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QUESTION: 1

A constant volume gas thermometer works on (1980)

Solution:

Note : At constant volume, Charle's law is used.

QUESTION: 2

A metal ball immersed in alcohol weighs W_{1} at 0°C and W_{2} at 50°C. The coefficient of expansion of cubical the metal is less than that of the alcohal. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

Solution:

W_{1} = mg – Vd_{a}g

QUESTION: 3

A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the meterial of A is twice that of B.Under thermal equilibrium, the temperature difference across the wall is 36°C. The temperature difference across the layer A is

Solution:

QUESTION: 4

An ideal monatomic gas is taken round the cycle ABCDA as shown in the P – V diagram (see Fig.). The work done during the cycle is

Solution:

The work done during the cycle = area enclosed in the curve

QUESTION: 5

If one mole of a monatomic gas is mixed with one mole of a diatomic gas , the value of γ for mixture is

Solution:

QUESTION: 6

From the following statements concerning ideal gas at any given temperature T, select the correct one(s)

Solution:

For an ideal gas PV = nRT

⇒ Coefficient of volume expansion

Note : Average translation K.E. for O2 is 3/2 KT

(Three degrees of freedom for translational motion).

Now decrease in pressure increases the volume.

⇒ It increases mean free path of the molecules. Also average K.E. does not depend on the gas, so molecules of each component of mixture of gases have same average translational energy.

QUESTION: 7

Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles traingle ABC, right-angled at B. The points A and B are maintained at temperatures T and (√2) T respectively. In the steady state, the temperature of the point C is T_{c}. Assuming that only heat conduction takes place, T_{c} / T is

Solution:

Heat flow from B to A, A to C and C to B (for steady state condition, ΔQ/Δt is same)

QUESTION: 8

Two metallic spheres S_{1} and S_{2} are made of the same material and have got identical surface finish. The mass of S_{1} is thrice that of S_{2}. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S_{1 }to that of S_{2} is

Solution:

According to Stefan's law

QUESTION: 9

The average translational kinetic energy of O_{2} (relative molar mass 32) molecules at a particular temperature is 0.048 eV.

The translational kinetic energy of N_{2} (relative molar mass 28) molecules in eV at the same temperature is

Solution:

Average translational kinetic energy of an ideal gas molecule is 3/2 KT which depends on temperature only. Therefore, if temperature is same, translational kinetic energy of O2 and N2 both will be equal.

QUESTION: 10

A vessel contains 1 mole of O_{2} gas (relative molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (relative molar mass 4) at a temperature 2T has a pressure of

Solution:

Therefore, if T is doubled, pressure also becomes two times, i.e.., 2P.

QUESTION: 11

A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. if the radius were halved and the temperature doubled, the power radiated in watt would be

Solution:

The energy radiated per second by a black body is given by Stefan's Law

Dividing (ii) and (i), we get

QUESTION: 12

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity.Then the pressure in the compartment is

Solution:

When a enclosed gas is accelerated in the positive x-direction then the pressure of the gas decreases along the positive x-axis and follows the equation ΔP = – r a dx where r is the density and a the acceleration of the container.

The result will be more pressure on the rear side and less pressure on the front side.

QUESTION: 13

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

Solution:

The internal energy of n moles of a gas is

where F = number of degrees of freedom.

Internal energy of 2 moles of oxygen at temperature T is

Internal energy of 4 moles of argon at temperature T is

Total internal energy = 11 RT

QUESTION: 14

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is

Solution:

QUESTION: 15

A monatomic 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 a temperature T_{2} by releasing the piston suddenly. If L_{1} and L_{2} are the length of the gas column before and after expansion respectively,

then is given by

Solution:

QUESTION: 16

A block of ice at –10°C is slowly heated and converted to steam at 100°C. Which of the following curves represents the phenomenon qualitatively ?

Solution:

1. The temp. of ice changes from –10°C to 0°C.

2. Ice at 0°C melts into water at 0°C.

3. Water at 0°C changes into water at 100°C.

4. Water at 100°C changes into steam at 100°C.

QUESTION: 17

An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ΔT, pressure remaining constant. The quantity

varies with temperature as

Solution:

We know that V/T = constant

QUESTION: 18

Starting with the same initial conditions, an ideal gas expands from volume V_{1} to V_{2} in three different ways. The work done by the gas is W_{1} if the process is purely isothermal, W_{2} if purely isobaric and W_{3} if purely adiabatic. Then

Solution:

Work done is equal to area under the curve on PV diagram.

QUESTION: 19

The plots of intensity versus wavelength for three black bodies at temperature T_{1}, T_{2} and T_{3} respectively are as shown. Their temperatures are such that

Solution:

According to Wien's law,λT = constant From graph λ1 < λ3 < λ2

∴T1 > T3 > T2

QUESTION: 20

Three rods made of same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0^{o}C and 90^{o}C respectively. The temperature of the junction of the three rods will be

Solution:

Let θ°C be the temperature at B. Let Q is the heat flowing per second from A to B on account of temperature difference.

