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:

For a system without friction:

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)

• \(E_q\): heat energy (J)
• \(m\): mass (kg)
• \(L\): latent heat constant (J/kg)

Specific heat (temperature change)

• \(c\): 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):
\(m_1c(T_f-T_1) + m_2c(T_f-T_2)=0\)
\(3(T_f-10) + 10(T_f-60)=0\)
\(13T_f - 630 = 0 \Rightarrow T_f = \frac{630}{13} \approx 48.5^\circ\text{C}\)