Thermal

Question 1

Phases of matter

Answer 1

Solid:

• Particles are closely packed in a fixed lattice structure, held by strong intermolecular forces.
• Particles can only vibrate about fixed positions and have low energy.
• Solids have high density and are incompressible.

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Liquid:
- Particles are closely packed, randomly arranged, and held by weaker intermolecular forces than solids.
- Particles can flow past each other and have higher energy than solids but lower than gases.
- Liquids have a fixed volume, take the shape of their container, and are difficult to compress.

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Gas:
- Particles have negligible intermolecular forces, are randomly arranged, and are far apart.
- Particles move freely in all directions at various speeds and have higher energy than solids and liquids.
- Gases take the shape of their container, have no fixed volume, are compressible, and have the lowest densities.

Question 2

Brownian motion

Answer 2

• The random movement of small particles suspended in a liquid or gas, caused by collisions with faster-moving atoms or molecules.
• Supports the idea of molecular motion and explains the concept of pressure in gases.
• Smaller molecules affect larger particles due to their high speeds and momentum transfer during collisions.

Question 3

Energy during change of phase

Answer 3

Phase Changes:

• During phase changes, energy increases or decreases electrostatic potential energy instead of kinetic energy, so temperature remains constant.

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Melting or Boiling:

• Energy breaks intermolecular bonds, increasing electrostatic potential energy and moving molecules further apart.

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Freezing or Condensation:

• Energy forms bonds, decreasing electrostatic potential energy and moving molecules closer together.

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Kinetic Energy:

• Stays constant, indicating no temperature change during a phase transition.

Question 4

Specific heat capacity

Answer 4

Amount of energy needed to raise the temperature of unit mass (1 kg) of a substance by 1 K (unit temp)

Question 5

Internal energy

Answer 5

• The sum of the randomly distributed kinetic and potential energies of atoms or molecules within a substance.
• ΔU ∝ ΔT: Internal energy is proportional to temperature change.
• Stronger intermolecular forces result in higher potential energy.

Question 6

Thermal equilibrium

Answer 6

Heat Flow and Thermal Equilibrium:

• Heat flows from a hotter object to a colder one until both reach the same temperature (thermal equilibrium).
• Thermal equilibrium occurs when two substances in contact no longer exchange heat energy and reach the same temperature.
• The final temperature depends on the initial temperature difference between the objects (e.g., ice cubes melting in room temperature water).

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Energy Balance:

• Energy lost by hotter object = Energy gained by colder object.
• For ice:
  Energy gained = ml + mc(T -T₁)
• For hot drink:
  Energy lost = mc(T₂ - T):

Question 7

Specific Latent Heat

Answer 7

Specific Latent Heat:

1. Fusion:
   
   • Energy required to convert 1 kg of solid to liquid with no temperature change.
2. Vaporisation:
   
   • Energy required to convert 1 kg of liquid to gas with no temperature change.

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Key Points:

• Evaporating 1 kg of water requires seven times more energy than melting 1 kg of ice.
• Ice melting: Increases molecular separation.
• Boiling water: Fully separates molecules, breaking all intermolecular forces.

Question 8

Triple-Point

Answer 8

The specific temperature and pressure where a substance exists as a solid, liquid, and gas simultaneously.

Question 9

Gas Laws

Answer 9

Boyle’s Law:

• p ∝ V^-1 (at constant temperature).
• If temperature increases, the graph is further from the origin, and vice versa.
• The area under the graph represents energy.

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Pressure Law:

• p ∝ T

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Charles’s Law:

• V ∝ T

Question 10

Avogadro Constant

Answer 10

Mole:

• The SI base unit for the amount of substance, defined as the amount containing as many particles (e.g., atoms or molecules) as there are in 12 g of carbon-12.

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Avogadro’s Constant (N_a):

• The number of atoms in 12 g of carbon-12.

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Equation:

• N = n × N_a
  Where:
• n: Number of moles
• N_a: Avogadro’s Constant
• N: Number of particles

Question 11

Molar mass

Answer 11

Molar Mass

• The mass of one mole of a substance, measured in grams per mole (g mol⁻¹).

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Equation:

• n × M = m

Where:
- n: Number of moles
- m: Mass of the substance (g)
- M: Molar mass (g mol⁻¹)

Question 12

Molar Gas Constant (R)

Answer 12

• The constant in the equation pVT^-1 depends on the amount of gas (measured in moles, n).
• Equation: constant=nR
• Relates energy to temperature in thermal physics for a mole of particles at a given temperature.