By symmetry, the same will be the case for heat flow from C to B.

∴ The heat flowing per second from B to D will be

Dividing eq. (ii) by eq. (i)

QUESTION: 21

In a given process on an ideal gas, dW = 0 and dQ < 0. Then for the gas

Solution:

From the first law of thermodynamics

dQ = dU + dW

Here dW = 0 (given)

∴ dQ = dU

Now since dQ < 0 (given)

∴ dQ is negative

⇒ dU = – ve ⇒ dU decreases.

⇒ Temperature decreases.

QUESTION: 22

P-V plots for two gases dur ing adiabatic pr ocesses are shown in the figure. Plots 1 and 2 should correspond respectively to

Solution:

For adiabatic process

Also for monoatomic gas

for diatomic gas

⇒ Graph 1 is for diatomic and graph 2 is for mono atomic.

QUESTION: 23

When a block of iron floats in mercury at 0^{o}C, fraction k_{1} of its volume is submerged, while at the temperature 60^{o}C, a fraction k_{2} is seen to be submerged. If the coefficient of volume expansion of iron is γ_{Fe} and that of mercury is γ_{Hg}, then the ratio k_{1}/k_{2} can be expressed as

Solution:

For equilibrium in case 1 at 0° C Upthrust = Wt. of body

For equilibrium in case 2 at 60° C Note : When the temperature is increased the density will decrease.

QUESTION: 24

An ideal gas is taken through the cycle as shown in the figure. If the net heat supplied to the gas in the cycle is 5J, the work done by the gas in the process C⇒A is

Solution:

For cyclic process;

QUESTION: 25

Which of the followin g graphs cor rectly represents the variation of with P for an ideal gas at constant temperature ?

Solution:

PV = constant. Differentiating,

∴ Graph between b and P will be a rectangular hyperbola.

QUESTION: 26

An ideal Black-body at room temperature is thrown into a furnace. It is observed that

Solution:

Note : According to Kirchoff's law, good absorbers are good emitters as well.

At high temperature (in the furnace), since it absorbs more energy, it emits more radiations as well and hence is the brightest.

QUESTION: 27

The graph, shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies

Solution:

The graph sh ows that for the same temperature difference (T_{2} – T_{1}), less time is taken for x. This means the emissivity is more for x. According to Kirchoff's law, a good emitter is a good absorber as well.

QUESTION: 28

Two rods, one of aluminum and the other made of steel, having initial length l_{1} and l_{2} are connected together to form a single rod of length l_{1} + l_{2}. The coefficients of linear expansion for aluminum and steel are α_{a} and α_{s} and respectively. If the length of each rod increases by the same amount when their temperature are raised by t^{0}C, then find the ratiol_{1}/(l_{1} + l_{2})

Solution:

The lengths of each rod increases by the same amount

QUESTION: 29

The PT diagram for an ideal gas is shown in the figure, where AC is an adiabatic process, find the corresponding PV diagram.

Solution:

If we study th e P – T gr aph we fin d AB to be a isothermal process, AC is adiabatic process given. Also for an expansion process, the slope of adiabatic curve is more (or we can say that the area under the P – V graph for isothermal process is more than adiabatic process for same increase in volume).

Only graph (b) fits the above criteria.

QUESTION: 30

2 kg of ice at –20^{0}C is mixed with 5kg of water at 20^{0}C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water & ice are 1kcal/kg/^{0}C & 0.5 kcal/kg/^{0}C while the latent heat of fusion of ice is 80 kcal/kg

Solution:

Heat required to convert 5 kg of water at 20°C to 5 kg of water at 0°C

Heat released by 2 kg. Ice at – 20°C to convert into 2 kg of ice at 0°C

How much ice at 0°C will convert into water at 0°C for giving another 80 kcal of heat

Therefore the amount of water at 0°C

Thus, at equilibrium, we have, [6 kg water at 0°C + 1kg ice at 0°C].

QUESTION: 31

Three discs A, B and C having radii 2, 4, and 6 cm respectively are coated with carbon black. Wavelength for maximum intensity for the three discs are 300, 400 and 500 nm respectively. If Q_{A}, Q_{B} and Q_{C} are power emitted by A, B and D respectively, then

Solution:

We know that λ_{m}T = Constant

From comparison Q_{B} is maximum.

QUESTION: 32

If liquefied oxygen at 1 atmospheric pressure is heated from 50 k to 300 k by supplying heat at constant rate. The graph of temperature vs time will be

Solution:

∴ From 50 K to boiling temperature, T increases linearly.

During boiling, equation is Q = mL Temperature remains constant till boiling is complete After that, again eqn. (i) is followed and temperature increases linearly.

QUESTION: 33

Two identical rods are connected between two containers one of them is at 100ºC and another is at 0ºC. If rods are connected in parallel then the rate of melting of ice is q_{1} gm/ sec. If they are connected in series then the rate is q_{2}. The ratio q_{2}/ q_{1} is

Solution:

QUESTION: 34

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 complete process which of the following is true

Solution:

In the first process W is + ve as ΔV is positive, in the second process W is – ve as ΔV is – ve and area under the curve of second process is more

∴ Net Work < 0 and also P_{3} > P_{1}.

