Lecture_17 - Lecture 17 1 step model processes Many"real...

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Lecture 17 — 1 step model processes Many “real” thermodynamic processes (apart from irreversibility) can be modeled as composed of a succession of “one-step” processes. Important examples of these building-block processes are: – workfree (no change in volume, or zero external pressure); – reversible isothermal (no change in temperature); – reversible adiabatic (no heat flow). Example 1: Take O 2 from 1 bar, 300K to 5 bar at fixed volume. Compute Δ U . Workfree, so dU = dQ . Need model to compute dQ ; use ideal gas. Pv = RT implies T 2 = 5 T 1 = 1500 K . Now use dU = C v dT ; need model for C v . C v = 20 + 0 . 05 T ; integrate. Example 2: Take O 2 at 50bar, 1500K to 50bar, 750K. Compute Δ U . Isobaric (constant pressure), so W = P Δ v . Need to know v 1 , v 2 . Again need EOS; use ideal gas. v = RT/P ; so W = R Δ T . (( R = 8 . 314J / (molK); 1Cal = 4 . 19J.)) Now compute Δ U : assume (again) ideal gas. So U = U ( T ) only; Δ U = T 2 T 1 C v ( T ) dT . Again use C v model above; integrate. Finally, compute Q : Δ U = Q + W , so Q = Δ U - W .
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