MEDIUM

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The figure below shows the plot of $\frac{p V}{n T}$ versus p for oxygen gas at two different temperatures.

Read the following statements concerning the above curves.
1. The dotted line corresponds to the ideal gas behaviour.
2. $T_{1} > T_{2}$
3. The value of $\frac{p V}{n T}$ at the point where the curves meet on the $y$ -axis is the same for all gases.

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Important Questions on Thermal Properties of Matter

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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

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The maximum temperature attained in this process is close to

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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.

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

For the

P - V

diagram given for an ideal gas
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Out of the following which one correctly represents the

T - P

diagram?

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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.

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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-

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Absolute Temperature and Ideal Gas Equation

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?

Important Questions on Thermal Properties of Matter

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