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_
Related questions
A perfect crystal at 0 K has W equal to 1, which makes its entropy:Boltzmann's model related the entropy of a system to which quantity?An endothermic process that involves an increase in system entropy is spontaneous when temA process whose enthalpy and entropy changes share the same arithmetic sign will show:At minus 10.00 degrees Celsius the entropy change of the universe for melting is negative,Melting is described as spontaneous at 10.00 degrees Celsius because at that temperature:Free energy is described as the energy available to do useful work, being the difference bBesides indicating spontaneity, the free energy change gives information about the amount