Work Done in Isothermal and Adiabatic Processes

One mole of gas expands from 1 L to 8 L. In a heat bath it does a large amount of work. Wrapped in insulation it does less work, and it comes out cold. Why?

How to count work and give it the right sign (general / IUPAC convention, w is work done on the system), why the route matters, and how to solve isothermal and adiabatic problems, reversible and irreversible, step by step. One running example (1 mol, 300 K, 1 L to 8 L) is used throughout, so you can compare all four routes on one P-V graph.

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In this video

• 0:00The puzzle: same gas, two routes, different work
• 1:00Sign convention and the work formula
• 2:09Reversible vs irreversible paths
• 3:59Isothermal process: formula, numbers, units
• 6:25Adiabatic process: why an expanding gas cools
• 8:02Reversible adiabatic: PV^gamma = constant (derivation)
• 10:18Irreversible adiabatic: finding T2 the exam way
• 12:31All four routes on one graph
• 14:22Three extras: delta H, cycles, where gamma comes from
• 16:15Six traps to remember
• 18:03Recap and close