Kinetic Theory of Gases | Visual Physics for IIT JEE / NEET
Introduction

Understanding the Pressure, Volume, Temperature of a gas interms of activity of its molecules. Understanding Mole and how it converts the units from Micro to Macro world.

Gas Laws

Understanding Boyle?s Law, Charles? Law, Gay-Lussac?s Law and Avogadro?s Law

Ideal Gas Eqn

Ideal Gas Equation and derivation of all other gas laws from it. Boltzmann constant.

Q1

Statement - 1 The figure shows the V-T graphs of a certain mass of an ideal gas at two pressures P1 and P2. It follows from the graphs that P1 is greater than P2. Statement - 2 The slope of V-T graph for an ideal gas is directly proportional to pressure.

Q2

Statement-1: The figure shows PV/T versus P graph for a certain mass of oxygen gas at two temperatures T1 and T2. It follows from the graph that T1 > T2. Statement-2 : At higher temperature, real gas behaves more like and ideal gas.

Q3

A cylinder whose inside diameter is 1 m contains air compressed by a piston of mass M = 10 kg, which can slide freely in the cylinder. The entire arrangement in immersed in a water bath whose temperature can be controlled. The system in initially in equilibrium at temperature T1 = 27 oC. The initial height of the piston above the bottom of the cylinder is h1 = 10 cm. The temperature of the water bath is gradually increased to a final temperature T2 = 77 oC. Calculate the height h2 of the piston. Starting from the same initial condition the temperature is again gradually raised, and weights are added to the piston to keep its height fixed at h1. Calculate the mass that has been added when the temperature has reached T2 = 77 oC.

Q4

A vessel contains 1 mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has pressure of

Q5

4.6 g of CO2 is contained in a vessel of volume 5 litre and at a temperature 1800 K. Assume that 30% of the molecules are disassociated at this temperature. Find the pressure of the gas.

Kinetic Theory

Introduction to Kinetic Theory of Gases. Mentions the assumptions on which the model of Kinetic Theory is based.

KE Pressure Temp

Derivation of equations of Total Kinetic Energy of particles of gas, Pressure exerted by gas and Temperature of gas

Q6

Using the equation of pressure from Kinetic model, express Pressure interms of a) Number Density b) Density of gas c) Number of moles and Molar mass

Q7

1 L volume container contains 100 g of gas at a pressure of 100 kPa. The mass of each gas particle is 8.0 ? 10-26 kg. Find the average translational kinetic energy of each particle.

Q8

The pressure of a gas in a 100 mL container is 200 kPa and the average translational Kinetic energy of each gas particle is 6.0 ? 10-21 J. Find the number of gas particles in the container. How may moles are in the container?

Mean Time & Path

Average time between collisions between 2 particles and Average distance travelled by a particle between 2 collisions as per the Kinetic Theory.

Mol Speeds - 1

Maxwell-Boltzmann Distribution of Molecular speeds. Understanding Probability Density function and Probability Distribution function.

Mol Speeds - 2

Finding the Average, RMS and Most Probable speed from Maxwell-Boltzmann Distribution of Molecular speeds.

Q9

Mark if the following statements are True or False. a) The root-mean-square speed of the molecules of different ideal gases at the same temperature are the same. b) The average translational kinetic energy of molecules of different ideal gases at the same temperature is the same.

Q10

Three closed vessels A, B and C are at the same temperature. Vessel A Contains only O2, B only N2 and C a mixture of equal quantities of O2 and N2. If the average speed of O2 molecules in vessel A is v1, that of N2 molecules in vessel B is v2, the average speed of O2 molecules in vessel C is

Q11

At room temperature (27 oC) the rms speed of the molecules of a certain diatomic gas is found to be 1920 ms-1. This gas is (a) H2 (b) F2 (c) O2 (d) Cl2

Q12

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume. True / False

Q13

Statement 1: The rms speed of oxygen molecules (O2) at an absolute temperature T is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the rms speed remains unchanged. Statement 2: The rms speed of the molecules of a gas is directly proportional to T/M where M is the molar mass.

Q14

The graph shows Maxwell velocity distribution for oxygen. a) what will be the most probable speed of N2 molecules at 600 K?

K Th & Gas Laws

Understanding Gas Laws from Kinetic Theory of Gases. Dalton?s Law of Partial Pressure. Graham?s Law of Diffusion.

Molar Heat Cap

Molar Heat Capacity at constant Volume and Molar Heat Capacity at constant Pressure of Monoatomic gases. Adiabatic Constant.

EquiPart of Energy

Molar Heat Capacity for Diatomic and Polyatomic Gases. Concept of Equipartition of Energy and Degrees of Freedom.

Q15

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the mixture is

Q16

A vessel conatins a mixture of 1 mole of oxygen and 1 mole of nitrogen at 300 K. The ratio of the rotational kinetic energy per mole of O2 to that per mole of N2 is a) 1 : 1 b) 1 : 2 c) 2 : 1 d) depends on the moment of inertia of the two molecules.

Q17

Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then (a) Cp - Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas (b) Cp + Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas (c) Cp/Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas (d) Cp . Cv is larger for a diatomic ideal gas than for a mono atomic ideal gas

Gaseous Mixtures

Properties of a Mixture of Gases.

Q18

One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. 1) The molar specific heat of the mixture at constant volume is (R = molar gas constant) a) R b) 2 R c) 3.5 R d) 4.5 R

1

The air density of Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000 cc at sea level (pressure 1 atmosphere, temperature 27 oC). Assuming that the temperature around Mount Everest is -130 oC and that the oxygen cylinder has a capacity of 5.2 litre, the pressure at which oxygen be filed (at site) in the cylinder is (a) 2.75 atm. (b) 5.0 atm. (c) 5.77 atm. (d) 1 atm.

2

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m2. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soapwater water used to make bubbles is 0.04 N/m. Find the ratio nB/nA, where nA and nB are the number of moles of air in bubbles A and B, respectively.

3

A vertical hollow cylinder of height 1.52 m is fitted with a movable piston of negligible mass thickness. The lower half portion of the cylinder contains an ideal gas and the upper half is filled with mercury. The cylinder is initially at 300 K. When the temperature is raised, half of the mercury comes out the cylinder. Find the temperature assuming the thermal expansion of mercury to be negligible.

4

An electric bulb of volume 500 cm3 was sealed off during manufacture at a pressure of 10-3 mm of Hg at 27 oC. Find the a) number of molecules in the bulb. b) number density of molecules c) average distance between the molecules

5

A gaseous mixture at temperature T and pressure P containing helium and nitrogen has a density r. What is the concentration of helium and nitrogen in the given mixture ?

6

During an experiment, an ideal gas is found to obey an additional law VP2 = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2V, the temperature becomes

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