Final Answer:
The statement Energy output = Energy input (1st law) summarizes the First Law of Thermodynamics which states that energy cannot be created or destroyed in an isolated system. In other words the total energy of a closed system remains constant.
Step-by-step explanation:
The First Law of Thermodynamics, expressed as ΔU = Q - W signifies the change in internal energy (ΔU) of a system is equal to the heat added (Q) minus the work done by the system on its surroundings (W). When the system is in a state of equilibrium ΔU is zero and we obtain the simplified form Q = W indicating that the heat added to the system is equal to the work done by the system. This is applicable to various energy transformations from mechanical work to heat transfer.
Consider for example a piston-cylinder system undergoing an adiabatic process. In this scenario where no heat is exchanged with the surroundings (Q = 0) the work done by the system (W) equals the energy input (Q). Mathematically this can be represented as W = -PΔV where P is pressure and ΔV is the change in volume. Consequently the equality Q = W holds illustrating the conservation of energy as per the First Law.
In conclusion the statement Energy output = Energy input (1st law) encapsulates the fundamental principle that within an isolated system the total energy remains constant, emphasizing the conservation of energy across various thermodynamic processes. This principle is crucial for understanding and analyzing energy transfers and transformations in diverse physical systems.