiple options can be correct

QUESTION: 60

'n' moles of an ideal gas undergoes a process A → B as shown in the figure. The maximum temperature of the gas during the process will be :

Solution:

The equation for the line is

For temperature to be maximum dT/dv= 0

Differentiating e.q. (iii) by 'v' we get

*Multiple options can be correct

QUESTION: 61

A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20° C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (a) of the metal of the pendulum shaft are respectively :

Solution:

Time lost/gained per day

*Multiple options can be correct

QUESTION: 62

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PV^{n} = constant, then n is given by (Here C_{P} and C_{V} are molar specific heat at constant pressure and constant volume, respectively) :

Solution:

For a polytropic process

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