Question 13

Boltzmann’s constant

Answer 13

• Boltzmann constant (k_B) links the average kinetic energy of particles in a gas to its temperature.
  
  • k_B = R / Nₐ
• Derivation of nR = Nk_B:
  
  • k_B = R / Nₐ
  • R / (N/n) = k_B
  • nR/N = k_B
  • nR= Nk_B

Question 14

Kinetic Theory of Gases (R.A.V.E.D.)

Answer 14

1. R | Random:
   
   • A large number of gas particles move randomly in straight lines until they collide with each other or the container walls.
2. A | Attraction:
   
   • No intermolecular forces between particles except during collisions.
3. V | Volume:
   
   • Negligible volume of particles compared to the volume of the gas.
4. E | Elastic:
   
   • Elastic collisions: Collisions between particles and with container walls are perfectly elastic.
5. D | Duration:
   
   • Negligible time spent on each collision compared to the time between collisions.

Question 15

Pressure in terms of the kinetic theory of gases and Newtonian thoery

Answer 15

Gas Particle Motion:

• Gas particles move randomly with constant velocities and no intermolecular forces, following Newton’s 1st law (objects in motion stay in motion unless acted upon).

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Collisions and Force:

• When particles collide with the walls of the container, they exert a force on the wall, and the wall exerts an equal and opposite force (Newton’s 3rd law).
• The force on the wall is calculated using Newton’s 2nd law (force = rate of change of momentum).
• The momentum change during a collision (from mu to -mu) results in a force proportional to the particle’s mass and velocity.

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Pressure:

• Although each particle exerts a tiny force, billions of particles create a combined force, leading to a steady, uniform pressure on the walls.
• Pressure results from many collisions between particles and the container walls.
• Equation:
  Pressure = (Rate of momentum ÷ area) × number of particles

Question 16

Root Mean Square

Answer 16

Gas Particle Motion:

• Gas particles move in random directions, resulting in a net velocity of zero.
• Squaring the velocities ensures all values are positive, avoiding cancellation.

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Root-Mean-Square Speed (c_rms):

• c_rms =√mean(c²).
• Provides the average speed of particles by taking the square root of the mean square speed.

Question 17

Maxwell-Boltzmann distribution

Answer 17

Maxwell-Boltzmann Distribution:

• Shows the range of kinetic energies of gas particles, with most particles moving at moderate speeds, and fewer at very high or low speeds.
• The curve starts at (0, 0) because no molecules have zero energy, and it peaks at the most-probable energy/speed.
• Kinetic energy is proportional to the square of speed, so the distribution can also represent particle speeds.

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Effect of Temperature:

• As temperature increases, the average speed, most-probable speed, and maximum speed all increase, and the curve becomes broader and flatter.

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Collisions and Energy:

• Collisions between particles redistribute momentum and energy, creating a skewed bell-shaped curve while maintaining the gas’s total energy.

Question 18

Kinetic energy of a molecule

Answer 18

Kinetic Theory of Gases:

• Connects the microscopic properties of gas particles (e.g., mass and speed) to their macroscopic properties (e.g., pressure and volume).

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Key Equations:

1. 1/3N mc² = N k_bT where:
   
   • m = mass of one molecule.
   • c = speed of molecules.
   • k_b = Boltzmann constant.
   • T = temperature.
2. Pressure:
   pressure = 1/3ρc² where Nm/V = ρ
3. Rearranged for Energy:
   1/2mc² = 3/2k_bT

Question 19

Internal energy of an ideal gas

Answer 19

Internal Energy of an Ideal Gas:

• Entirely due to the kinetic energy of its particles.
• Electrostatic forces between particles are negligible except during collisions, meaning there is no electrostatic potential energy.

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Heating the Gas:

• When the container is heated, gas molecules move faster, increasing kinetic energy and internal energy.

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Change in Internal Energy (∆U):

• Equal to the total kinetic energy (E_k) of all the particles.

Question 20

Kinetic theory equation derivation

Answer 20

Force Exerted by a Molecule on the Wall:

• F = -2mv / t
  where:
  
  • m = mass of molecule.
  • v = velocity.
  • t = time between collisions.

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Time Between Collisions (t):

• t = 2L / v
  , where L = length of the container.

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Pressure (p):

• p = F/A,
  where A = area of the wall.
• Substituting F and t :
  p = mv² / V,
  where V = volume of the container V = L × A

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For N Molecules:

• p = (Nm × v²) / 3V where v² = mean square velocity.

Question 21

Absolute Zero

Answer 21

• The lowest possible temperature, defined as 0 K or -273°C.
• At absolute zero, molecules have zero kinetic energy, and no further energy can be removed from the system.