- stems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law establishes the concept of temperature.
b. First Law of Thermodynamics (Law of Energy Conservation)
- Energy cannot be created or destroyed, only transformed from one form to another.
- For a closed system, the change in internal energy (( \Delta U )) is equal to the heat added to the system (( Q )) minus the work done by the system (( W )):
[
\Delta U = Q – W
]
c. Second Law of Thermodynamics
- Heat naturally flows from hotter objects to cooler ones, and it is impossible to convert all heat energy into work without some waste heat.
- Entropy: A measure of the disorder of a system; in any energy transfer, the total entropy of the universe increases.
d. Third Law of Thermodynamics
- As the temperature of a system approaches absolute zero (0 K), the entropy of a perfect crystal approaches zero.
5. Methods of Heat Transfer
Heat can be transferred through three primary mechanisms:
a. Conduction
- Definition: The transfer of heat through a solid material without any motion of the material itself. It occurs due to collisions between particles.
- Fourier’s Law of Heat Conduction: The rate of heat transfer through a material is proportional to the temperature gradient and the area through which heat is conducted:
[
Q = -kA \frac{dT}{dx}
]
Where: - ( Q ) = heat transfer (J),
- ( k ) = thermal conductivity (W/m·K),
- ( A ) = area (m²),
- ( \frac{dT}{dx} ) = temperature gradient (K/m).
- Example: Touching a hot metal rod and feeling the heat transfer to your hand.
b. Convection
- Definition: The transfer of heat through the movement of fluids (liquids and gases). This occurs when warmer, less dense fluid rises, and cooler, denser fluid sinks.
- Natural Convection: Caused by buoyancy differences due to temperature gradients (e.g., warm air rising).
- Forced Convection: Occurs when an external force (like a fan or pump) moves the fluid (e.g., air conditioning systems).
- Example: Boiling water, where hot water rises to the surface, and cooler water sinks.
c. Radiation
- Definition: The transfer of heat through electromagnetic waves (such as infrared radiation) without the need for a medium.
- All objects emit radiation depending on their temperature (blackbody radiation).
- The Stefan-Boltzmann Law describes the power radiated by a black body in terms of its temperature:
[
P = \epsilon \sigma A T^4
]
Where: - ( P ) = power radiated (W),
- ( \epsilon ) = emissivity (a measure of how closely a real object behaves like a black body),
- ( \sigma ) = Stefan-Boltzmann constant (( 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 )),
- ( A ) = surface area (m²),
- ( T ) = absolute temperature (K).
- Example: Feeling warmth from the sun on your skin.
6. Specific Heat Capacity
- Specific Heat Capacity (( c )): The amount of heat required to raise the temperature of a unit mass of a substance by 1 °C (or 1 K).
- Formula:
[
Q = mc\Delta T
]
Where: - ( Q ) = heat added (J),
- ( m ) = mass (kg),
- ( c ) = specific heat capacity (J/kg·K),
- ( \Delta T ) = change in temperature (K or °C).
- Examples of Specific Heat Capacities:
- Water: ( 4.186 \, \text{J/g·°C} ) (high specific heat, good for temperature regulation).
- Aluminum: ( 0.897 \, \text{J/g·°C} ).
7. Phase Changes and Heat
When substances change state (phase transitions), heat is involved without a temperature change:
a. Melting
- The transition from solid to liquid (e.g., ice to water). Heat energy is absorbed.
- Latent Heat of Fusion: The amount of heat required to change a unit mass of a solid into a liquid at constant temperature.
b. Freezing
- The transition from liquid to solid. Heat energy is released.
- Latent Heat of Solidification: The heat released when a unit mass of a liquid freezes.
c. Vaporization
- The transition from liquid to gas (e.g., water to steam). Heat energy is absorbed.
- Latent Heat of Vaporization: The amount of heat required to change a unit mass of liquid into vapor without changing temperature.
d. Condensation
- The transition from gas to liquid. Heat energy is released.
- Latent Heat of Condensation: The heat released when a unit mass of vapor condenses.
e. Sublimation
- The transition directly from solid to gas (e.g., dry ice to carbon dioxide gas) without passing through the liquid state.
- Latent Heat of Sublimation: The heat required for this phase change.
8. Heat Engines and Refrigerators
a. Heat Engines
- Devices that convert heat energy into mechanical work using the principles of thermodynamics.
- Efficiency: The efficiency of a heat engine is defined as the ratio of useful work output to heat input:
[
\text{Efficiency} = \frac{W_{\text{out}}}{Q_{\text{in}}}
] - Carnot Engine: An idealized engine that operates between two heat reservoirs, achieving maximum efficiency determined by the temperatures of the reservoirs:
[
\text{Efficiency} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}
]
Where ( T ) is in Kelvin.
b. Refrigerators
- Devices that remove heat from a cold reservoir and transfer it to a hot reservoir, using work input.
- Coefficient of Performance (COP): A measure of efficiency for refrigerators:
[
\text{COP} = \frac{Q_{\text{removed}}}{W_{\text{input}}}
]
9. Applications of Heat
Heat plays a critical role in various fields, including:
a. Heating Systems
- Central heating, space heaters, and heat pumps for maintaining comfortable indoor temperatures.
b. Engines and Transportation
- Internal combustion engines, steam engines, and turbines convert heat energy into mechanical work.
c. Cooking
- Heat transfer methods (conduction, convection, and radiation) are utilized in cooking processes.
d. Climate and Weather
- Heat affects atmospheric temperature and dynamics, influencing weather patterns and climate.
e. Industrial Processes
- Heat is crucial in manufacturing processes, such as metal forging, glass blowing, and chemical reactions.
10. Key Equations and Constants
| Concept | Equation |
|---|---|
| First Law of Thermodynamics | ( \Delta U |
= Q – W ) |
| Fourier’s Law of Heat Conduction | ( Q = -kA \frac{dT}{dx} ) |
| Specific Heat Capacity | ( Q = mc\Delta T ) |
| Latent Heat of Fusion | ( Q = mL_f ) |
| Latent Heat of Vaporization | ( Q = mL_v ) |
| Efficiency of Heat Engine | ( \text{Efficiency} = \frac{W_{\text{out}}}{Q_{\text{in}}} ) |
| Carnot Efficiency | ( \text{Efficiency} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} ) |
Conclusion
Heat is a vital aspect of physics that underlies many natural processes and technological applications. Its study encompasses understanding energy transfer, the laws governing thermodynamic systems, and practical applications in various fields. By grasping these concepts, we can better appreciate the role heat plays in our everyday lives and the functioning of the universe.