Temperature & Heat Lecture

Temperature

Temperature is a measure of the average kinetic energy of a material.

  • Absolute Zero: The theoretical point where there is minimal kinetic energy. Due to quantum mechanics, electrons still move, but it's the lowest possible energy state.
  • Kelvin Scale: Absolute zero is 0 Kelvin, which corresponds to -273 degrees Celsius.
  • Celsius Scale: 0 degrees Celsius is the freezing point of water, equivalent to 273 Kelvin.
  • A change of 1 Kelvin is the same as a change of 1 Celsius.

Internal Energy

Internal energy is the sum of all kinetic energies in a material.

  • Example: A hot cup of coffee has a high temperature, but a large iceberg has higher internal energy due to its mass.
  • Doubling Kelvin Temperature: Twice the Kelvin temperature means twice the average kinetic energy. For example, doubling 273K results in 546K.

Heat

Heat is the flow of energy from a high-temperature object to a low-temperature object.

  • Energy Transfer: When objects of different temperatures are in contact, collisions between atoms cause energy to transfer from the hotter to the colder object.
  • Internal Energy vs. Heat: Objects possess internal energy, while heat refers to the flow of energy.
  • Heat Flow Condition: Heat only flows if there is a temperature difference. No temperature difference means no heat flow.
  • Equalization: Heat flows until the temperatures of the objects are equalized.

Heat Equation

The amount of heat (Q) required to change the temperature of a substance is given by:

Q = mc\Delta T
Where:

  • Q = Heat (in joules).
  • m = Mass of the substance.
  • c = Specific heat capacity.
  • \Delta T = Change in temperature.

Thermal Inertia

Thermal inertia is the resistance to change in temperature, equal to the product of mass and specific heat capacity (m \times c).

Specific Heat Capacity of Water

  • Water has a high specific heat capacity: 4 \frac{J}{g \cdot °C}.
  • 1 calorie (cal) is equal to 4 Joules, so the specific heat capacity of water is also 1 \frac{cal}{g \cdot °C}.
  • Food Calorie (Cal): 1 Cal = 1000 cal. It's the energy to change 1 kilogram of water by 1 degree Celsius.

Effects of Water's High Specific Heat Capacity

  • Weather Moderation: Islands near large bodies of water have moderate temperatures, while deserts experience extreme temperature variations.

Thermal Expansion

Most materials expand when heated.

  • Bridges: Expansion joints allow bridges to expand and contract with temperature changes without causing damage.
  • Power Lines: Overhead power lines sag more on hot days due to expansion. Engineers must consider the coldest expected weather to prevent snapping.
  • Bimetallic Strip: Two metals with different expansion rates are bonded together. As the temperature changes, the strip bends and can be used in thermostats.

Anomalous Expansion of Water

Water is an exception to thermal expansion; it expands as it nears its freezing point.

  • Ice Density: Ice is less dense than water because of the way water crystallizes.
  • Crystallization: Water molecules start to crystallize even above 0°C, reducing density.
  • Maximum Density: Water is most dense at 4°C, where 1 gram has a volume of 1 cubic centimeter.

Freezing of Ponds

  • Cooling Process: Water cools on the surface, becomes denser, and sinks until the entire pond reaches 4°C.
  • Ice Formation: Only after the entire pond is at 4°C can the surface freeze.
  • Density Difference: Ice is about 90% the density of water.
  • Crystallization Effects: Even at 4°C, some water molecules start to form crystals, and the water expands significantly when it freezes.

Types of Heat Transfer

Three types of heat transfer:

  • Conduction
  • Convection
  • Radiation

Conduction

Heat transfer through a material due to collisions between atoms or movement of electrons.

  • Mechanism: Atoms collide and transfer energy; electrons move and transfer energy more quickly.
  • Good Conductors: Materials with many free electrons (e.g., metals) are good conductors of heat and electricity because electrons can move quickly and transfer energy.
  • Insulators: Materials where electrons are stuck in shells are insulators because they cannot transfer energy quickly.
  • Example: Tile feels cooler than wood because it's a better conductor, drawing heat away from your foot.
  • Walking on Hot Coals: Ash is an insulator. Moving keeps heat transfer slow.

Convection

Heat transfer through the movement of a fluid (liquid or gas).

  • Mechanism: Hot air rises because it is less dense than cooler air.
  • Natural Convection: Hot air rises, leading to temperature gradients.
  • Forced Convection: Using a fan or pump to move the fluid, like a car radiator.
  • Ovens: Convection ovens use a fan to distribute hot air more evenly.
  • Insulation: Air is a poor conductor. Insulation traps air to prevent convection.

Radiation

Heat transfer through electromagnetic waves.

  • Mechanism: All objects with a temperature radiate light
  • Infrared Radiation: At lower temperatures, objects emit infrared light, which is invisible.
  • Frequency and Temperature: The average frequency of light is proportional to temperature. Higher temperature = Higher frequency.
  • Color and Temperature: As temperature increases, the emitted light progresses from red to orange to yellow to white.
  • Good Radiators: Good radiators are also good absorbers, while poor radiators tend to be shiny and reflective.
  • Asphalt vs. Concrete: Asphalt absorbs more sunlight and heats up faster during the day, while concrete reflects more sunlight.

Greenhouse Effect

Car Example

Visible light enters the car through the windows and is absorbed by the interior. The interior heats up and emits infrared radiation, which cannot escape through the glass, trapping heat inside the car.

Global Scale

Greenhouse gases trap infrared light on Earth, causing the planet to warm.

Newton's Law of Cooling

Law stating that the rate of cooling is proportional to the difference in temperature between an object and its surroundings.

  • Cooling Rate: Rate \propto \Delta T
    Adding Salt to Ice

Adding salt to ice lowers its freezing point, allowing it to cool below 0°C.

  • Ice Cream Churning: Salted ice can cool ice cream mix enough to solidify it.

Radiative Cooling

  • Mechanism: Hotter objects radiate more energy than colder objects.
  • Nighttime Effect: The Earth's surface radiates heat into the cold night sky, with little radiation returning.
  • Dew Formation: Grass cools to the dew point, causing water to condense.
  • Frost Formation: The air temperature is cold enough that water vapor turns directly into ice (frost).

Thermos Design

Thermoses use various methods to minimize heat transfer:

  • Old-Fashioned Thermos: Silver-lined, double-walled glass with a vacuum to minimize radiation, conduction, and convection.
  • Plastic Thermoses: Double-walled with white plastic to minimize conduction and convection (but may not be a vacuum).
  • Modern Thermos (Yeti): Steel with a vacuum between the walls to minimize all three types of heat transfer. Two walls with a vacuum in between.