Energy is the capacity to produce changes, do work, or transfer heat.

  • SI unit: joule (J)
  • Other common units: kilocalorie (kcal) and kilowatt-hour (kWh) $1\,\text{kcal} = 4184\,\text{J}, \text{kWh} = 3.6 \times 10^6\,\text{J}$

Laws of Thermodynamics

1. Zeroth Law: If two systems are each in thermal equilibrium with a third one, they are in equilibrium with each other. 2. First Law (Energy conservation): Energy cannot be created or destroyed, only transformed. 3. Second Law: In real processes, energy tends to spread out and become less available for useful work (entropy increases).

Energy Sources

  • Renewable: solar, wind, hydroelectric, geothermal, biomass.
  • Non-renewable: coal, oil, natural gas, nuclear fuels.

Thermal Energy and Heat Transfer

Thermal energy depends on particle motion and amount of matter. Heat flows from higher to lower temperature.

Three transfer mechanisms

  • Conduction: direct contact between particles.
  • Convection: transfer through fluid motion (liquids and gases).
  • Radiation: transfer by electromagnetic waves, no material medium required.

Everyday examples

  • A tile floor feels colder than a carpet because tile conducts heat away from your skin faster.
  • Air conditioners are usually high because cool air sinks.
  • Heaters are usually low because warm air rises.
  • Dark clothes absorb more solar radiation than light clothes.

Waves

Waves transfer energy, not matter.

  • Transverse waves: vibration is perpendicular to propagation (example: light).
  • Longitudinal waves: vibration is parallel to propagation (example: sound).

Main wave quantities

  • Amplitude $A$ (m)
  • Wavelength $\lambda$ (m)
  • Frequency $f$ (Hz)
  • Period $T$ (s)
  • Wave speed $v$ (m/s) $v = \frac{\lambda}{T}$

Mechanical Energy

Mechanical energy is the sum of kinetic and potential energies:

$$ E_m = E_k + E_g $$
$$ E_k = \frac{1}{2}mv^2, \qquad E_g = mgh $$

For a system without friction:

$$ E_{g1} + E_{k1} = E_{g2} + E_{k2} $$
Example 1 A $2\,\text{kg}$ ball is thrown downward from $20\,\text{m}$ with initial speed $10\,\text{m/s}$.

Using $g=9.8\,\text{m/s}^2$:

$mgh + \frac{1}{2}mv_0^2 = \frac{1}{2}mv^2$

$2\cdot 9.8\cdot 20 + \frac{1}{2}\cdot 2\cdot 10^2 = \frac{1}{2}\cdot 2\cdot v^2$

$392 + 100 = v^2 \Rightarrow v = \sqrt{492} \approx 22.18\,\text{m/s}$

Heat and Changes of State

Latent heat (phase change)

$$ E_q = mL $$
  • $E_q$: heat energy (J)
  • $m$: mass (kg)
  • $L$: latent heat constant (J/kg)

Specific heat (temperature change)

$$ E_q = mc\Delta T $$
  • $c$: specific heat capacity (J/kg K)
  • $\Delta T$: temperature change (K or degC)
Example 2 How much energy is needed to melt $2\,\text{kg}$ of ice at $0^\circ\text{C}$ and then heat the water to $80^\circ\text{C}$?

Given: $L_f=334000\,\text{J/kg}$ and $c=4184\,\text{J/(kg K)}$.

$E_q_{\text{melt}} = mL_f = 2\cdot 334000 = 668000\,\text{J}$

$E_q_{\text{heat}} = mc\Delta T = 2\cdot 4184\cdot (80-0) = 669440\,\text{J}$

$E_q_{\text{total}} = 668000 + 669440 = 1337440\,\text{J}$

Example 3 Find the final temperature when mixing $3\,\text{kg}$ of water at $10^\circ\text{C}$ with $10\,\text{kg}$ at $60^\circ\text{C}$.

Energy balance (no losses):

$m_1c(T_f-T_1) + m_2c(T_f-T_2)=0$

$3(T_f-10) + 10(T_f-60)=0$

$13T_f - 630 = 0 \Rightarrow T_f = \frac{630}{13} \approx 48.5^\circ\text{C}$