Test: Kinetic Theory - 2 - JEE MCQ

Explanation:

The theory for ideal gases makes the following assumptions

1. Gases consist of particles in constant, random motion. They continue in a straight line until they collide with something—usually each other or the walls of their container.

2. Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases.

3. No molecular forces are at work. This means that there is no attraction or repulsion between the particles.

4. Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions.

5. The time it takes to collide is negligible compared with the time between collisions.

6. The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and kinetic energy of the gas refer to the average of these speeds.

7. The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move.

8. All gases at a given temperature have the same average kinetic energy.

9. Lighter gas molecules move faster than heavier molecules.

A diatomic molecule has 5 degrees of freedoms - 3 translational degrees each in one principal axis and 2 rotational degrees of freedom.

Explanation:Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".

Mass, m = 14.5 kg
Length of the steel wire, l = 1.0 m
Angular velocity, ω = 2 rev/s = 2 × 2π rad/s = 12.56 rad/s
Cross-sectional area of the wire, a = 0.065 cm² = 0.065 × 10^-4 m²
Let Δl be the elongation of the wire when the mass is at the lowest point of its path.
When the mass is placed at the position of the vertical circle, the total force on the mass is:
F = mg + mlω²
= 14.5 × 9.8 + 14.5 × 1 × (12.56)²
= 2429.53 N
Young’s modulus = Strss / Strain
Y = (F/A) / (∆l/l)
∴ ∆l = Fl / AY
Young’s modulus for steel = 2 × 10¹¹ Pa
∆l = 2429.53 × 1 / (0.065 × 10^-4 × 2 × 10¹¹)   =   1.87 × 10^-3 m
Hence, the elongation of the wire is 1.87 × 10^–3 m
Hence 1.87 × 10^–3 m

Explanation:

for monoatomic  gas C_V = 1.5R, C_P =  2.5R

At const volume, 

Q = 500 J

Q=nCVΔT

500=1×1.5×8.31(T₁−300)

T₁=340K

At const pressure Q = 500 J

Q=nCPΔT

500=1×2.5×8.31(340−T₂)

T₂=316K

Explanation:The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.It will applicable only for gases

Explanation:Degrees of freedom of a system refers to the possible independent motions a system can have.Monoatomic gas molecule can have 3 independent motion and hence have 3 degrees of freedom (all are translational).

Explanation:

Helium is a monoatomic gas.(C_V = 1.5R)

change in internal  energy 

ΔU=nCVΔT=3×1.5×8.31×2=75J

Explanation:

At const volume, 

Q = 500 J

Q=nCPΔT

500=1×2.5×8.31ΔT

ΔT=24.06

W=nRΔT=1×8.31×24.06=200J

Explanation:Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. It also relates measurable properties of gases such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.

Explanation:the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.

Explanation:atomic hypothesis that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.

Explanation:

for monoatomic gas 

from conservation of energy

Explanation:Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules"For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Explanation:

Hydrogen is a diatomic gas. (C_P = 3.5R)

energy transferred by heat to the gas

Q=nCPΔT=1×3.5×8.31×120=3490J=3.49KJ

Explanation:

Atoms in a gas are well separated with no regular arrangement. Atoms vibrate and move freely at high speeds

Atoms in a liquid are close together with no regular arrangement. Atoms vibrate, move about, and slide past each other.

Atoms in a solid are tightly packed, usually in a regular pattern. Atoms vibrate (jiggle) but generally do not move from place to place.

Explanation:

Hydrogen is a diatomic gas. (C_V = 2.5R)

Change in internal energy 

ΔU = nCVΔT = 1 x 2.5 x 8.31 x 120 = 2493J = 2.49KJ

Explanation:the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties

Explanation:At room temperature (=300K) the noble gases are all in the gas phase, they are banging around and colliding into one another like little pool balls. At this temperature, when the atoms collide they appear to elastically bounce off of one another, but this bounce is actually a result of atomic repulsion. The atoms are traveling so fast and they approach each other so quickly that their momentum 'squeezes' them together until the atomic repulsion pushes them back apart.

Explanation:All collisions between molecules among themselves or between molecules and the walls are elastic. So that total kinetic energy and total momentum is conserved. Also the average properties of gas are remains constant.

Explanation:

In  isobaric process 

W=nR(TF−TI)=1×8.31×(420−300)=0.98kJ

Explanation:

PV=nRT

Hence the value of PV/T where the curves meet on the y-axis is 0.26 jK^-1

= 1351m/sec = 1.35 Km/sec

F = YA (∆l/l)
F = Mg, Y = Sy, A = A using this we get
So, Mg ≤ Sy x A => A ≥ Mg/Sy