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Figure shows a horizontal cylindrical container of length 30 cm, which is partitioned by a tight-fitting separator. The separator is diathermic but conducts heat very slowly. Initially the separator is in the state shown in the figure. The temperature of left part of cylinder is 100 K and that on right part is 400 K. Initially the separator is in equilibrium. As heat is conducted from right to left part, separator displaces to the right. Find the displacement of separator after a long when gases on the two parts of cylinder are in thermal equilibrium.

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Important Questions on Kinetic Theory

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

An ideal gas undergoes a circular cycle centred at $4 atm$ , $4 L$ as shown in the diagram.

Question Image

The maximum temperature attained in this process is close to

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

A long cylindrical pipe of radius $20 cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When $a$ $50 kg$ mass is attached to the other end of piston, it moves down by a distance, $Δ l$ before coming to equilibrium. Assuming air to be an ideal gas, $\frac{Δ l}{l}$ (see figure) is close to $(g = 10 m s^{- 2}$ , one atmospheric pressure is $10^{5} Pa$ ),

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

The average distance between molecules of an ideal gas at STP is approximately of the order of

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

Modern vacuum pumps can evacuate a vessel down to a pressure of

4.0 \times 1 0^{- 15}

atm. at room temperature (300 K). Taking R = 8.3 JK^-1 mole^-1, 1 atm = 10⁵ Pa and

N_{Avogadro} = 6 \times 1 0^{23} {mole}^{- 1}

, the mean distance between molecules of gas in an evacuated vessel will be of the order of :

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

A cylinder closed at both ends is separated into two equal parts (

45 cm

each) by a piston impermeable to heat. Both the parts contain the same masses of gas at a temperature of

300 K

and a pressure of

1 atm

. If now the gas in one of the parts is heated such that the piston shifts by

5 cm

, then the temperature and the pressure of the gas in this part after heating is

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?
Question Image

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

For the

P - V

diagram given for an ideal gas
Question Image

Out of the following which one correctly represents the

T - P

diagram?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

Three moles of an ideal gas are in a rigid cubical box with sides of length

0.170 m

. The ratio of the forces that the gas exerts on each of the six sides of the box when the gas temperature are

27 ° C

and

127 ° C

is.

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

An ideal gas filled in a cylinder occupies volume,

V

. The gas is compressed isothermally to the volume,

\frac{V}{3}

. Now the cylinder valve is opened and the gas is allowed to leak keeping the temperature the same. What percentage of the number of molecules escape to bring the pressure in the cylinder back to its original value.

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

One mole of an ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume,

V

is-

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

An open glass tube is immersed in mercury in such a way that a length of

8 cm

extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional

46 cm

. What will be length of the air column above mercury in the tube now ?
(Atmospheric pressure =

76 cm

of Hg)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

A given sample of an ideal gas occupies a volume,

V

at a pressure,

P

and absolute temperature,

T

. The mass of each molecule of the gas is

m

. Which of the following gives the density of the gas?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

One mole of an ideal gas passes through a process where pressure and volume obey the relation

P = P_{o} [1 - \frac{1}{2} {(\frac{V_{o}}{V})}^{2}]

. Here

P_{o}

and

V_{o}

are constants. Calculate the change in the temperature of the gas if its volume changes from

V_{o}

2 V_{o}

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

An ideal gas follows a process described by

P V^{2} = C f r o m (P_{1}, V_{1}, T_{1}) t o (P_{2}, V_{2}, T_{2})

(C is a constant). Then

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

The equation of state for

2 g

of oxygen at a pressure

p

and temperature

T

, when occupying a volume

V

will be

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

Initially a gas of diatomic molecules is contained in a cylinder of volume

V_{1}

at a pressure

P_{1}

and temperature

250 K

. Assuming that

25 %

of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature

2000 K,

when contained in a volume

2 V_{1}

is given by

P_{2}

. The ratio

P_{2} / P_{1}

is -

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

The change in the magnitude of the volume of an ideal gas when a small additional pressure

∆ P

is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity

∆ T

at constant pressure. The initial temperature and pressure of the gas were

300 K

and

2 atm

respectively. If

| ΔT | = C | ΔP |

then value of

C

(K / atm)

is __________

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

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

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

The temperature of an open room of volume

30 m^{3}

increases from

17 ° C

27 ° C

due to the sunshine. The atmospheric pressure in the room remains

1 \times 10^{5} Pa

. If

n_{i}

and

n_{f}

are the number of molecules in the room before and after heating, then

n_{f} - n_{i}

will be:

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Molecular Nature of Matter

A vertical closed cylinder is separated into two parts by a frictionless piston of mass

m

and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is

l_{1},

and that below the piston is

l_{2},

such that

l_{1} > l_{2} .

Each part of the cylinder contains

n

moles of an ideal gas at equal temperature

T .

If the piston is stationary, its mass

m

will be given by:
(

R

is universal gas constant and

g

is the acceleration due to gravity)

Important Questions on Kinetic Theory

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