Oxygen gas having a volume of 1200 cm 3 at 40 . 0 ° C and 1 . 01 × 10 5 Pa expands until its temperature is 493 K and its pressure is 1 . 06 × 10 5 Pa . Find ( a ) the number of moles of oxygen present and b the final volume of the sample.

The given gas is oxygen, treat this as an ideal gas, We have ideal gas equation, P V = n R T (a) The initial state of gas, P i V i = n R T i ...... 1 Here, initial pressure, P i = 1 . 01 × 10 5 Pa Initial volume, V i = 1200 cm 3 = 1 . 2 × 10 - 3 m 3 Initial temperature, T i = 40 ° C = 313 K From 1 the number of moles present in the given gas, n = P i V i R T i ⇒ n = 1 . 01 × 10 5 Pa 1 . 2 × 10 - 3 m 3 8 . 314 J mol - 1 K - 1 313 ⇒ n = 4 . 66 × 10 - 2 mol b The final state of the gas, P f V f = n R T f ..... 2 ⇒ V f = n R T f P f Here, n = 4 . 6 × 10 - 2 mol , R = 8 . 31 J mol - 1 K - 1 , P f = 1 . 06 × 10 5 Pa and T f = 493 K ⇒ V f = 4 . 66 × 10 - 2 × 8 . 31 × 493 1 . 06 × 10 5 = 1800 cm 3 Therefore, the final volume is 1800 cm 3 .

In the temperature range 310 K to 330 K , the pressure P of a certain non-ideal gas is related to volume V and temperature T by P = ( 24 . 9 J K - 1 ) T V - 0 . 00662 J K - 2 T 2 V . How much work is done by the gas if its temperature is raised from 315 K to 330 K , while the pressure is held constant?

The work done by non-ideal gas at constant pressure, W = P V 2 - V 1 ...... 1 The given equation of pressure is, P = 24 . 9 J K - 1 T V - 0 . 0062 J K - 2 T 2 V ⇒ P V = 24 . 9 J K - 1 T - 0 . 0062 J K - 2 T 2 Let us consider of temperature T 1 , the volume of gas V 1 . ⇒ P V 1 = 24 . 9 J K - 1 T 1 - ( 0 . 0062 J K - 2 ) T 1 2 , At the temperature, T 2 , the volume of the gas V 2 , then, ⇒ P V 2 = 24 . 9 J K - 1 T 2 - ( 0 . 0062 J K - 2 ) T 2 2 The net work done by the gas, when temperature is raised from T 1 to T 2 at constant pressure W = P V 2 - P V 1 = 24 . 9 T 2 - 0 . 0062 T 2 2 - 24 . 9 T 1 - 0 . 0062 T 1 2 = 24 . 9 T 2 - T 1 - 0 . 0062 T 2 2 - T 1 2 J Where, T 1 = 315 K and T 2 = 330 K W = 24 . 9 330 - 315 - ( 0 . 0062 ) 330 2 - 315 2 ⇒ W = 313 . 5 J Therefore, the work done at constant pressure is 313 . 5 J .

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IMPORTANT

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An ideal diatomic gas, with rotation but no oscillation undergoes an adiabatic compression. Its initial pressure and volume are $1.20$ atm and $0.200 m^{3} .$ Its final pressure is $3.60 atm$ . How much work is done by the gas?

Important Questions on The Kinetic Theory of Gases

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IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 27

A certain gas occupies a volume of

0.76 L

at a pressure of

1.2 atm

and a temperature of

4000 K

. It is expanded adiabatically to a volume of

4.3 L

. Determine
(a) the final pressure and
(b) the final temperature, assuming the gas to be an ideal gas for which

γ = 1.4

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IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 28

The most probable speed of the molecules in a gas at temperature

T_{2}

is equal to the average speed of the molecules at the temperature

T_{1}

. Find

\frac{T_{2}}{T_{1}}

MEDIUM

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IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 29

The volume of an ideal gas is adiabatically reduced from $350 L$ to $130 L$ . The initial pressure and temperature are $2.00 atm$ and $380 K$ . The final pressure is $8.00 atm$ .

(a) Is the gas monatomic, diatomic or polyatomic?
(b) What is the final temperature?
(c) How many moles are in the gas?

Ginen:- $\log (35) = 1.544 and \log (13) = 1.114$

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 30

Under constant pressure, the temperature of

3.00 mol

of an ideal monatomic gas is raised

15.0 K

. What are

(a)

the work done

W

by the gas,

(b)

the energy transferred as heat

Q

(c)

the change

Δ E_{int}

in the internal energy of the gas and

(d)

the change in average kinetic energy

Δ K

per atom?

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IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 31

An automobile tyre has a volume of

1.64 \times 10^{- 2} m^{3}

and contains air at a gauge pressure (pressure above atmospheric pressure) of

165 kPa

, when the temperature is

0.00 ° C

. What is the gauge pressure of the air in the tyres when its temperature rises to

37.0 ° C

and its volume increases to

1.67 \times 10^{- 2} m^{3}

? Assume the atmospheric pressure is

1.01 \times 10^{5} Pa

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IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 32

Two containers are at the same temperature. The first contains gas with pressure

P_{1},

molecular mass

m_{1}

and

rms

speed

v_{rms 1}

. The second contains gas with pressure

1.5 P_{1},

molecular mass

m_{2}

and average speed

v_{avg 2} = 2.0 v_{rms1}

. Find the mass ratio

\frac{m_{1}}{m_{2}}

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 33

Oxygen gas having a volume of $1200 {cm}^{3}$ at $40.0 ° C$ and $1.01 \times$ $10^{5} Pa$ expands until its temperature is $493 K$ and its pressure is $1.06 \times 10^{5} Pa .$ Find

$(a)$ the number of moles of oxygen present and
$(b)$ the final volume of the sample.

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 19 - The Kinetic Theory of Gases>Problems>Q 34

In the temperature range $310 K$ to $330 K,$ the pressure $P$ of a certain non-ideal gas is related to volume $V$ and temperature $T$ by
$P = (24.9 J K^{- 1}) \frac{T}{V} - (0.00662 J K^{- 2}) \frac{T^{2}}{V}$ .

How much work is done by the gas if its temperature is raised from $315 K$ to $330 K$ , while the pressure is held constant?

An ideal diatomic gas, with rotation but no oscillation undergoes an adiabatic compression. Its initial pressure and volume are 1.20 atm and 0.200 m3. Its final pressure is 3.60 atm. How much work is done by the gas?

Important Questions on The Kinetic Theory of Gases

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An ideal diatomic gas, with rotation but no oscillation undergoes an adiabatic compression. Its initial pressure and volume are $1.20$ atm and $0.200 m^{3} .$ Its final pressure is $3.60 atm$ . How much work is done by the gas?