📋 Table of Contents
📜 Historical Background
The development of thermodynamics in the 19th century revolutionized our understanding of heat and energy:
- Count Rumford (1798): Observed that mechanical work could produce heat during cannon boring
- James Joule (1840s): Precisely measured the mechanical equivalent of heat
- Rudolf Clausius (1850): Formulated the first law of thermodynamics
- William Thomson (Lord Kelvin): Developed the absolute temperature scale
These developments established heat as a form of energy and led to the principle of energy conservation.
Introduction to Heat and First Law of Thermodynamics
🔬 What is Thermodynamics?
Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. The first law of thermodynamics is essentially a statement of the conservation of energy principle applied to thermal systems.
When objects at different temperatures are placed in thermal contact, energy flows from the hotter to the colder object until thermal equilibrium is reached. This energy flow is what we call heat.
📝 Chapter Overview
In this chapter, we explore:
- The nature of heat and how it differs from temperature and internal energy
- Various heat capacities and how they relate to material properties
- Energy changes during phase transitions (latent heat)
- The concept of internal energy as a state function
- The relationship between heat capacities at constant pressure and volume
- The first law of thermodynamics and its applications to various processes
- Different mechanisms of heat transfer
Fundamental Concepts
25.1 Heat
Heat is energy that flows between a system and its environment due to a temperature difference between them. Heat is measured in joules (J) or calories (cal).
Heat and Temperature
Temperature is a measure of molecular motion.
Heat is energy in the process of being transferred between objects by random molecular collisions.
Internal energy is an object's energy of random molecular motion and molecular interaction.
Calorie and Mechanical Equivalent
25.2 Calorie
A calorie is defined as the amount of heat required to raise the temperature of 1 g of water from 14.5°C to 15.5°C.
25.3 Mechanical Equivalent of Heat
The mechanical equivalent of heat is defined as "The mechanical work required to produce unit quantity of heat."
Where J is the mechanical equivalent of heat, with value:
This means 4.2 J of work produces 1 calorie of heat, and 4200 J of work produces 1 kilocalorie of heat.
Heat Capacity and Specific Heat
25.4 Heat Capacity
Heat capacity is the amount of heat required to raise the temperature of a substance by 1°C.
Its SI unit is J/°C or J/K.
25.5 Specific Heat Capacity
Specific heat capacity is the amount of heat required to raise the temperature of 1 kg of a substance by 1°C.
Its SI unit is J/kg·°C or J/kg·K.
25.6 Molar Heat Capacity
Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by 1°C.
Where n is the number of moles.
Heat of Transformation and Internal Energy
25.7 Heat of Transformation
The amount of heat per unit mass transferred during a phase change is called heat of transformation or latent heat, denoted by L.
Where m is the mass of the sample.
Latent Heat of Fusion: The latent heat during melting or freezing.
Latent Heat of Vaporization: The latent heat during boiling or condensing.
The alcohol evaporates, absorbing energy from the skin to lower the skin temperature.
25.8 Internal Energy
Internal energy is the energy associated with the random, disordered motion of molecules. It includes kinetic energy of molecular motion and potential energy of molecular interactions.
Internal energy is a state function - it depends only on the state of the system, not on how it reached that state.
Relation between Cp and Cv
🧮 Derivation of Cp - Cv = R
Step 1: Definitions
Step 2: First Law of Thermodynamics
Step 3: At Constant Volume
Step 4: At Constant Pressure
Step 5: For Ideal Gas
Step 6: For One Mole
Special Cases for Different Gases
📊 Heat Capacities for Different Gases
| Gas Type | Degrees of Freedom | Cv | Cp | γ = Cp/Cv |
|---|---|---|---|---|
| Monatomic | 3 | 3/2 R | 5/2 R | 5/3 ≈ 1.67 |
| Diatomic | 5 | 5/2 R | 7/2 R | 7/5 = 1.4 |
| Polyatomic | 6 | 3 R | 4 R | 4/3 ≈ 1.33 |
First Law of Thermodynamics
25.10 First Law of Thermodynamics
The first law of thermodynamics is a statement of energy conservation:
Where:
- ΔU = Change in internal energy of the system
- Q = Heat added to the system
- W = Work done by the system
Sign conventions:
- Q is positive when heat is added to the system
- W is positive when work is done by the system
Sample Problems
A system undergoes a process in which 200 J of heat is added to it and it does 100 J of work. What is the change in its internal energy?
