Understanding the First Law of Thermodynamics
The law is an affirmation of the conservation of energy principle. It states that energy cannot be created or destroyed but only transformed from one form to another or transferred between systems.
The Mathematical Representation
The first law is often expressed with the equation
Q = ΔU + W
- Q: The total heat added to the system, accounting for the energy transferred due to a temperature difference.
- ΔU: The change in the system’s internal energy, reflecting the total energy stored within the system.
- W: The work done by or on the system, representing the energy transferred by mechanical means.
First Law of Thermodynamics
Image Courtesy OpenStax
Diving Deeper into Energy Transfers
Energy can either enter or leave a system through work or heat. The relationship amongst these parameters and the internal energy is not just a mathematical equation but a conceptual framework to understand intricate energy transformations.
Internal Energy
Components and Influencing Factors
The internal energy of a system is a sum of the kinetic and potential energies of its constituent particles. It fluctuates with energy transfers via heat or work and is affected by state variables such as volume, pressure, and temperature.
- Kinetic Energy: Constitutes the energy of particles in motion. At higher temperatures, particles move faster, increasing the kinetic energy and consequently the internal energy.
- Potential Energy: Originates from the interactions between particles. It's influenced by the distance and orientation of particles relative to each other.
Heat Energy (Q)
The transfer of energy as heat is central to thermodynamics. It occurs due to a temperature gradient between the system and surroundings.
- Positive Q: Indicates heat addition, elevating the internal energy and possibly the temperature.
- Negative Q: Signifies heat extraction, reducing the internal energy and possibly leading to a temperature decline.
Work and Internal Energy
Work is another mechanism through which energy is transferred. It’s especially prominent in systems involving gases, where expansion and compression are common.
Work Done by or on a Closed System
Work done in thermodynamics is largely associated with gases, expressed as:
W = PΔV
Work done on a closed system
Image Courtesy OpenStax
- Positive Work: When work is done on the system, leading to an increase in internal energy.
- Negative Work: When work is done by the system on its surroundings, resulting in a reduction of its internal energy.
Practical Insights
Understanding the nature and calculation of work is instrumental in various applications, including the design and operation of engines, where the work output is a crucial efficiency determinant.
Change in Internal Energy
The internal energy change correlates with temperature variations, encapsulated in the equation:
ΔU = (3/2) NkBΔT = (3/2) nRΔT
- N: Number of particles
- kB: Boltzmann’s constant
- n: Number of moles
- R: Universal gas constant
Temperature and Internal Energy
- Increasing Temperature: Leads to enhanced particle motion, increasing the internal energy.
- Decreasing Temperature: Reduces particle kinetic energy, leading to a drop in internal energy.
Change in Internal Energy
Image Courtesy Chemistry Learner
Theoretical and Practical Applications
Analytical Tools
The first law is an essential analytical tool for physicists, enabling intricate energy analyses in various processes. It supports the prediction and interpretation of outcomes of experiments and natural phenomena.
Thermodynamic Processes
In thermodynamics, processes are often categorised based on held constant parameters:
- Isovolumetric: Volume remains constant.
- Isobaric: Pressure is constant.
- Isothermal: Temperature doesn’t change.
- Adiabatic: No heat exchange with surroundings.
Each process type offers unique insights into energy transformations and is governed by the first law, underscoring the law’s universality and applicability.
Engineering Applications
Engineers often harness the principles outlined in the first law to optimise energy transfer and transformation in machines and processes. From internal combustion engines to refrigeration systems, understanding the nuanced interplay of work, heat, and internal energy is paramount.
A Closer Look at Energy Conservation
Energy Equilibrium
Systems often strive for an energy equilibrium. The first law aids in predicting and understanding how systems respond to energy disparities, offering insights into their evolution and eventual stabilisation.
Environmental Implications
The law also finds relevance in environmental science. For instance, Earth’s energy balance involves intricate energy exchanges between the planet and its atmosphere, influenced by solar radiation. Understanding these exchanges is foundational to studying climate change and other environmental phenomena.
FAQ
In biological systems like human metabolism, the first law of thermodynamics is manifested in the energy balance between the energy intake, in the form of food, and energy expenditure through basal metabolic rate, physical activity, and thermogenesis. Energy is neither created nor destroyed but converted from chemical energy in food to other forms like kinetic energy, potential energy, and thermal energy. The law helps in understanding and quantifying these energy transformations, providing a foundation for studies related to diet, exercise, and overall energy balance in biological organisms, emphasising the universality of this law across physical and biological realms.
The first law of thermodynamics is considered a statement of energy conservation because it asserts that energy cannot be created or destroyed, only transformed from one form to another. This law encapsulates the perpetual constancy of total energy in a closed system, underscoring the transformation between internal energy, heat, and work. Distinguishing it from the conservation of mass principle, while the latter posits the constancy of mass in closed systems, the first law of thermodynamics focuses explicitly on energy transactions and transformations, serving as a cornerstone for understanding complex energetic interactions in physical systems.
Yes, the first law of thermodynamics can be extended to open systems by incorporating terms that account for the energy associated with mass entering or leaving the system. In such cases, the law adapts to include not just the energy transferred as heat and work, but also the energy carried by the mass that is added or removed. This energy includes the internal, kinetic, and potential energies of the incoming or outgoing mass. Engineers and scientists often use this extended version of the first law to analyse systems like rockets and jets, where both mass and energy are exchanged with the surroundings.
External factors such as atmospheric pressure directly impact the work done by or on a system. For instance, in the context of a gas enclosed in a piston, the atmospheric pressure exerts a force on the piston. The work done in expanding or compressing the gas is not only dependent on the internal pressure of the gas but also on the external atmospheric pressure. In calculations involving work done, especially in isobaric processes, the net pressure (the difference between internal and external pressures) is considered to accurately evaluate the work associated with the volume change, crucial for applying the first law of thermodynamics effectively.
The type of gas particles affects the change in internal energy through the degrees of freedom of the particles, which in turn influences the specific heat capacity. Monatomic gases have 3 degrees of freedom, diatomic have 5, and polyatomic have 6 or more, depending on their structure. The more degrees of freedom, the more ways the gas can store internal energy. Consequently, for a given amount of heat added, diatomic and polyatomic gases would have a smaller rise in temperature compared to monatomic gases, due to their higher heat capacity. This understanding is integral to applying the first law of thermodynamics in diverse scenarios involving different types of gases.
Practice Questions
The final internal energy of the system can be calculated using the first law of thermodynamics, which states that Q = ΔU + W. Since work done on the system is 250 J and the heat lost is 150 J, by substituting these values, the equation becomes -150 J = ΔU + 250 J. Solving for ΔU gives ΔU = -400 J. The initial energy of the system was 500 J; thus, the final internal energy becomes 500 J - 400 J = 100 J.
The internal energy of a monatomic ideal gas would increase if the volume is kept constant while the temperature is increased. With constant volume, no work is done on or by the gas, as expressed by W = PΔV and ΔV = 0 in this case. According to the first law of thermodynamics, Q = ΔU + W, and since W = 0, the equation simplifies to Q = ΔU. Therefore, any heat added to the system will result in a direct increase in internal energy, making these two quantities directly proportional in an isovolumetric process.
