Physics previous year question Of Heat and Kinetic Theory of Gases for NDA

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previous year question Of Heat and Kinetic Theory of Gases for NDA

previous year question

Q 2824680551

Consider the following properties

I. Gaseous at room temperature
II. Low latent heat of evaporation
III. Early liquefied by increase) in pressure even at room temperature
Important properties of a good refrigerant would include

(A)

Both I and II

(B)

Both II and Ill

(C)

Both I and III

(D)

I, II and Ill

Solution:

Correct Answer is `=>` (D) I, II and Ill

Q 2854580454

Consider the following three statements

I. Heating `1 kg` of water from `10^0 C` to `50^0 C`
II. Melting `600 g` of ice at `0^0C`.
III. Converting `300 g` of ice at `0^0 C` to water at `50^0C`.
Which one of the following shows the correct arrangement of the quantity of heat required in the above process in increasing order of magnitude? Choose the correct answer from the codes given above

(A)

I , II and Ill

(B)

II, I and Ill

(C)

Ill, II and I

(D)

Ill, I and II

Solution:

Correct Answer is `=>` (D) Ill, I and II

Q 2824580451

Which of the following will take place when the temperature of `1 kg` of water is raised from `30^0C` to `140^0C?` Choose the correct answer from the codes given below
I. There will be a physical change of state.
II. It goes through a chemical change.
III. The change of state requires latent heat.
IV. The boiling point of water will depend on the atmospheric pressure.

(A)

Both I and II

(B)

I, Ill and IV

(C)

II, Ill and IV

(D)

Both II and Ill

Solution:

Correct Answer is `=>` (B) I, Ill and IV

Q 2884480357

Which of the following statements are true regarding heat? Select the correct answer from the codes given below
I. Heat is a form of energy.
II. Heat can be reflected by a mirror.
III. Heat is an electromagnetic radiation.
IV. Heat cannot pass through vacuum.

(A)

I, II and Ill

(B)

I, II and IV

(C)

II, Ill and IV

(D)

I, Ill and IV

Solution:

Correct Answer is `=>` (C) II, Ill and IV

Q 2864480355

Assertion : The root mean square and most probable speeds of the molecules in a gas are the same

Reason : The Maxwell distribution for the speed of molecules in a gas symmetrical

(A)

Both A and R individually true and R is the correct explanation of A

(B)

Both A and R are individually true but R is not the correct explanation of A

(C)

A is true but R is false

(D)

A is false but R is true

Solution:

Correct Answer is `=>` (D)

Q 2844480353

Assertion : The ratio of specific heat gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monatomic gas

Reason : The molecules of a monoatomic gas have more degree of freedom than those of a diatomic gas.

(A)

Both A and R individually true and R is the correct explanation of A

(B)

Both A and R are individually true but R is not the correct explanation of A

(C)

A is true but R is false

(D)

A is false but R is true

Solution:

Correct Answer is `=>` (D)

Q 2834480352

Oxygen boils at `-183^0C` this temperature is

(A)

`-297^0 F`

(B)

`-229^0 F`

(C)

`-260^0 F`

(D)

`-200^0 F`

Solution:

By using formula, `(F - 32)/180 = C/100 = (-183)/100`

`=> F-32 = 18/10 (-183) = -329.4 `

`=> F = 32-329.4 = -297.4 approx -297^0 F`

Correct Answer is `=>` (A) `-297^0 F`

Q 2814480350

A cylinder of fixed capacity (of `44.8` litres) contains `2` moles of helium gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by `200C`

(A)

`996 J`

(B)

`831 J`

(C)

`498 J`

(D)

`374 J`

Solution:

Since, the volume of cylinder is fixed, the heat required is determined by `C_v` . It is a monoatgornic gas Therefore, its molar specific heat at constant is `C_v = 3/2 R`

`therefore` Heat required = number of moles `xx` molar specific `xx` rise in temperature

` = 2 xx 3/2 R xx 20 =60R `

` = 60xx8.31 = 498.6 J`

Correct Answer is `=>` (C) `498 J`

Q 2884380257

The temperature of an ideal gas is increased from `27^0 C` to `127^0 C` then percentage increase in v is

(A)

`37%`

(B)

`11%`

(C)

