Thermal

Question 1

Phases of matter

Answer 1

• Solid
  
  • Particles in solids are closely packed in a fixed lattice structure and held by strong intermolecular forces.
  • Particles can only vibrate about fixed positions and have low energy compared to liquids and gases.
  • Solids have high density and are incompressible.
• Liquid
  
  • Particles in liquids 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.
• Gas
  
  • Particles in gases have negligible intermolecular forces, are randomly arranged, and are far apart compared to solids and liquids.
  • Particles move freely in all directions at various speeds and have higher energy than those in 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

• Brownian motion is the random movement of small particles suspended in a liquid or gas, caused by collisions with faster-moving atoms or molecules.
• This phenomenon 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

• During phase changes, energy increases or decreases electrostatic potential energy instead of kinetic energy, so temperature remains constant.
• In melting or boiling, energy breaks intermolecular bonds, increasing electrostatic potential energy and moving molecules further apart.
• In freezing or condensation, energy forms bonds, decreasing electrostatic potential energy and moving molecules closer together.
• 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
• Stronger intermolecular forces mean higher potential energy

Question 6

Thermal equilibrium

Answer 6

• Heat flows (thermal energy) from a hotter object to a colder one until both objects reach the same temperature, known as thermal equilibrium.
• Thermal equilibrium occurs when two substances in contact no longer exchange heat energy and both reach the same temperature.
• The final temperature in thermal equilibrium depends on the initial temperature difference between the two objects. An example is ice cubes melting in room temperature water.
• Energy lost by hotter object = Energy gained by colder object
• (Ice)
  Energy gained = ml + mc (T-T1)
  Equal to
• Hot drink
  Energy lost = mc (T2-T)

Question 7

Specific Latent Heat

Answer 7

• Specific Latent Heat of Fusion:
  
  • Energy required to convert 1 kg of solid (unit mass) to liquid with no temperature change.
• Specific Latent Heat of Vaporisation:
  
  • Energy required to convert 1 kg of liquid to gas with no temperature change.
• Evaporating 1 kg of water requires seven times more energy than melting 1 kg of ice.
• Ice melting increases molecular separation, while 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 the temperature increases, the graph is further from the origin and vice versa
- area under graph is energy
-Pressure Law
- p ∝ T
-Charle’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.
• Avogadro’s Constant (N_a): The number of atoms in 12 g of carbon-12.
• Equation:
  Number of particles (N)= n * N_a
  Where:
  • n: Number of moles
  • N_a: Avogadro’s constant

Question 11

Molar mass

Answer 11

• Molar Mass: The mass of one mole of a substance, measured in grams per mole (g mol⁻¹).
• Equation:
  n = m * M⁻¹
  Where:
  • n: Number of moles
  • m: Mass of the substance (g)
  • M: Molar mass (g mol⁻¹)

Question 12

molar gas constant

Answer 12

• pVT^-1= constant depends on the amount of gas used, which can be measured in moles (n)
• This constant is known as the molar gas constant (R).
• constant=nR
• relates the energy to temperature in thermal physics, when a mole of particles at the state temperature is considered

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 an ideal gas assumptions

Answer 14

• R | RANDOM:
  Large number of Gas particles move randomly and in straight lines until they collide with each other or the container walls.
• A | ATTRACTION:
  No intermolecular forces between particles except during collisions.
• V | VOLUME:
  Negligible volume of particles compared to the volume of the gas.
• E | ELASTIC:
  Elastic collisions: collisions between particles and with container walls are perfectly elastic.
• D | DURATION:
  Negligible time spent on each collision compared to time between collisions.

Question 15

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

Answer 15

• 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).
• 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 on the particle (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.
• Although each particle exerts a tiny force, with billions of particles in the container, the combined force is much larger, leading to a steady, uniform pressure on the walls.
• Pressure is the result of many collisions between particles and the container walls, leading to the equation for pressure in an ideal gas.
• (Rate of momentum ÷ area) * number of particles

Question 16

Root Mean Square

Answer 16

• Gas particles move in random directions, resulting in a net velocity of zero; squaring the velocities ensures all values are positive, avoiding cancellation.
• The root-mean-square speed (rms), calculated as c_rms =√mean², provides the average speed of particles by taking the square root of the mean square speed.

Question 17

Maxwell-Boltzmann distribution

Answer 17

• The Maxwell-Boltzmann distribution shows the range of kinetic energies of gas particles, with most particles moving at moderate speeds, 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.
• As temperature increases, the average speed, most-probable speed, and maximum speed all increase, and the curve becomes broader and flatter.
• 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, such as mass and speed, to their macroscopic properties like pressure and volume.
• 1/3N mc² = N k_bT
  m is mass of 1 molecule
  pressure=1/3(density)c² as Nm/V = density
• which can rearrange to give energy

Question 19

Internal energy of an ideal gas

Answer 19

• Internal energy of an ideal gas is entirely due to the kinetic energy of its particles.
• Electrostatic forces between particles in an ideal gas are negligible except during collisions, meaning there is no electrostatic potential energy.
• When the container is heated, gas molecules move faster, resulting in higher kinetic energy and increased internal energy.
• Change in internal energy ∆U is equal to the total kinetic energy E_k of all the particles.

Question 20

Kinetic theory equation derivation

Answer 20

• F = -2mv / t
• t = distance (2L) ÷ velocity
• p = F / Volume