First Law of Thermodynamics PDF

First Law of Thermodynamics The First Law of Thermodynamics states that "Energy can neither be created nor destroyed; it can only be transformed from one form to another." This principle, grounded in observation and experiment, forms the basis for understanding how energy flows within physical syste...

First Law of Thermodynamics The First Law of Thermodynamics states that "Energy can neither be created nor destroyed; it can only be transformed from one form to another." This principle, grounded in observation and experiment, forms the basis for understanding how energy flows within physical systems. Internal Energy (U) In thermodynamics, internal energy (U) represents the total energy contained within a system. For a system composed of atoms, ions, or molecules (such as an ideal gas), this internal energy includes: Translational energy: due to the movement of particles in space. Rotational energy: resulting from particles rotating around their own axes. Vibrational energy: associated with the vibrations of atoms within molecules. Electronic energy storage: energy related to electrons in atoms or molecules. For an ideal gas, which serves as a simplified model in thermodynamics, there are no energy contributions from interactions between the gas molecules because these interactions are assumed to be negligible. Therefore, the internal energy of an ideal gas depends solely on the types of motion and energy storage within individual molecules. Internal Energy in an Isolated System In an isolated system (where no energy or matter can enter or leave), the internal energy UUU is constant. This means that, while energy can change form within the system—such as from translational to vibrational energy—the total internal energy does not change as long as the system remains isolated. This law has practical implications for pharmaceuticals and other complex systems, where understanding energy conservation helps predict how substances interact, change, or maintain stability under different conditions. Changes to the internal energy of a system When a system is in contact with its surroundings, changes in its internal energy (ΔU) can occur. According to the First Law of Thermodynamics, the total energy of the combined system (system + surroundings) remains constant: This relation implies that any energy change within the system is exactly balanced by an opposite energy change in the surroundings: Understanding ΔU The change in internal energy of a system, ΔU, represents the difference between the system's energy after and before a process occurs: For instance, if energy flows into the system (e.g., through heating), ΔU will be positive. Conversely, if energy leaves the system (e.g., by performing work on the surroundings), ΔU will be negative, with an equal amount of energy transferred to the surroundings. This concept is essential in thermodynamics for calculating energy exchanges in processes like chemical reactions, phase changes, or heat transfers in pharmaceutical and other physical systems. Changes to the internal energy of a system Changes in the internal energy of a system can occur through two main mechanisms, assuming no new phases or components are generated (i.e., no chemical reactions or phase changes like crystallization): 1. Heat Transfer: o When heat is transferred to the system from its surroundings, it increases the system’s internal energy. o Conversely, if the system loses heat to its surroundings, its internal energy decreases. 2. Work Done: o Work can be done on the system (e.g., compression of a gas), which increases the internal energy. o If the system does work on the surroundings (e.g., gas expansion against a piston), the system’s internal energy decreases. First Law of Thermodynamics can be formulated as: Heat (q): This is the energy transferred due to a temperature difference between the system and its surroundings. o When heat is absorbed by the system, q is positive. o When the system releases heat to the surroundings, q is negative. Work (w): This is the energy transferred in a way that can perform physical work (like lifting a weight) due to a force applied over a distance. o When work is done on the system (e.g., compressing a gas), w is positive. o When the system does work on its surroundings (e.g., gas expansion), w is negative. So, the change in internal energy (ΔU) of a system depends on these two types of energy transfer: This relationship means that the internal energy of the system changes based on the amount of heat absorbed or released and the amount of work done on or by the system. Relating work (w) to P and V In thermodynamics, work done by a gas in a system at constant pressure can be expressed in terms of pressure P and a small change in volume dV. Here’s the process in more detail: 1. Work (w) in terms of Pressure and Volume: When a gas expands in a cylinder, it pushes against the piston, exerting a force over a distance. This force over distance can be expressed as: where dV is the small change in volume, and P is the constant pressure. 2. Sign Convention: o If the gas expands, it does work on the surroundings, meaning the system’s energy is used up to push the piston out. Here, w is negative. o If the gas is compressed, work is done on the gas, adding energy to the system, so w is positive. 3. Total Work for a Finite Volume Change: To calculate the total work done over a finite volume change, integrate the small changes over the range of volume. For a constant pressure P, the work done is: where Vi is the initial volume and Vf is the final volume. 