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An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross-section $8 \times 10^{- 3} m^{2}$ . Initially the gas is at $300 K$ and occupies a volume of $2.4 \times 10^{- 3} m^{3}$ and the spring is in its relaxed position. The gas is heated by a small electric heater until the piston moves out slowly by $0.1 m$ . Calculate the final temperature of the gas and the heat supplied (in $J$ ) by the heater. The force constant of the spring is $8000 N m^{- 1}$ and atmospheric pressure $1 \times 10^{5} N m^{- 2}$

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Important Questions on Kinetic Theory

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)

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

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 $10^{5} Pa$ ),

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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

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

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

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

HARD

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

Two closed bulbs of equal volume

(V)

containing an ideal gas initially at pressure

p_{i}

and temperature

T_{1}

are connected through a narrow tube of negligible volume, as shown in the figure below. The temperature of one of the bulbs is then raised to

T_{2} .

The final pressure

P_{f}

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-

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

EASY

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

A gas such as carbon monoxide would be most likely to obey the ideal gas law at:

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

MEDIUM

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

The volume of gas $A$ is twice than that of gas $B$ . The compressibility factor of gas $A$ is thrice than that of gas $B$ at same temperature. What are the pressures of the gases for equal number of moles?

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 :

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

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}

EASY

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

10 moles of a mixture of hydrogen and oxygen gases at a pressure of 1 atm at a constant volume and temperature, react to form 3.6 g of liquid water. The pressure of the resulting mixture will be closest to:

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

An open vessel at

27^{o} C

is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature to which the vessel has been heated is:

Important Questions on Kinetic Theory

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