Concept:The first law of thermodynamics defines the conservation of internal energy (\( \Delta E \)) relative to heat exchange (\( q \)) and work (\( w \)).
Formula:$$ \Delta E = q + w $$
Solution:- The universally standard expression is that the change in internal energy equals the heat added to the system plus the work done on the system.
- Hence, the correct mathematical equation is \( \Delta E = q + w \).
- Note: In some physics conventions, work done by the system is used, leading to \( \Delta E = q - w \) or \( \Delta E = q - P\Delta V \), but the primary IUPAC chemical convention is \( q + w \).
Why other options are incorrect:Option B uses minus q, which misaligns with conservation rules. Option D uses minus \( p\Delta v \) but paired with a delta q (heat is not a state function, so \( \Delta q \) is improper notation).
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