Solids, Liquids, and Gases: A Comprehensive Study Guide

Fundamentals of Matter and Particle Theory

• All matter is composed of tiny particles that are in constant motion.

• The specific arrangement and movement of these particles determine the physical properties of a material, including its state at room temperature and its density.

• Substances exist in three main states: solid, liquid, and gas.

• While some substances are familiar in multiple states (e.g., water as ice, liquid, or steam), others are typically encountered in only one (e.g., iron as a solid, oxygen as a gas).

Processes of State Change

• Matter changes state through specific heating and cooling processes:

  • Melting: Solid to liquid (heating).

  • Evaporating/Boiling: Liquid to gas (heating).

  • Freezing: Liquid to solid (cooling).

  • Condensing: Gas to liquid (cooling).

Properties of the Different States of Matter

• Solids

  • Possess a definite, rigid shape and often exhibit high density.

  • Density is a measure of how tightly packed the particles are.

  • Particles are closely packed in a regular arrangement (crystal structure).

  • Strong forces exist between particles, providing definite shape and structural strength.

  • Particles do not move freely but vibrate about fixed positions.

  • Heating increases particle vibration, which manifests as an increase in kinetic energy and, consequently, temperature.

• Liquids

  • Lack a definite shape but, unlike gases, have particles that stick together.

  • They occupy the lowest part of a container.

  • Liquids have much greater densities than gases because particles remain very close together (similar to solids).

  • Particles are bound by strong forces and attract one another, but there is no fixed pattern.

  • Particles can move around more freely than in solids.

  • Heating increases the energy of particle movement.

• Gases

  • Particles are very spread out with large spaces between them.

  • Forces holding particles together are very small.

  • Characterized by very low densities and no definite shape.

  • Gases are easily compressed (squashed into smaller spaces).

  • Particles move randomly at all times.

  • Pressure is exerted on the walls of a container due to the forces caused by the random collisions of gas particles with those walls.

Summary Table of State Properties

• Property: Definite Shape

  • Solids: Yes

  • Liquids: No

  • Gases: No

• Property: Easily Compressed

  • Solids: No

  • Liquids: No

  • Gases: Yes

• Property: Relative Density

  • Solids: High

  • Liquids: High

  • Gases: Low

• Property: Can Flow (Fluid)

  • Solids: No

  • Liquids: Yes

  • Gases: Yes

• Property: Expands to Fill Available Space

  • Solids: No

  • Liquids: No

  • Gases: Yes

Specific Heat Capacity (s.h.c.)

• Supplying heat energy to matter increases the kinetic energy of its molecules, which is detected as a rise in temperature.

• Different substances require different amounts of energy for the same temperature increase.

• Definition: Specific heat capacity ($c$) is the amount of energy required to increase the temperature of $1\,kg$ of a substance by $1\,^\circ C$.

• Unit: $J/kg\,^\circ C$.

• The Heat Equation:

  • $\Delta Q = m \times c \times \Delta \theta$

  • $\Delta Q$ = change in thermal energy ($joules$)

  • $m$ = mass ($kilograms$)

  • $c$ = specific heat capacity ($J/kg\,^\circ C$)

  • $\Delta \theta$ = change in temperature ($^\circ C$)

• Key Symbols:

  • $\Delta$ (Greek letter delta): Represents a change in the following quantity.

  • $\theta$ (Greek letter theta): Represents temperature.

  • If a substance cools, $\Delta \theta$ and $\Delta Q$ are negative, indicating the removal of thermal energy.

Examples and Calculations for Specific Heat Capacity

• Example 1: Heating Water in a Kettle

  • Mass ($m$) = $300\,g = 0.3\,kg$

  • Specific heat capacity ($c$) of water = $4200\,J/kg\,^\circ C$

  • Temperature change ($\Delta \theta$) from $15\,^\circ C$ to boiling ($100\,^\circ C$) = $85\,^\circ C$

  • Calculation: $\Delta Q = 0.3\,kg \times 4200\,J/kg\,^\circ C \times 85\,^\circ C = 107,100\,J$

  • Note: In practice, more energy is needed as some is lost to the surroundings or heats the kettle itself.

• Example 2: Measuring s.h.c. of Aluminium

  • Cylinder mass ($m$) = $0.5\,kg$

  • Thermal energy supplied ($\Delta Q$) = $16,500\,J$

  • Temperature rise ($\Delta \theta$) from $20\,^\circ C$ to $50\,^\circ C$ = $30\,^\circ C$

  • Calculation: $c = \frac{\Delta Q}{m \times \Delta \theta} = \frac{16,500\,J}{0.5\,kg \times 30\,^\circ C} = 1100\,J/kg\,^\circ C$

  • Observation: This result is higher than the accepted value ($900\,J/kg\,^\circ C$) because some heat supplied is lost to the immersion heater and the surroundings.

