Test: Kinetic Theory (October 14) - NEET MCQ

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

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: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:

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: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:

for monoatomic gas 

from conservation of energy

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: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: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.

PV=nRT

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