4. Application in an Ideal Gas (in a cylinder): Imagine an ideal gas trapped in a cylinder with a piston. As the gas expands or compresses, work is done due to the movement of the piston. This relationship helps us understand how pressure, volume, and temperature changes impact the energy and work in the system. This concept is essential in thermodynamic processes like isothermal (constant temperature), isobaric (constant pressure), and adiabatic (no heat exchange) processes, where volume changes directly influence the work done by or on the gas. Expansion of gas from volume Vi to volume Vf at constant pressure P When a gas expands from an initial volume Vi to a final volume Vf at constant pressure P, the work done by the gas on the surroundings can be understood as the summation (or integral) of all small work increments PdV for each infinitesimal change in volume: 1. Work Definition: Since work (w) done by the system (expanding gas) is equal to the product of the pressure and the small change in volume dV, we can write: 2. Constant Pressure Condition: At constant pressure, P can be taken outside the integral, leading to: 3. Sign Convention: o Since the system is doing work on the surroundings by expanding, this work is taken as negative in thermodynamic sign convention, meaning: 4. Equilibrium During Expansion: In this process, the system is assumed to reach equilibrium after each infinitesimal change in volume dV, ensuring that P remains constant throughout the expansion. This is an idealization that simplifies calculation, often applicable in theoretical or quasi-static (very slow) processes. In summary, the total work done by the gas during expansion is the summation of all infinitesimal PdV contributions across the entire volume change, which simplifies to w=− P(Vf−Vi) under constant pressure. This calculation is crucial for understanding energy transfer in thermodynamic processes where gases expand or contract. In thermodynamics, the behavior of a system at constant volume and constant pressure has important implications for how we understand changes in internal energy ΔU and heat transfer: 1. Constant Volume Process (ΔV=0): o When a process occurs at constant volume, there is no work done by the system because work (w=PΔV) depends on a change in volume ΔV o Therefore, any change in the internal energy ΔU is due only to heat  exchange with the surroundings, which we denote as qv (where the subscript v stands for constant volume): o This condition is often used in theoretical calculations and controlled laboratory settings where volume is fixed. 2. Constant Pressure Process: o In many pharmaceutical processes, reactions and interactions occur at constant pressure (e.g., atmospheric pressure). o Under constant pressure, the change in internal energy ΔU is affected both by the heat transfer qp and by the work done due to any volume change ΔV: o Here, qp is the heat transferred at constant pressure, and PΔV represents the work done by the system as it expands or contracts. o Often in these cases, we use the enthalpy change ΔH\Delta HΔH, defined as: which, at constant pressure, simplifies to: making it a useful measure for heat changes in constant-pressure processes. In summary: This distinction is critical for understanding energy transfer in different pharmaceutical processes, especially for reactions or processes involving gases or solutions where pressure or volume may vary. Enthalpy H Enthalpy (H) is a thermodynamic quantity that provides insight into the heat content of a system, particularly in processes that occur at constant pressure. It combines the internal energy of the system U with the product of pressure P and volume V, representing the total "heat energy" when both internal energy and work done by the system are considered. The relationship for enthalpy is given by: This definition helps in expressing changes in heat transfer for constant-pressure processes, which are common in both laboratory and pharmaceutical settings. Derivation of Enthalpy Change For a system undergoing a process at constant pressure, the change in internal energy can be expressed as: Rearranging this expression to solve for qp (the heat transfer at constant pressure): Since enthalpy is defined as H=U+PV, the change in enthalpy ΔH during a process becomes: Thus, at constant pressure: This equation shows that the enthalpy change (ΔH) represents the heat absorbed or released by the system at constant pressure. This property is especially useful for understanding heat changes in reactions or processes where the system is open to the atmosphere and pressure remains constant. Thermochemistry Thermochemistry is the branch of chemistry that deals with the heat changes that occur during chemical reactions and physical transformations. It is especially relevant in pharmaceuticals because it helps understand the energetics of processes like drug formulation, interactions, and stability. Key Concepts: Enthalpy Change (ΔH): The heat absorbed or released during a process at constant pressure. o Endothermic Process: Heat is absorbed by the system (ΔH>0), e.g., melting or dissolution of a drug. o Exothermic Process: Heat is released by the system (ΔH fumaric acid (at 298K) Solution 1) Question 2) Glucose (C6H12O6) is metabolized in the presence of oxygen (O2) to give carbon dioxide (CO2) and water (H2O). (i) write a balanced equation for the reaction of glucose and oxygen to give carbon dioxide and water (ii) using the following data (305K), calculate the enthalpy of the process. Hf ⁰ C6H12O6 (s) = −1273.0 kJ mol−1 Hf ⁰ O2 (g) = 0 kJ mol−1 (element) Hf ⁰ H2O (l) = −285.8 kJ mol−1 Hf ⁰ CO2 (g) = −393.5 kJ mol−1 Solution 2)