• Example 3: Measuring s.h.c. of Water in an Electric Kettle

  • Mass ($m$) = $1\,kg$ ($1\,litre$)

  • Power ($P$) = $2.4\,kW = 2400\,W$

  • Time ($t$) = $2.5\,minutes = 150\,s$

  • Energy supplied: $\Delta Q = P \times t = 2400\,W \times 150\,s = 360,000\,J$

  • Temperature change from $20\,^\circ C$ to $100\,^\circ C$: $\Delta \theta = 80\,^\circ C$

  • Calculation: $c = \frac{360,000\,J}{1\,kg \times 80\,^\circ C} = 4500\,J/kg\,^\circ C$

Practical Investigation: Specific Heat Capacity

• Apparatus: Electric immersion heater, thermometer, insulation, low-voltage power supply, and an electronic balance.

• Procedure (Metal Block):

  1. Measure the mass ($m$) of the metal cylinder using a balance.

  2. Insert the heater and thermometer into pre-drilled holes in the cylinder.

  3. Measure the initial temperature.

  4. Record voltage ($V$), current ($I$), and time ($t$) to calculate energy: $\Delta Q = V \times I \times t$.

  5. Record final temperature and calculate $\Delta \theta$.

  6. Substitute values into $c = \frac{\Delta Q}{m \times \Delta \theta}$.

• Safety: The immersion heater and block become hot enough to burn skin. If used in water, do not immerse the top of the heater.

• Insulation: Used to minimize heat loss to the surroundings, which otherwise makes the calculated s.h.c. value higher than the true value.

Energy and Changes of State

• Supplying energy to a substance usually raises its temperature, but this is not true during a change of state.

• Boiling Water: When water reaches $100\,^\circ C$, the temperature remains constant during boiling. The energy supplied is used as "work" to separate water molecules rather than increasing temperature.

• Melting Naphthalene:

  • Naphthalene (used in mothballs) has a melting point of approximately $80\,^\circ C$.

  • It is flammable and must be heated indirectly in a water bath.

  • During melting, the temperature remains constant at $80\,^\circ C$ until all solid has turned to liquid.

• General Rule: During any change of state (melting, freezing, boiling, condensing), the temperature of the substance remains constant because thermal energy is used to overcome or form molecular bonds.

Boyle's Law and Compressibility of Gases

• Gases are compressible because their molecules are widely spread out. Squashing a gas into a smaller volume increases collision frequency with container walls.

• Robert Boyle (1627–1691): Discovered that air is "squashy" and springs back to its original volume.

• Boyle's Law Statement: For a fixed mass of gas at a constant temperature, the pressure ($p$) is inversely proportional to the volume ($V$).

  • $\text{pressure} \propto \frac{1}{\text{volume}}$

  • Equation: $P_1 V_1 = P_2 V_2$

• Pressure Units: One Pascal ($Pa$) is equal to $1\,N/m^2$.

• Example 4: Pressure Change via Volume Reduction

  • $P_1 = 100\,kPa$, $V_1 = 2\,m^3$, $V_2 = 0.2\,m^3$

  • $P_2 = \frac{100\,kPa \times 2\,m^3}{0.2\,m^3} = 1000\,kPa$

Absolute Zero and the Kelvin Scale

• Absolute Zero: The theoretical temperature at which gas pressure would be zero because particles have no thermal or kinetic energy. This occurs at $-273\,^\circ C$.

• Kelvin Scale: A temperature scale starting from absolute zero ($0\,K$).

  • Converting Celsius to Kelvin: $T (K) = θ (^\circ C) + 273$

  • Converting Kelvin to Celsius: $θ (^\circ C) = T (K) - 273$

• Kelvin Proportionality: The Kelvin temperature of a gas is directly proportional to the average kinetic energy of its molecules.

• Pressure and Temperature Law: For a fixed mass of gas at constant volume, pressure is proportional to the Kelvin temperature.

  • Equation: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

  • Constraint: Temperature must be in Kelvin for this equation.

• Example 5: Kelvin Conversions

  • Water freezes ($0\,^\circ C$) at $273\,K$.

  • Room temperature ($20\,^\circ C$) is $293\,K$.

  • $400\,K$ is equivalent to $127\,^\circ C$.

Kinetic Theory Explanations for Gas Laws

• Constant Volume heating: When a gas in a fixed volume is heated, particles move faster (higher average kinetic energy). Collisions with the walls become more frequent and harder, resulting in increased pressure.

• Cooling: Particles move more slowly as kinetic energy decreases. At $0\,K$ (absolute zero), movement ceases entirely, and no pressure is exerted.

• Extension Note: Gas laws fail when a gas is cooled or compressed to the point it becomes a liquid (e.g., liquefying helium or hydrogen near $0\,K$).

Example 6: Pressure in a Heated Tin

• A sealed tin is heated from room temperature ($20\,^\circ C$) to $50\,^\circ C$.

• Initial Pressure ($P_1$) = $100\,kPa$

• Initial Temperature ($T_1$) = $20 + 273 = 293\,K$

• Final Temperature ($T_2$) = $50 + 273 = 323\,K$

• Calculation:

  • $P_2 = P_1 \times \frac{T_2}{T_1}$

  • $P_2 = 100\,kPa \times \frac{323\,K}{293\,K} = 110\,kPa$