Introduction to Thermodynamics: Dimensions and Units

Chapter 1: Introduction to Thermodynamics

• Thermodynamics studies the relationships between heat, work, and energy.
• It deals with macroscopic properties without requiring knowledge of microscopic structure.
• It's based on fundamental laws applicable to all physical systems.
• Chemical engineering thermodynamics applies thermodynamic principles to chemical processes.
• It aids in designing and analyzing chemical reactors and separation processes.

Dimensions and Units

Dimensions

• Dimensions are fundamental physical quantities describing physical phenomena.
• Primary dimensions include mass (M), length (L), time (t), and temperature (T).

Units

• Units are standards for measuring dimensions.
• Common systems include SI (Système International d'Unités) and English Engineering Units.

SI Units

• Mass is measured in Kilograms (kg).
• Length is measured in Meters (m).
• Time is measured in Seconds (s).
• Temperature is measured in Kelvin (K).
• Amount of substance is measured in Moles (mol).

English Engineering Units

• Mass is measured in Pound-mass (lbm).
• Length is measured in Feet (ft).
• Time is measured in Seconds (s).
• Temperature is measured in Rankine (°R).
• Amount of substance is measured in Pound-mole (lbmol).

Force

• Force is the product of mass and acceleration, according to Newton's second law: $F = ma$.

SI Units

• Force is measured in Newtons (N): $1 N = 1 kg \cdot m/s^2$.

English Engineering Units

• Force is measured in Pound-force (lbf): $1 lbf = 32.174 lbm \cdot ft/s^2$.

Temperature

• Temperature measures the average kinetic energy of molecules in a system.
• Temperature scales include Celsius (°C), Fahrenheit (°F), Kelvin (K), and Rankine (°R).

Conversion

• $T(K) = T(°C) + 273.15$
• $T(°R) = T(°F) + 459.67$
• $T(°F) = 1.8T(°C) + 32$

Pressure

• Pressure is force per unit area: $P = F/A$.

SI Units

• Pressure is measured in Pascals (Pa): $1 Pa = 1 N/m^2$.

English Engineering Units

• Pressure is measured in Pound-force per square inch (psi): $1 psi = 1 lbf/in^2$

Conversion

• $1 atm = 101325 Pa = 14.696 psi$

Volume

• Volume is the amount of space occupied by a substance.

SI Units

• Measured in cubic meters ($m^3$).

English Engineering Units

• Measured in cubic feet ($ft^3$).

Specific Volume

• Specific volume is volume per unit mass or mole.
• $\hat{V} = V/m$ (volume per mass).
• $\bar{V} = V/n$ (volume per mole).

Density

• Density is mass per unit volume: $\rho = m/V$.

Flow Rate

• Mass flow rate is the mass of fluid passing a point per unit time: $\dot{m} = \rho \dot{V}$.

Concentration

• Molarity (M) is moles of solute per liter of solution.
• Molality (m) is moles of solute per kilogram of solvent.
• Mole fraction ($x_i$) is moles of a component per total moles in a mixture: $x_i = n_i / n_{total}$

Introduction to Energy

• Energy is the capacity to do work.
• Forms of energy include kinetic, potential, internal, chemical, and thermal.

Work

• Work is done when a force causes displacement: $W = F \cdot d$.

Heat

• Heat is the transfer of energy due to a temperature difference.

Example Conversions

• Conversion of 20 lbm to kilograms: $20 lbm * 0.453593 kg/lbm = 9.07 kg$.
• Conversion of 10 $ft^3$ to $m^3$: $10 ft^3 * (0.3048 m/ft)^3 = 0.283 m^3$.

Analisi Matematica 1 - Ing. Edile-Architettura

• 12 Febbraio 2024 - Compito A
• Contains Examination questions

List of Topics

• Limits
• Function Analysis
• Integrals
• Series
• Cauchy Problems