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When studying thermodynamics, one of the first principles you'll encounter is the First Law of Thermodynamics, a pivotal concept. This law is a version of the Law of Conservation of Energy, tailored for thermodynamic processes. It essentially states that energy can neither be created nor destroyed. In thermodynamic terms, the law is expressed as:\[ \Delta Q = \Delta U + \Delta W \]where:- \( \Delta Q \) is the heat added to the system- \( \Delta U \) is the change in internal energy- \( \Delta W \) is the work done by the systemThis equation means that the heat supplied to a system does two things: it changes the internal energy of the system, and it performs work. Understanding this balance is crucial for grasping how energy moves and changes form in physical systems.

Internal energy is the energy contained within a system. It's the sum of all microscopic kinetic and potential energies of the particles within the system. In the context of an ideal gas, internal energy primarily arises from the kinetic energy of gas molecules moving randomly. For a monatomic ideal gas, the change in internal energy \( \Delta U \) is given by the formula:\[ \Delta U = \frac{3}{2}nR\Delta T \]Here:- \( n \) is the number of moles of gas- \( R \) is the universal gas constant- \( \Delta T \) is the change in temperatureThis formula shows that internal energy changes are proportional to temperature changes. This relationship is fundamental for calculations involving heat and work in thermodynamic processes involving ideal gases.

The Ideal Gas Law links pressure, volume, and temperature of an ideal gas through the equation:\[ PV = nRT \]where:- \( P \) is pressure- \( V \) is volume- \( n \) is the amount of gas in moles- \( R \) is the universal gas constant- \( T \) is temperature in KelvinIn cases where an ideal gas undergoes a process at constant pressure, the Ideal Gas Law helps relate changes in temperature and volume. When a gas expands at constant pressure, as in the exercise, it performs work given by:\[ \Delta W = P\Delta V \]This work done during expansion is specifically related to the volume change of the gas, illustrating how the gas uses some of the heat energy supplied to it.

Heat transfer is the movement of thermal energy from one place to another due to temperature difference. In thermodynamic processes, heat transfer is a key factor that causes changes in the system's energy.For an ideal gas, the heat added \( \Delta Q \) impacts both internal energy and mechanical work. As described by the First Law of Thermodynamics, the total heat added is the sum of changes in internal energy and the work done by the gas:\[ \Delta Q = \Delta U + \Delta W \]This distinction is crucial because it tells us exactly how energy supplied as heat is used. Some portion increases the internal kinetic energy of molecules, while another part makes the gas do work, such as expanding against a piston. For a monatomic ideal gas expanding at constant pressure, calculations show that 60% of heat increases internal energy, while 40% is used for doing work. Understanding these proportions provides deeper insight into energy allocation in thermodynamic processes.