B.1: Thermal Energy Transfers

Flashcards covering molecular theory, internal energy, specific heat, latent heat, mechanisms of heat transfer (conduction, convection, radiation), plate tectonics, black-body radiation, Wien's displacement law, the Stefan-Boltzmann law, and apparent brightness.

How does molecular motion differ between solids and liquids according to molecular theory?

In a solid, molecules can only vibrate and cannot translate, whereas in a liquid, molecules can both vibrate and move about freely within a fixed volume.

What occurs to intermolecular bonds when matter transitions from solid to liquid and from liquid to gas?

In going from a solid to a liquid, some intermolecular bonds are broken; in going from a liquid to a gas, most intermolecular bonds are broken.

What are the scientific terms for the phase changes from solid directly to gas, and from gas directly to solid?

The transition from solid directly to gas is called sublimation (e.g., frost evaporation), and the transition from gas directly to solid is called deposition (e.g., frost).

What components make up the total internal energy ($E_{\text{INT}}$) of a substance?

Internal energy is the sum of the total random kinetic energy ($E_K$) arising from molecular vibration and translation, and the total intermolecular potential energy ($E_P$) arising from forces between molecules: $E_{\text{INT}} = E_K + E_P$.

In thermal physics, what aspect of internal energy does temperature reveal, and what does thermal expansion reveal?

Temperature reveals the internal kinetic energy, while thermal expansion reveals the internal potential energy.

How is density defined and calculated?

Density is mass per unit volume, given by the formula $\rho = \frac{m}{V}$.

What is absolute zero, and at what Celsius temperature does it occur based on the pressure-temperature extrapolation of gases?

Absolute zero is the lowest temperature that can exist, corresponding to the temperature at which the pressure of any gas extrapolates to zero, which is $-273.15^\circ\text{C}$ (or $-273^\circ\text{C}$, equal to $0\,\text{K}$).

What is the formula relating the Kelvin and Celsius temperature scales?

$T(\text{K}) = T(^\circ\text{C}) + 273$.

What formula relates the average kinetic energy ($E_K$) of a particle to its absolute temperature?

$E_K = \frac{3}{2} k_B T$, where $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23}\,\text{J K}^{-1}$) and $T$ is in Kelvin.

What is the definition of one kilocalorie, and what is its mechanical equivalent in joules?

One kilocalorie is the amount of heat needed to raise the temperature of one kilogram of water by exactly $1\,^\circ\text{C}$, and its mechanical equivalent is $1\,\text{kcal} = 4.186\,\text{kJ}$.

What historical apparatus is depicted, and what physical equivalence did it demonstrate?

It shows James Joule's paddle-wheel experiment, which demonstrated the mechanical equivalent of heat by converting mechanical work into thermal energy in water ($1\,\text{kcal} = 4.186\,\text{kJ}$).

How is specific heat capacity ($c$) defined, and what is its formula?

Specific heat capacity is the amount of heat energy needed per unit temperature increase per unit mass, defined by $Q = mc\Delta T$, with units of $\text{J kg}^{-1}{^\circ\text{C}}^{-1}$.

Why does temperature remain constant during a phase change despite the continuous addition of thermal energy?

Temperature measures internal kinetic energy, and during a phase change, added heat is stored exclusively as potential energy to break intermolecular bonds rather than increasing kinetic energy.

What formula calculates the thermal energy transferred during a phase change, and what are its components?

$Q = mL$, where $m$ is mass and $L$ is the specific latent heat ($L_f$ for fusion and $L_v$ for vaporization), measured in $\text{J kg}^{-1}$.

What are the primary differences between boiling and evaporation?

Boiling occurs throughout the entire liquid at a fixed temperature called the boiling point, whereas evaporation occurs only at the surface of a liquid and can happen at any temperature.

What are the three primary mechanisms of thermal energy transfer, and which mechanism does not require a physical medium?

The three mechanisms are conduction, convection, and thermal radiation; only thermal radiation transfers heat through empty space without needing a physical medium.

What equation gives the rate of thermal energy transfer by conduction through a material?

$\frac{\Delta Q}{\Delta t} = kA \frac{\Delta T}{\Delta x}$, where $k$ is thermal conductivity ($\text{J s}^{-1}\text{ m}^{-1}\text{ K}^{-1}$), $A$ is surface area, $\Delta T$ is temperature difference, and $\Delta x$ is thickness.

How does convection transfer thermal energy within a fluid?

When a fluid is heated, it expands, becomes less dense, and rises; as it rises, it cools, becomes denser, and sinks, forming a continuous cycle called a convection current.

How do convection currents in Earth's mantle drive spreading centers and subduction zones in plate tectonics?

Mantle convection pushes tectonic plates apart at spreading centers where magma wells up to form oceanic ridges and new crust, and pulls plates together at subduction zones where one plate is driven under another to form ocean trenches, mountains, and volcanoes.

What is a black body in thermal physics?

An idealized object that absorbs all incident electromagnetic radiation falling on it, with an emission spectrum and intensity that depend strictly on its thermodynamic temperature.

What is Wien's displacement law, and what is its equation?

Wien's displacement law states that the peak wavelength of black-body emission ($\lambda_{\text{max}}$) is inversely proportional to absolute temperature: $\lambda_{\text{max}} T = 2.90 \times 10^{-3}\,\text{m K}$.

Body Y is at a higher temperature than body X. Which graph correctly illustrates their black-body emission spectra?

Graph B, because a higher temperature increases emission intensity at all wavelengths (placing curve Y above curve X) and shifts the peak intensity to a shorter wavelength (to the left).

What is the Stefan-Boltzmann law for a black body, and what do its variables represent?

$L = \sigma A T^4$, where $L$ is luminosity (power), $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8}\,\text{W m}^{-2}\text{ K}^{-4}$), $A$ is surface area, and $T$ is absolute temperature in Kelvin.

What formula defines the apparent brightness ($b$) of a radiating body at a distance $d$?

$b = \frac{L}{4\pi d^2}$, representing the radiated energy received per unit time per unit area.

What is the solar constant, and what is its value at Earth's distance from the Sun?

The solar constant is the rate at which solar energy reaches the top of Earth's atmosphere per unit area, equal to $I = \frac{P}{4\pi r^2} = 1380\,\text{W m}^{-2}$.