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Concept · Thermodynamics
Laws of thermodynamics
First Law ΔU=Q+W (sign convention: Q>0 absorb, W>0 work done ON gas/compression; equivalently ΔU=Q-Wbygas), work by gas W=P*ΔV, Second Law (Clausius & Kelvin statements, irreversibility, no perpetual motion of the second kind)
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Named traps
13 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Adiabatic heat nonzeroIncludes a heat term Q for an adiabatic process where Q=0, instead of setting ΔU equal to the work alone.→
- All heat raises temperatureAssumes all heat supplied to a gas raises its temperature, ignoring that during expansion some goes to work done by the gas.→
- Expansion work taken as +WUses positive W for an expanding gas in ΔU=Q+W, when expansion means work is done BY the gas so W on the gas is negative.→
- First-law sign convention wrongMis-signs Q or W in ΔU=Q+W, e.g. treats heat released or work done by the gas as positive against the stated convention.→
- Isothermal ΔU nonzeroAssigns a nonzero internal-energy change to an isothermal process for an ideal gas, where ΔU=0.→
- P-V work area misreadReads work as the area to the axis at a single state rather than the area under the P-V curve between the two states.→
- Real process treated as reversibleAssumes a real spontaneous process (mixing, free expansion, heat flow) can run backwards on its own, ignoring irreversibility.→
- Single-source engine 100% efficientBelieves a heat engine drawing from one reservoir can convert all absorbed heat into work, violating the Kelvin statement.→
- Spontaneous cold-to-hot allowedClaims heat can flow from cold to hot with no other change (no work input), violating the Clausius statement.→
- W=P*ΔV uses absolute VComputes work by the gas as P times the absolute volume rather than P times the volume change ΔV.→
- Work by/on gas swappedConfuses work done BY the gas (expansion) with work done ON the gas (compression), flipping the sign of W in the first law.→
- Work nonzero at constant volumeComputes nonzero work for a constant-volume process, ignoring that no volume change means W=P*ΔV=0.→
- ΔU depends on pathTreats the internal-energy change as path-dependent rather than a state function fixed by the endpoint states.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
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