`33%`

(D)

`15.5 %`

Solution:

`V_(rms) = sqrt((3RT)/M)`

`%` increase in

`V_(rms) = (sqrt((3RT_2)/M) - sqrt((3RT_1)/M))/sqrt((3RT_1)/M) xx 100 %`

` = (20-17.32)/(17.32) xx 100 = 15.5 %`

Correct Answer is `=>` (D) `15.5 %`

Q 2834380252

At what temperature the molecules of nitrogen will have the same r.m.s velocity as the molecules of oxygen at `127^0C`

(A)

`77^0 C`

(B)

`350^0 C`

(C)

`273^0 C`

(D)

`457^0 C`

Solution:

`v_(rms) = sqrt((3RT)/M) => T prop M \ \ \ \ [ because v_(rms) , R → text(constant) ]`

`=> T_(N_2)/T_(O_2) = M_(N_2)/M_(O_2)`

`=> T_(N_2)/(273+127) = 28/32`

`=> T = 350 K = 77^0 C`

Correct Answer is `=>` (A) `77^0 C`

Q 2814180059

If the ratio of vapour density for hydrogen and oxygen is `1/16` then under constant pressure the ratio of their rms velocities will be

(A)

`4/1`

(B)

`1/4`

(C)

`1/16`

(D)

`16/1`

Solution:

`v_(rms) = sqrt((3p)/rho)`

`=> V-1/V_2 = sqrt(rho_2/rho_1) = sqrt(16/1) = 4/1`

Correct Answer is `=>` (A) `4/1`

Q 2854180054

At room temperature, the r.m.s . speed of the :nolecules of certain diatomic gas is found to be 1930 m/s. The gas is

(A)

`H_2`

(B)

`F_2`

(C)

`O_2`

(D)

`Cl_2`

Solution:

`v_(rms) = sqrt((3RT)/M) => M = ( 3RT)/v_(rms)`

`therefore M = ( 3xx8.3xx300)/(1930)^2 = 2xx10^(-3) kg = 2 g`

`=> ` Gas is hydrogen

Correct Answer is `=>` (A) `H_2`

Q 2824180051

The root mean square velocity of the molecules in a sample of helium is `517th` that of molecules in a sample of hydrogen. If the temperature of hydrogen sample is` 0^0C`, then the temperature of the helium sample is about

(A)

`0^0 C`

(B)

`0 K`

(C)

`273^0 C`

(D)

`100^0 C`

Solution:

`v_(rms) = sqrt((3RT)/M) => v_(rms) prop sqrt(T/M)`

`v_(He)/v_(H_2) = 5/7 = sqrt(T_(He)/M_(He) xx M_(H_2)/T_(H_2))`

`=> T = 25/49 xx 4/2 xx 273 approx 0^0 C`

Correct Answer is `=>` (A) `0^0 C`

Q 2804178958

A gas at `27^0 C` temperature and `30` atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes `10` times its initial volume, then the final temperature becomes

(A)

`100^0 C`

(B)

`173^0 C`

(C)

`273^0 C`

(D)

`-173^0 C`

Solution:

`(p_1 V_1)/T_1 = (p_2 V_2)/T_2 => T_2 = ( p_2 V_2)/(p_1 V_1) xx T_1`

`T_2 = 1/30 xx 10/1 xx 300 = 100 K`

` = - 173^0 C`

Correct Answer is `=>` (D) `-173^0 C`

Q 2854178954

Gas at `27^0 C` has a volume `V` and pressure `P` on heating its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be

(A)

`1800^0 C`

(B)

`162^0 C`

(C)

`1527^0 C`

(D)

`600^0 C`

Solution:

`( p_1 V_1)/T_1 = (p_2 V_2)/T_2`

`therefore T_2 = ( p_2 V_2 )/T_2 T_1 = 2/1 xx 3/1 xx 300 = 1800 K`

` = 1527^0 C`

Correct Answer is `=>` (C) `1527^0 C`

Q 2814178950

At constant temperature on increasing the pressure of a gas by `5%` its volume will decrease by

(A)

`5%`

(B)

`5.26 %`

(C)

`4.26 %`

(D)

`4.76 %`

Solution:

`P prop 1/V => V_2/V_1 = p_1/p_2 = 100/105`

`V_2 = 100/105 V_1 = 0.953 V_1`

`%` change in volume ` = ( V_1 - V_2)/V_1 xx 100 = 4.76 % `

Correct Answer is `=>` (D) `4.76 %`

Q 2834078852

When a piece of metal weighing `48.3 g` at `10.7^0 C` is immersed in a current of steam at `100^0 C , 0.762 g` of steam is condensed on it. What is the specific heat of metal?

