State functions explained (LearnChemE.com, 5min). Properties like those listed in the steam tables are functions of P, V, T, etc. They depend only on the state variables and knowing two of the variables is enough to figure out all the rest. Other functions are like heat and work; they depend on the path by which you proceed to evaluate their changes. Path function sample calculations (uakron, 9min) are useful in providing concrete illustrations of how the path matters for work and heat.

Comprehension Questions: 1. Consider a monatomic ideal gas in an insulated piston/cylinder with a vaccuum outside the piston, originally at 300K and 1bar. Suppose the volume is suddenly doubled with zero resistance against the piston. Compute the change in U and the work accomplished. 2. Consider the same ideal gas etc as above. Now suppose the volume is slowly doubled (e.g. using grains of sand). Compute the change in U and the work accomplished. 3. Continuing from #2 above, the insulation is removed and the piston/cylinder is allowed to equilibrate to its original temperature in #1 above. Compute the change in U and the work accomplished for this stage. 4. Compare the entire process from 2-3 above with the process in #1. Compute the change in U and the work accomplished overall. Also compare the final pressures. Is pressure a state function or a path function?

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## Path Properties vs. State Functions Explained

State functions explained (LearnChemE.com, 5min). Properties like those listed in the steam tables are functions of P, V, T, etc. They depend only on the state variables and knowing two of the variables is enough to figure out all the rest. Other functions are like heat and work; they depend on the path by which you proceed to evaluate their changes. Path function sample calculations (uakron, 9min) are useful in providing concrete illustrations of how the path matters for work and heat.

Comprehension Questions:

1. Consider a monatomic ideal gas in an insulated piston/cylinder with a vaccuum outside the piston, originally at 300K and 1bar. Suppose the volume is suddenly doubled with zero resistance against the piston. Compute the change in U and the work accomplished.

2. Consider the same ideal gas etc as above. Now suppose the volume is slowly doubled (e.g. using grains of sand). Compute the change in U and the work accomplished.

3. Continuing from #2 above, the insulation is removed and the piston/cylinder is allowed to equilibrate to its original temperature in #1 above. Compute the change in U and the work accomplished for this stage.

4. Compare the entire process from 2-3 above with the process in #1. Compute the change in U and the work accomplished overall. Also compare the final pressures. Is pressure a state function or a path function?