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The source's usual convention treats the pressure inside a tank as the P used in W = PΔV, with work done by the system counted as positive. It also notes that many other textbooks instead define work against the external pressure, as W = -P_ext x ΔV. According to the source, what form does the first law take under that alternate convention?

AΔU = Q - W, exactly as in the usual convention
BΔU = Q + W, with the sign of W reversed
CΔU = W - Q, with heat and work swapped
DΔU = 0, since the two conventions cancel out
Answer & Solution
Correct answer: B. ΔU = Q + W, with the sign of W reversed
1. The source's default convention defines W using the gas's own internal pressure, giving ΔU = Q - W with work done by the system taken as positive. 2. It then notes that many textbooks instead define work as W = -P_ext x ΔV, based on the external pressure the gas pushes against. 3. Because this second definition flips the sign of W relative to the first, it must also flip the sign in front of W in the first law. 4. This is stated directly: the alternate definition reverses the sign convention for work and turns the first law into ΔU = Q + W. 5. Option A ignores that the sign of W has been redefined, and option C swaps the roles of heat and work rather than just the sign of W. 6. Neither convention makes ΔU vanish identically, since ΔU still tracks the real change in a system's internal energy, ruling out option D. _Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.2 The First Law of Thermodynamics and Some Simple Processes_
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