(A)

`0.95 cal//g^0C`

(B)

`9.5 cal//g^0 C`

(C)

`95 cal//g^0C`

(D)

`0.095 cal // g^0 C`

Solution:

`P prop 1/V => V_2/V_1 = p_1/p_2 = 100/105`

`V_2 = 100/105 V_1 = 0.953 V_1`

`%` change in volume ` = ( V_1 - V_2)/V_1 xx 100 = 4.76 % `

Correct Answer is `=>` (D) `0.095 cal // g^0 C`

Q 2884878757

The quantity of heat required to convert `2.5 kg` of ice at `0^0` to water at `20^0C` (assuming the latent heat of ice to be `80` cal per gram) is

(A)

200 kcal

(B)

150 kcal

(C)

250 kcal

(D)

225 kcal

Solution:

`P prop 1/V => V_2/V_1 = p_1/p_2 = 100/105`

`V_2 = 100/105 V_1 = 0.953 V_1`

`%` change in volume ` = ( V_1 - V_2)/V_1 xx 100 = 4.76 % `

Correct Answer is `=>` (C) 250 kcal

Q 2834878752

A steel scale reads correctly at `0^0 C` Given that the coefficient of linear expansion of steel is `12xx10^(-6) `per K the correction
that must be applied to a length of `25 m` measured by the scale at `30^0 C` will be

(A)

`0.006 m`

(B)

`0.009 m`

(C)

`0.007 m`

(D)

`0.018 m`

Solution:

`P prop 1/V => V_2/V_1 = p_1/p_2 = 100/105`

`V_2 = 100/105 V_1 = 0.953 V_1`

`%` change in volume ` = ( V_1 - V_2)/V_1 xx 100 = 4.76 % `

Correct Answer is `=>` (B) `0.009 m`

Q 2854778654

An iron tyre is to be fitted onto a wooden wheel, `1` min diameter. The diameter of the tyre is `6 mm` smaller than that of the wheel. Find the increase in temperature of tyre, so that it fits exactly on wooden wheel

(A)

`1.666^0 C`

(B)

`16.66^0 C`

(C)

`167.6^0 C`

(D)

`1666^0 C`

Solution:

According to question,
Given, diameter of wooden tyre

`1000-6 = 994 mm`

Radius, `R = 994/2 = 497 mm`

Change in diameter `= 6 mm`

`DeltaR = 6/2 = 3 mm`

`because 2pi DeltaR = 2pi R xx Y xx Delta t`

`Deltat = ( DeltaR)/(RY)`

` = 3/(497xx3.6xx10^(-5)) = 167.6^0 C`

Correct Answer is `=>` (C) `167.6^0 C`

Q 2874678556

When a gas filled in a closed vessel is heated through `1^0C`, its pressure increases by `0.4%`, then the initial temperature of the gas was

(A)

`30^0 C`

(B)

`200 K`

(C)

`2500 K`

(D)

`250^0 C`

Correct Answer is `=>` (D) `250^0 C`

Q 2854678554

What is the resulting temperature `t` when `150 g` of ice at `0^0C` is mixed with `300 g` of water at `50^0C?`

(A)

`33.3^0 C`

(B)

`6.6^0 C`

(C)

`25^0 C`

(D)

`13.4^0 C`

Solution:

Latent heat taken by ice

`Q = mL = 150xx80 = 12000`

Amount of heat given = Amount of heat taken

`300 ( 50- t) = 12000+150( t - 0)`

`300xx50-300t = 12000+150t`

`450t = 3000`

`t = 3000/450 = 6.6^0C`

Correct Answer is `=>` (B) `6.6^0 C`

Q 2814678550

Two liquids of equal volume are mixed throughly. Their specific heats are `s_1, s_2`, temperature `theta_1 , theta_2` and densities `rho_1` and `rho_2`, then the final temperature of the mixture is

