1. Concept:The First Law of Thermodynamics serves as the energy conservation ledger for thermal systems, tracking heat input, energy storage, and work output.
2. Formula:$$Q = \Delta U + W$$
3. Solution:- By standard convention (where work done BY the gas is positive), the heat energy supplied to the system (\(Q\)) serves two simultaneous purposes:
- First, it increases the kinetic energy of the molecules, thus raising the internal energy (\(\Delta U\)).
- Second, any remaining energy pushes the piston outward, performing mechanical work (\(W\)) on the environment.
- Therefore, the total input equals the sum of the outcomes: \(Q = \Delta U + W\).
4. Why other options are incorrect:Equations like \(W = Q + \Delta U\) would violate energy conservation by suggesting work output is greater than heat input when internal energy also increases.
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