Fundamental Concept of the First Law
The First Law of Thermodynamics is succinctly expressed by the equation:
ΔU = q + W
In this expression:
- ΔU represents the change in internal energy of the system.
- q denotes the heat added to the system.
- W signifies the work done on the system.
First Law of Thermodynamics
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Internal Energy (ΔU)
- Definition and Significance: Internal energy is the sum of all microscopic forms of energy in a system. It includes the kinetic energy of particles (due to their motion) and potential energy (arising from the forces between particles).
- Properties of Internal Energy:
- It is a state function, dependent only on the state of the system and independent of the process undertaken to reach that state.
- Alterations in internal energy occur when the system either gains or loses energy, either as heat or through work.
Change in Internal Energy
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Heat Added to the System (q)
- Defining Heat in Thermodynamics: Heat in thermodynamics is energy in transit. It's the energy transferred due to a temperature difference between a system and its surroundings.
- Mechanisms of Heat Transfer: Heat can be transferred through conduction (direct contact), convection (fluid movement), or radiation (electromagnetic waves).
- Quantifying Heat Transfer: The formula q = mcΔT, where m is mass, c is specific heat capacity, and ΔT is the change in temperature, is used to calculate the heat transfer in many practical situations.
Work Done on the System (W)
- Understanding Work in Thermodynamics: Work in this context often involves the expansion or compression of gases.
- Calculation of Work: For processes involving volume changes at constant pressure, work is calculated using W = pΔV, where p represents pressure and ΔV is the change in volume.
- Directionality of Work: Work can be done by the system (during expansion) or on the system (during compression).
Work done on a closed system
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Practical Applications of the First Law
The First Law finds its relevance in numerous real-world scenarios, from mechanical systems to biological processes.
In Heat Engines and Refrigeration
- Heat Engines: These devices, like car engines, convert heat into work. The First Law aids in understanding the efficiency of these conversions.
- Refrigeration Systems: Refrigerators and air conditioners illustrate the First Law in action, where work is used to transfer heat against the natural flow (from cooler to warmer areas).
Biological Systems
- Metabolism: The First Law applies to the human body, where the energy from food (q) is either utilized for work (W) or stored as internal energy (ΔU).
Detailed Examples and Case Studies
To deepen understanding, let’s explore specific examples:
Example 1: Heating Water in a Closed Container
- Scenario: Water is heated in a sealed container.
- Process: As heat (q) is supplied, the internal energy (ΔU) of water increases. Since the container's volume does not change, no work (W) is done.
Example 2: Compressing Air in a Cylinder
- Scenario: Air is compressed in a cylinder with a piston.
- Process: When the piston compresses the air, work (W) is done on the gas. If no heat is exchanged (adiabatic process), the work done increases the internal energy (ΔU) of the air.
Misconceptions and Clarifications
- Heat and Work as Modes of Energy Transfer: Heat and work are not forms of stored energy but are ways energy is transferred into or out of a system.
- Changes in Internal Energy in Isolated Systems: In isolated systems, where no heat or work crosses the boundary (q = 0, W = 0), internal energy (ΔU) can still change due to internal chemical or nuclear processes.
In-depth Analysis of Key Terms
- Internal Energy: It's important to understand that internal energy is a collective term for microscopic kinetic and potential energies. It includes vibrational, rotational, translational kinetic energies, and energies due to intermolecular forces.
- Heat Transfer: The concept of heat transfer is fundamental in thermodynamics. It's crucial to differentiate it from temperature; heat is energy in transit, while temperature is a measure of the thermal state of a system.
- Work in Thermodynamics: The work done in thermodynamics often involves gas expansion or compression. It's important to understand that this is just one form of work. In other contexts, electrical or gravitational work might be involved.
Conclusion
The First Law of Thermodynamics is a fundamental concept that underpins much of A-Level Physics. Its applications stretch across various fields, offering insights into energy transformations in mechanical systems, natural phenomena, and even biological processes. Mastery of this topic provides a strong foundation for further studies in physics and engineering.
FAQ
The efficiency of a heat engine is calculated based on the First Law of Thermodynamics. The efficiency (η) is defined as the ratio of the work output (W) to the heat input (qh). According to the First Law, ΔU = qh - qc + W, where qh is the heat absorbed from the hot reservoir, qc is the heat released to the cold reservoir, and W is the work done by the engine. In a cycle, ΔU = 0, so qh = qc + W. The efficiency becomes η = W/qh = 1 - qc/qh. This equation highlights that efficiency depends on how much of the heat input is converted to work and how much is lost as waste heat.
The First Law of Thermodynamics, being a law of nature, cannot be violated under normal circumstances. It is a statement of conservation of energy, implying that energy can neither be created nor destroyed, only transformed from one form to another. If there appears to be a violation of this law, it usually indicates a misunderstanding or misinterpretation of the system being studied. For instance, a seemingly unaccounted change in internal energy might be due to unmeasured heat transfer or work done. In physics, any valid theory or experiment must conform to this fundamental law.
The First Law of Thermodynamics is essentially a restatement of the conservation of energy principle, tailored for thermodynamic systems. It states that the energy of an isolated system is constant. Energy within the system can change forms, like from potential to kinetic energy, or transfer between the system and its surroundings as heat or work, but the total energy remains constant. This law enforces that in any process, energy cannot be created or destroyed. It can only be transferred or converted from one form to another, thus upholding the fundamental principle of energy conservation in all physical processes.
In a cyclic process, a system returns to its original state after completing a series of changes. Since the system's state is the same at the beginning and end of the cycle, the change in internal energy (ΔU) over one complete cycle is zero. According to the First Law of Thermodynamics (ΔU = q + W), this implies that the net heat added to the system (q) is equal to the net work done by the system (W) over one complete cycle. This principle is fundamental in the operation of heat engines, where the engine goes through a cyclic process, converting heat into work.
In an isothermal process, the temperature of the system remains constant. According to the First Law of Thermodynamics, ΔU = q + W. However, for an ideal gas undergoing an isothermal process, the change in internal energy (ΔU) is zero because internal energy is a function of temperature, which doesn't change. Therefore, in such a scenario, the heat added to the system (q) is completely converted into work done by the system (W), making q = W. This relationship is particularly evident in isothermal expansion or compression of an ideal gas, where the work done can be calculated using the equation W = nRT ln(V2/V1), with n being the amount of substance, R the gas constant, and V1 and V2 the initial and final volumes.
Practice Questions
To calculate the work done on the gas, we use the formula W = pΔV. Here, p = 100 kPa = 100,000 Pa, and ΔV is the change in volume, which is the final volume minus the initial volume. So, ΔV = 0.015 m³ - 0.02 m³ = -0.005 m³. Substituting these values into the formula, we get W = 100,000 Pa × (-0.005 m³) = -500 J. The negative sign indicates that work is done on the gas. This work leads to an increase in the internal energy of the gas, as per the First Law of Thermodynamics.
To find the change in internal energy (ΔU), we apply the First Law of Thermodynamics: ΔU = q + W. In this case, q = 500 J (heat added to the gas) and W = -300 J (work done by the gas, hence negative). Substituting these values, we get ΔU = 500 J - 300 J = 200 J. This means the internal energy of the gas increases by 200 J. The increase in internal energy could be due to an increase in the kinetic energy of the gas particles, reflecting a rise in temperature.