(A)

`( rho_1 s_1 theta_1 + rho_2 s_2 theta_2)/(rho_1 s_1 + rho_2 s_2)`

(B)

`( rho_1 s_1 theta_2+ rho_2 s_2 theta_1)/( rho_1 theta_2+ rho_2 theta_1)`

(C)

`( rho_1 s_1 theta_1 + rho_2 s_2 theta_2)/(s_1+s_2)`

(D)

`( rho_1 s_1 + rho_2 s_2)/( s_1 theta_1+s_2 theta_2)`

Correct Answer is `=>` (A) `( rho_1 s_1 theta_1 + rho_2 s_2 theta_2)/(rho_1 s_1 + rho_2 s_2)`

Q 2824578451

`1g` of water at `100^0C` is converted to steam at the same temperature. The amount of heat required is nearest to a value of

(A)

`2257 J`

(B)

`540 J`

(C)

zero

(D)

`336 J`

Solution:

`therefore` Amount of required heat ` = mxx L`

` = 1xx540 = 540 cal = 540xx4.18 J = 2257 J`

Correct Answer is `=>` (A) `2257 J`

Q 2874478356

Which one of the following is the amount of that given up when `20 g` of steam at `100^0 C` is condensed and cooled to `20^0 C`

(A)

10000 cal

(B)

11400 cal

(C)

12400 cal

(D)

13600 cal

Solution:

`therefore` Latent heat `Q_1 = ml`

` = 20 xx 540 = 10800`
and heat, `Q_2 = mxx sxx Deltat`

`= 20xx1xx(100-20) = 20xx80 = 1600`

Total heat `Q = Q_1+Q_2`

` = 10800+1600 = 12400 cal`

Correct Answer is `=>` (C) 12400 cal

Q 2804378258

`1 g` of ice at `0^0 C` is mixed with `1 g` of steam at `100^0 C` After thermal equilibrium, the temperature of t;he mixture is

(A)

`0^0 C`

(B)

`50^0 C`

(C)

`80^0 C`

(D)

`10^0 C`

Solution:

`therefore ` Latent beat taken by ice,

`Q = ml = 1 xx 80 = 80^0 C`

`because m xx s xx ( 100 - t) = 80+ m xx s xx ( t - 0)`

`(100 - t) = 80+t`

` => 20 = 2t `

`=> t = 10^0 C`

Correct Answer is `=>` (D) `10^0 C`

Q 2834278152

From what height a block of ice must fall into a well. so that `1/100`th of its mass may be melted? The temperature of the water in the well is `0^0 C`. Latent heat of fusion of ice `80` cal/g and `d = 4.2 xx 10^7` erg / cal.

(A)

`342m`

(B)

`34.2 m`

(C)

`3.42 m`

(D)

`342.86 m`

Solution:

`because b = m/(100 m) (( JL)/g)`

`=> b = 1/100 xx ( (4.2xx80)/(9.8)) xx 1000`

` b = 342.86 m`

Correct Answer is `=>` (D) `342.86 m`

Q 2854178054

A bullet of mass `10 g` moving with speed of `210 m//s` is stopped suddenly. If all its kinetic energy is convertes into heat, then what is the amount of heat produced in calories?

(A)

`52.5xx10^2`

(B)

`52.5xx10^4`

(C)

`525`

(D)

`52.5`

Solution:

`because ` All kinetic energies arc converted into heat.

`therefore Q = 1/2 mv^2`

`Q = 1/2 xx 10/1000 xx 210 xx 210`

`Q = 220.5/J = (220.5)/(4.2) = 52.5 cal `

Correct Answer is `=>` (D) `52.5`

Q 2834067852

If the pressure and volume of certain quantity of ideal gas are halved, then its temperature

(A)

is doubled

(B)

becomes one-fourth

(C)

remains constant

(D)

is halved

Solution:

According to ideal gas law

`( P_1 V_1)/T_1 = (P_2V_2)/T_2`

or `T_2 / T_1= ( P_2V_2)/(P_1 V_1)`

Here `P_1 = P , V_1 = V T_1 = T`

`P_2 = P/2 , V_2 = V/2 , T_2 = ?`

`therefore T_2 = ( T (P/2) (V/2))/(P V)`

`=> T_2 = T/4`

Correct Answer is `=>` (B) becomes one-fourth

Q 2884867757

For an ideal gas of diatomic molecules

(A)