A gas expands from 1.0 L to 3.0 L at constant pressure of 2.0 atm. Calculate the work done by the gas.
Applications of First Law
Adiabatic Process
25.11 Adiabatic Process
An adiabatic process is one in which no heat enters or leaves the system (Q = 0).
For an ideal gas undergoing adiabatic process:
Where γ = Cp/Cv is the adiabatic index.
Isothermal Process
25.12 Isothermal Process
An isothermal process is one in which the temperature remains constant (ΔT = 0).
For an ideal gas, internal energy depends only on temperature, so ΔU = 0.
For an ideal gas undergoing isothermal expansion/compression:
Constant Volume Process
25.13 Constant Volume Process
A constant volume process is one in which the volume remains constant (ΔV = 0).
Since no volume change occurs, no work is done (W = 0).
All heat added goes into increasing the internal energy.
Cyclic Process
25.14 Cyclic Process
A cyclic process is one in which the system returns to its initial state.
Since internal energy is a state function, ΔU = 0 for a complete cycle.
The net heat added equals the net work done.
Free Expansion
25.15 Free Expansion
Free expansion is an irreversible process in which a gas expands into a vacuum.
No work is done (W = 0) and no heat is transferred (Q = 0).
For an ideal gas, temperature remains constant during free expansion.
📊 Summary of Thermodynamic Processes
| Process | Condition | First Law | Special Features |
|---|---|---|---|
| Adiabatic | Q = 0 | ΔU = -W | PVγ = constant |
| Isothermal | T = constant | Q = W | ΔU = 0 |
| Constant Volume | V = constant | ΔU = Q | W = 0 |
| Cyclic | Returns to initial state | Qnet = Wnet | ΔU = 0 |
| Free Expansion | Into vacuum | ΔU = 0 | Q = 0, W = 0 |
Heat Transfer Mechanisms
25.16 Heat Transfer
Heat can be transferred by three mechanisms:
- Conduction
- Convection
- Radiation
Conduction
25.17 Conduction
Conduction is the transfer of heat through a material without bulk motion of the material.
The rate of heat conduction is given by:
Where:
- k = Thermal conductivity
- A = Cross-sectional area
- Th - Tc = Temperature difference
- L = Length
Convection
25.18 Convection
Convection is the transfer of heat by the bulk motion of a fluid.
Natural convection occurs due to density differences caused by temperature variations.
Forced convection occurs when the fluid is moved by external means (fans, pumps).
Radiation
25.19 Radiation
Radiation is the transfer of heat by electromagnetic waves, requiring no medium.
The rate at which an object emits radiant energy is given by Stefan's law:
Where:
- σ = Stefan-Boltzmann constant (5.67 × 10-8 W/m²·K4)
- ε = Emissivity (0 ≤ ε ≤ 1)
- A = Surface area
- T = Absolute temperature
Frequently Asked Questions
Heat and temperature are related but distinct concepts:
- Temperature is a measure of the average kinetic energy of molecules in a substance. It determines the direction of heat flow.
- Heat is the energy transferred between objects due to a temperature difference. It's the process of energy transfer, not a property of the object itself.
For example, a spark from a fire has a very high temperature but contains little heat, while the ocean has a relatively low temperature but contains enormous amounts of heat energy.
Cp is always greater than Cv because:
- At constant volume, all heat added goes into increasing the internal energy (temperature)
- At constant pressure, some of the heat added goes into doing work (expansion) against the external pressure
- Therefore, more heat is required at constant pressure to achieve the same temperature increase
For an ideal gas, the difference is exactly R (the gas constant) per mole: Cp - Cv = R
The first law of thermodynamics has profound implications:
- Energy Conservation: It establishes that energy cannot be created or destroyed, only converted from one form to another
- Perpetual Motion Machines: It proves that perpetual motion machines of the first kind (machines that create energy) are impossible
- State Functions: It introduces the concept of internal energy as a state function, depending only on the current state of the system
- Process Analysis: It provides a framework for analyzing energy transfers in thermodynamic processes
📚 Master Thermodynamics
Understanding heat and the first law of thermodynamics is fundamental to physics, engineering, and many areas of science. Continue your journey into the fascinating world of energy transformations and thermal systems.
Read More: Physics HRK Notes of Thermodynamics© House of Physics | HRK Physics Chapter 25: Heat and First Law of Thermodynamics
Based on Halliday, Resnick, and Krane's "Physics" with additional insights from university physics curriculum
House of Physics | Contact: aliphy2008@gmail.com
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