QUESTION: 35

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure. Which of the following option is the correct match ?

Solution:

According to Wein's displacement law

The temperature of Sun is higher than that of welding arc which in turn is greater than tungsten filament.

QUESTION: 36

In which of the following process, con vection does not take place primarily

Solution:

Heat transfer of glass bulb from filament is through radiation. A medium is required for convection process. As a bulb is almost evacuated, heat from the filament is transmitted through radiation.

QUESTION: 37

A spherical body of area A and emissivity e = 0.6 is kept inside a perfectly black body. Total heat radiated by the body at temperature T

Solution:

When a non black body is placed inside a hollow enclosure, the total radiation from the body is the sum of what it would emit in the open ( with ϵ<1 ) and the part of the incident radiation from the walls reflected by it. The two add up to a black body radiation.

Hence the total radiation emitted by the body is 1.0ϵAT^{4}.

QUESTION: 38

Calorie is defined as the amount of heat required to raise temperature of 1 g of water by 1^{o}C and it is defined under which of the following conditions?

Solution:

1 Calor ie is th e amoun t of heat required to raise temperature of 1 gm of water from 14.5°C to 15.5°C at 760 mm of Hg.

QUESTION: 39

Water of volume 2 litre in a container is heated with a coil of 1 kW at 27^{ o}C. The lid of the container is open and energy dissipates at rate of 160 J/s. In how much time temperature will rise from 27^{o}C to 77^{o}C [Given specific heat of water is 4.2 kJ/kg]

Solution:

As shown in the figure, the net heat absorbed by the water to raise its temperature = (1000 – 160) = 840 J/s Now, the heat required to raise the temperature of water from 27°

C to 77°C is

Q = mcΔt = 2 × 4200 × 50 J

Therefore the time required

QUESTION: 40

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is r, the surface tension of water is T and the atmospheric pressure is P_{0}.

Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Solution:

Note : In the first part the force is created due to pressure and in the second part the force is due to surface tension T.

∴ Force = 2P0Rh + Rrgh2 – 2RT

QUESTION: 41

An ideal gas is expanding such that PT^{2} = constant. The coefficient of volume expansion of the gas is –

Solution:

PT^{2} = constant (given) Also for an ideal gas PV/T= constt

From the above two equations, after eliminating P.

We know that change in volume due to thermal expansion is given by dV where γ = coefficient of volume expansion.

From (i) and (ii)

QUESTION: 42

A real gas behaves like an ideal gas if its

Solution:

A real gas behaves as an ideal gas when the average distance between the gas molecules is large enough so that (i) the force of attraction between the gas molecules becomes almost zero (ii) the actual volume of the gas molecules is negligible as compared to the occupied volume of the gas.

The above conditions are true for low pressure and high temperature.

QUESTION: 43

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T_{1, }the work done in the process is

Solution:

Initially

The number of moles of gas is

Finally (after adiabatic compression) V2 = 0.7l For adiabatic compression

We know that work done in adiabatic process is

QUESTION: 44

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds

Solution:

QUESTION: 45

Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

Solution:

The heat is supplied at constant pressure.

Therefore

QUESTION: 46

Two rectangular blocks, having identical dimensions, can be arranged either in configuration-I or in configuration-II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration-I.

The time to transport the same amount of heat in the configuration-II is

Solution:

Where k_{1} and k_{2} are the equivalent conductivities in configuration I and II respectively.

For configuration I :

For configuration II :

option (a) is correct

QUESTION: 47

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

Solution:

QUESTION: 48

Parallel rays of light of intensity I = 912 Wm^{–2} are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant s = 5.7 × 10^{–8} Wm^{–2}K^{–4} and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

Solution:

In steady state Energy lost = Energy gained

QUESTION: 49

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is

(Specific heat of water is 4.2 kJ kg^{–1}K^{–1} and the density of water is 1000 kg m^{–3})

Solution:

QUESTION: 50

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure P_{i }= 10_{5} Pa and volume V_{i }= 10^{–3} m^{3} changes to a final state at P_{f} = (1/ 32) × 10^{5} Pa and V_{f} = 8 × 10^{–3} m^{3} in an adiabatic quasi-static process, such that P^{3}V^{5} = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at P_{i} followed by an isochoric (isovolumetric) process at volume V_{f} . The amount of heat supplied to the system in the two-step process is approximately

Solution:

For adiabatic process

From first law of thermodynamics

Now applying first law of thermodynamics for process

QUESTION: 51

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10°C. Now the end P is maintained at 10°C, while the end S is heated and maintained at 400 °C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 × 10^{–5} K_{–1}, the change in length of the wire PQ is

Solution:

The heat flow rate is same

The temperature gradient access Pd is

Therefore change temperature at a cross-section M distant ‘x’ from P is

Extension in a small elemental length ‘dx’ is

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