The correct mathematical expression for the first law of thermodynamics

Explanation

The first law of thermodynamics states that the total energy of a closed system remains constant. In other words, energy can neither be created nor destroyed, but it can be transformed from one form to another. This principle can be expressed mathematically as:ΔE = q + wwhere:ΔE is the change in the internal energy of the system (in Joules)q is the heat transferred to the system (in Joules)w is the work done by the system on the surroundings (in Joules)However, there is a difference between enthalpy (H) and internal energy (E):Enthalpy (H) represents the total heat content of a system, including both its internal energy and the potential energy associated with its volume and pressure.Internal energy (E) represents only the kinetic and potential energy of the particles within the system.The relation between these quantities is given by:ΔH = ΔE + PΔVwhere:P is the pressure (in Pascals)ΔV is the change in volume of the system (in cubic meters)By rearranging the enthalpy equation, we can express the change in internal energy as:ΔE = ΔH - PΔVSubstituting this into the first law of thermodynamics equation:ΔE = q + wwe get:ΔH - PΔV = q + wCombining like terms and rearranging again, we arrive at the correct expression:ΔE = q - w