Temperature and Kinetic Energy

Temperature Basics

• Temperature, often abbreviated as T, is difficult to define simply.
• Macroscopically, temperature indicates the direction of thermal energy transfer, which always moves from hotter to cooler objects.
• Temperature is independent of an object's size, until atomic/molecular levels are reached.
• The temperature of boiling water remains at 100°C at sea level, regardless of the amount.
• Thermal energy depends on the system's size and the material's composition, where different amounts of substances can have different thermal energies, even at the same temperature.

Kinetic Energy and Temperature

• Temperature relates to the average kinetic energy of particles: higher speed means higher temperature
• The relationship between the average kinetic energy of a simple monoatomic gas and temperature is given by KE = 1/2 m v(bar)^2 = 3/2 kT, where:
  • v(bar) is the average velocity
  • m is the mass
  • k is the Boltzmann constant
  • T is the temperature
• A single atom or molecule possesses kinetic energy, but not temperature.
• Temperature is a characteristic of a system, not its individual components.
• Individual molecules' kinetic energies fluctuate due to collisions, even when the system's temperature is constant.
• Individual kinetic energies are critical in chemical reactions.

Populations of Molecules

• Numerous collisions within a population of atoms/molecules cause a range of speeds and directions.
• Large numbers of particles in phenomena are treated as a population.
• A population is characterized by the distribution of the number or probability of molecules moving with various velocities.
• Statistical methods are used to characterize the population's behavior.
• The distribution of kinetic energies of atoms or molecules depends on the system temperature
• The Maxwell-Boltzmann distribution describes the probability of a molecule moving at a particular speed.
• As temperature increases, more particles move at higher speeds with more kinetic energy, which flattens and broadens the distribution curve.
• The most probable and average speeds increase with temperature.

Temperature, Kinetic Energy, and Gases

• The average kinetic energies of molecules are equal for any gas at the same temperature, regardless of the gas's identity (KE = 3/2kT).
• Molecules in a gas typically interact minimally, colliding like billiard balls.
• With two gases at the same temperature, molecules have the same average kinetic energy.
• At the same temperature, lighter molecules move faster than heavier molecules.
• The average speed of an atom or molecule depends on its mass, with heavier particles moving more slowly on average.
• Gas molecules move rapidly such as at 0 °C, the average H2 molecule moves at about 2000 m/s, whereas the average O2 molecule moves at approximately 500 m/s.
• Gas molecules' speed explains why smells travel quickly and why substances must be a gas to be smelled.

Vibrating, Bending, and Rotating Molecules

• At 0 K, a system has zero point energy due to the uncertainty principle.
• Complex molecules with multiple atoms store energy through vibration, bending, and rotation, in addition to translation.
• Vibrations, bends, and rotations are molecule-specific and quantized, depending on molecular shape and composition.
• Molecules can be identified by how they absorb or emit photons during transitions between vibrational or rotational states, which is the basis for infrared spectroscopy.
• More complex molecules require more energy to increase temperature due to the energy used in vibrations and rotations, as well as translations.

Heat Capacity and Molecular Structure

• The units of thermal energy are joules (J).
• Thermal energy is the sum of the kinetic and other potential energies of the particles in a system.
• Specific heat capacity (J/gºC) measures energy to raise the temperature of 1 g of material by 1 ºC.
• Molar heat capacity (J/molºC) measures energy to raise the temperature of one mole of particles by 1 ºC.
• More complex substances usually have a higher molar heat capacity due to more vibration, bending, and rotation possibilities.
• Substances with strong IMFs have higher heat capacities because energy is used to overcome molecular interactions to increase temperature.
• Water has a high specific heat due to its small size, resulting in more molecules per gram, and its ability to form up to four hydrogen bonds per molecule.
• Earth's oceans moderate temperature fluctuations due to water's high specific heat, with water absorbing solar energy during the day and releasing it at night.

Removing Thermal Energy from a Gas

• Cooling a gas involves transferring energy from gas molecules to the container walls, decreasing the average kinetic energy (temperature).
• As temperature decreases, molecular interactions like London dispersion forces, hydrogen bonds, and dipole-dipole interactions become more persistent.
• Molecules condense out of the gaseous phase to form a liquid, with the temperature where the liquid phase appears being the boiling (or condensation) point.
• Even below the boiling point, some molecules remain in the gaseous phase due to sufficient kinetic energy to overcome liquid interactions.
• Evaporative cooling occurs because molecules escaping the liquid phase lower the average kinetic energy of the liquid.

Liquids to Solids and Back Again

• Liquids flow because molecules move with respect to one another, breaking some interactions linking them to neighbors.
• As energy is removed, the frequency of molecules breaking interactions decreases, stabilizing interactions and forming a solid.
• The temperature at which a material goes from solid to liquid is its melting point, while the temperature at which a liquid turns solid is its freezing point.
• Molecular shape and interaction geometry determine the behavior of water (or any liquid) when cooled and frozen.
• In Ice Ih, water molecules arrange hexagonally, linked by hydrogen bonds, and are less dense than liquid water making ice float on water.
• Adding energy to ice causes molecules to vibrate more vigorously, eventually overcoming hydrogen bonds and melting the ice at 0 ºC until all ice is melted.

Open versus Closed Systems

• A system is the part of the universe being observed, separated from its surroundings by a boundary.
• In an isolated system neither energy nor matter moves between the system and the surroundings.
• In an open system both matter and energy can enter or leave, whereas in a closed system only energy can enter or leave.
• Biological systems are open systems, exchanging both energy and matter with the surroundings.
• In an open system of water, increasing temperature allows water molecules and dissolved gases to escape into the gaseous phase.
• At the boiling point, all energy supplied overcomes intermolecular forces, transforming the liquid to vapor without rising temperature until all liquid has vaporized.