# Lecture 21: Heat, Specific Heat, and Phase Changes ## Physics I — Mechanics & Thermodynamics --- ## Learning Objectives By the end of this lecture, students will be able to: 1. Define heat as energy transfer and distinguish it from temperature 2. Apply the specific heat equation to calculate heat transfer during temperature changes 3. Solve calorimetry problems using conservation of energy 4. Describe phase changes and calculate the energy involved using latent heat 5. Explain the three mechanisms of heat transfer: conduction, convection, and radiation --- ## Lecture Content ### I. Heat as Energy Transfer **Heat** (Q) is energy transferred between objects due to a temperature difference. It is important to understand that heat is not a property of an object; rather, it is energy in transit. An object does not "contain" heat but instead possesses internal (thermal) energy. Heat flows spontaneously from higher temperature to lower temperature. The SI unit of heat is the Joule (J). Other commonly used units include the calorie (1 cal = 4.186 J), the kilocalorie (1 kcal = 1 food Calorie = 4186 J), and the British thermal unit (1 BTU = 1055 J). The sign convention is that Q > 0 when heat flows into the system and Q < 0 when heat flows out. ### II. Specific Heat and Heat Capacity **Specific heat** (c) is the amount of heat required to raise the temperature of 1 kg of a substance by 1 K (or equivalently 1 C): Q = mc Delta T, with c = Q / (m Delta T) in units of J/(kg K). **Heat capacity** (C) is the total heat needed to raise the temperature of an entire object by 1 K: Q = C Delta T, where C = mc. Specific heat values vary widely among materials. Water has an exceptionally high specific heat of 4186 J/(kg K), making it an excellent thermal buffer. Ice has c = 2090 J/(kg K) and steam c = 2010 J/(kg K). Common metals have lower values: aluminum at 900, iron/steel at 450, and copper at 387 J/(kg K). The average specific heat of the human body is approximately 3500 J/(kg K). Water's high specific heat is responsible for moderating coastal climates and helping stabilize body temperature. ### III. Calorimetry **Calorimetry** is the measurement of heat transfer using an insulated container called a calorimeter. The governing principle is that in an isolated system, the heat lost by hot objects equals the heat gained by cold objects: Q_lost + Q_gained = 0. For two objects reaching a common final temperature, m_1 c_1 (T_f - T_1i) + m_2 c_2 (T_f - T_2i) = 0, which can be solved for the equilibrium temperature: T_f = (m_1 c_1 T_1i + m_2 c_2 T_2i) / (m_1 c_1 + m_2 c_2). The strategy is to let each Q carry its own sign (since Delta T can be positive or negative) and set the total to zero. When phase changes are involved, the latent heat terms must be included as well. ### IV. Phase Changes and Latent Heat A **phase change** (or phase transition) occurs at a constant temperature while heat is added or removed. The principal transitions are melting (solid to liquid), vaporization (liquid to gas), and sublimation (solid to gas), along with their reverse processes: freezing, condensation, and deposition. **Latent heat** (L) is the heat per unit mass required for a phase change at constant temperature: Q = mL. The latent heat of fusion L_f applies to the solid-liquid transition, and the latent heat of vaporization L_v to the liquid-gas transition. For water, L_f = 3.34 x 10^5 J/kg (334 kJ/kg) at 0 C, and L_v = 2.26 x 10^6 J/kg (2260 kJ/kg) at 100 C. The fact that L_v is much greater than L_f reflects the much greater energy required to completely break intermolecular bonds in vaporization. During a phase change, the temperature remains constant even though heat is continuously being added. A temperature vs. heat added graph for water, starting from ice at -20 C and ending as steam above 100 C. Five segments are shown: (1) ice warming from -20 C to 0 C (slope = 1/(m c_ice)), (2) flat segment at 0 C for melting (Q = m L_f), (3) liquid water warming from 0 C to 100 C (slope = 1/(m c_water)), (4) flat segment at 100 C for boiling (Q = m L_v), (5) steam warming above 100 C. Each segment is labeled with the relevant equation and the phase present. The vaporization plateau is much wider than the fusion plateau, reflecting L_v >> L_f. ### V. Conduction **Conduction** is heat transfer through a material without bulk motion of the material itself, driven by molecular collisions and, in metals, by electron transport. **Fourier's law of heat conduction** gives the rate of heat flow: P = Q/t = kA (T_H - T_C) / L, where P is the power in Watts, k is the thermal conductivity of the material in W/(m K), A is the cross-sectional area, L is the thickness, and (T_H - T_C) is the temperature difference. Good thermal conductors include metals such as copper (k = 401 W/(m K)) and aluminum (k = 237). Good insulators include air (k = 0.024), wood, foam, and fiberglass. The **R-value** (thermal resistance) is defined as R = L/k, with higher R indicating better insulation. For multiple insulating layers in series, the total thermal resistance is R_total = R_1 + R_2 + ... ### VI. Convection **Convection** is heat transfer by bulk fluid motion. **Natural (free) convection** is driven by buoyancy: hot fluid rises because it is less dense, and cold fluid sinks. **Forced convection** is driven by external means such as a fan, pump, or wind. Convection is the primary heat transfer mechanism in fluids. Examples abound in everyday life: a radiator heats a room as warm air rises and creates circulation; blood circulation transfers heat from the body's core to the skin; oceanic and atmospheric currents redistribute heat across the planet; and fans cool electronic components. Newton's law of cooling provides an approximate description: dT/dt = -h A (T - T_env) / (mc), indicating that the rate of cooling is proportional to the temperature difference between the object and its environment. ### VII. Radiation **Radiation** is heat transfer via electromagnetic waves, requiring no medium. All objects emit thermal radiation at a rate that depends strongly on temperature. The **Stefan-Boltzmann law** gives the radiated power: P = epsilon sigma A T^4, where sigma = 5.67 x 10^-8 W/(m^2 K^4) is the Stefan-Boltzmann constant, epsilon is the emissivity (ranging from 0 to 1, with 1 for a perfect blackbody), and T is the absolute temperature in Kelvin. The net radiative heat transfer between an object and its surroundings is P_net = epsilon sigma A (T^4 - T_env^4). **Wien's displacement law** describes the peak wavelength of emitted radiation: lambda_max = 2.898 x 10^-3 / T (in meters, with T in Kelvin). Hotter objects emit at shorter peak wavelengths; the Sun's emission peaks in the visible range, while the human body emits primarily in the infrared. Applications of thermal radiation include thermal imaging, the greenhouse effect, pyrometry, and the analysis of body heat loss. Three panels illustrating the three modes of heat transfer. Panel A (Conduction): A metal rod with one end in a flame and the other end cool. Temperature decreases linearly along the rod. Arrows show heat flow from hot to cold end. The equation P = kA Delta T / L is written. Panel B (Convection): A pot of water on a stove with circular arrows showing convection currents — hot water rising in the center, cooler water sinking at the sides. Panel C (Radiation): The Sun emitting electromagnetic waves toward Earth through the vacuum of space. The Stefan-Boltzmann equation is written below.