Thermodynamics Guide

Thermodynamics explores heat, energy, and their transformations, governing systems from engines to stars. This guide covers key principles, formulas, and applications with visualizations.

First Law (with Ideal Gas Law, Work)

The First Law states energy is conserved:

\[ \Delta U = Q - W \]

Where \( \Delta U \) is internal energy change, \( Q \) is heat added, \( W \) is work done by the system.

Related Formulas:

  • Ideal Gas Law: \( PV = nRT \)
  • Work: \( W = P \Delta V \)

Example: First Law

\( Q = 500 \, \text{J} \), \( W = 200 \, \text{J} \):

\[ \Delta U = 500 - 200 = 300 \, \text{J} \]

Example: Ideal Gas Law

1 mole, \( T = 300 \, \text{K} \), \( V = 0.0248 \, \text{m}^3 \):

\[ P \cdot 0.0248 = 1 \cdot 8.314 \cdot 300 \] \[ P \approx 100572.58 \, \text{Pa} \]

Example: Work

\( P = 100000 \, \text{Pa} \), \( \Delta V = 0.02 \, \text{m}^3 \):

\[ W = 100000 \cdot 0.02 = 2000 \, \text{J} \]

Heat Equation (with Efficiency, Entropy, Heat Transfer)

Heat transfer:

\[ Q = m c \Delta T \]

Related Formulas:

  • Efficiency: \( \eta = 1 - \frac{Q_C}{Q_H} \)
  • Entropy: \( \Delta S = \frac{Q}{T} \)
  • Conduction: \( Q = k A \frac{\Delta T}{\Delta x} t \)

Example: Heat Equation

1 kg water, \( \Delta T = 10 \, \text{°C} \), \( c = 4186 \, \text{J/kg°C} \):

\[ Q = 1 \cdot 4186 \cdot 10 = 41860 \, \text{J} \]

Example: Efficiency

\( Q_H = 1000 \, \text{J} \), \( Q_C = 600 \, \text{J} \):

\[ \eta = 1 - \frac{600}{1000} = 0.4 \, (40\%) \]

Example: Entropy

\( Q = 400 \, \text{J} \), \( T = 300 \, \text{K} \):

\[ \Delta S = \frac{400}{300} \approx 1.333 \, \text{J/K} \]

Visualizations

Efficiency of heat engines and entropy changes.

Applications

Engines

\( Q_H = 1500 \, \text{J} \), \( Q_C = 900 \, \text{J} \):

\[ W = 1500 - 900 = 600 \, \text{J} \]

Refrigeration

\( Q_C = 500 \, \text{J} \), \( W = 200 \, \text{J} \):

\[ Q_H = 500 + 200 = 700 \, \text{J} \]

Climate Systems

Heat transfer through wall (\( k = 0.8 \, \text{W/m°C} \)):

\[ Q = 0.8 \cdot 10 \cdot \frac{20}{0.1} \cdot 3600 = 5760000 \, \text{J} \]

Gas Expansion

\( W = 200000 \cdot 0.03 = 6000 \, \text{J} \).

Ice Melting

1 kg ice, \( \Delta S \approx 1223.44 \, \text{J/K} \).