`C_p = 5/2 R`

(B)

`C_v = 3/2 R`

(C)

`C_p- C_v = 2R`

(D)

`C_p = 7/2 R`

Correct Answer is `=>` (D) `C_p = 7/2 R`

Q 2854867754

A diatomic molecule has how many degrees of freedom

(A)

`3`

(B)

`4`

(C)

`5`

(D)

`6`

Correct Answer is `=>` (C) `5`

Q 2834767652

The r.m.s speed of gas molecule is given by

(A)

`2.5 sqrt((RT)/m)`

(B)

`1.73 sqrt((RT)/M)`

(C)

`2.5 sqrt(M/(RT))`

(D)

`1.73 sqrt(M/(RT))`

Correct Answer is `=>` (B) `1.73 sqrt((RT)/M)`

Q 2804667558

Mean free path of a gas molecules is

(A)

Inversely proportional to the number of molecules per unit volume

(B)

Inversely proportiona to the diameter of the molecule

(C)

directly proportional o the square root of the absolute temperature

(D)

Independent of temrerature

Correct Answer is `=>` (D) Independent of temrerature

Q 2854667554

In the relation `n = ( PV)/(RT)` where `n = `

(A)

number of molecules

(B)

atomic number

(C)

mass number

(D)

number of moles

Correct Answer is `=>` (D) number of moles

Q 2814567459

Which of the following statements about kinetic theory of gases is wrong

(A)

The molecules of a gas are in continuous random motion.

(B)

The molecules continuously undergo in elastic collisions.

(C)

The molecules do net interact with each other except during collisions

(D)

The collisions amongst the molecules are of short duration

Correct Answer is `=>` (B) The molecules continuously undergo in elastic collisions.

Q 2884567457

Molecules of a gas behaves like

(A)

inelastic rigid sphere

(B)

perfectly elastic non-rigid sphere

(C)

perfectly elastic rigid sphere

(D)

inelastic non-rigid sphere

Correct Answer is `=>` (C) perfectly elastic rigid sphere

Q 2864567455

SI unit of universal gas constant is

(A)

`cal //text()^0 C`

(B)

`j // mol`

(C)

`J mol^(-1) K^(-1)`

(D)

`J// kg`

Correct Answer is `=>` (C) `J mol^(-1) K^(-1)`

Q 2824567451

When pressure on piece of ice is increases its melting point

(A)

decreases

(B)

increases

(C)

remains unchanged

(D)

first increases and then decreases

Correct Answer is `=>` (B) increases

Q 2804467358

Paraffin wax contracts on solidification. The melting point of wax will

(A)

not change with pressure

(B)

decrease with pressure

(C)

increase with pressure

(D)

None of the above

Correct Answer is `=>` (C) increase with pressure

Q 2844467353

Real expansion of a liquid is always

(A)

greater than apparent expansion

(B)

less than apparent expansion

(C)

equal to apparent expansion

(D)

None of the above

Correct Answer is `=>` (A) greater than apparent expansion

Q 2804367258

When water is heated from `0^0 C` to `20^0 C` how does its volume change?

(A)

It shall increase

(B)

It shall decrease

(C)

It shall first increase and then decrease

(D)

It shall first decrease and then increase

Correct Answer is `=>` (D) It shall first decrease and then increase

Q 2864367255

Specific heat of a substance depends upon

(A)

mass of the substance

(B)

volume of the substance

(C)

shape of the body

(D)

nature of the substance

Correct Answer is `=>` (D) nature of the substance

Q 2864267155

The equivalence of two systems in thermal equilibrium is represented by the property

(A)

heat

(B)

temperature

(C)

energy

(D)

specific heat

Correct Answer is `=>` (B) temperature

Q 2854267154

The temperature for which the reading on Celsius and Fahrenheit scales are identical, is

(A)

`-40^0C`

(B)

`40^0 C`

(C)

`-30^0 C`

(D)

`30^0 C`

Correct Answer is `=>` (A) `-40^0C`