Reversible Air
Thermodynamics – process question?
One mol air is compressed from an initial condition of 1 bar and 25 degrees celsius to a final state of 5 bar and 25 degrees celsius by three different mechanically reversible processes in a closed system:
a) heating at constant volume followed by cooling at constant pressure
b) isothermal compression
c) adiabatic compression followed by cooling at constant volume
Assume air to be an ideal gas with constant heat capacities C_v = 5/2R and C_p = 7/2R. Calculate the work required, heat transferred, and the changes in internal energy and enthalpy of the air for each process.
Well the answer should be process independent (then again it’s been a long time since I’ve studied this stuff). Since the final temperature is the same as the initial, it’s easiest to just work out Q and W as if the process were isothermal.
ΔU = 0
They normally use U instead of H for a closed system.
ΔH = ΔU + Δ(PV) = Δ(nRT) = 0 as well
PV = nRT = constant
W = ∫ PdV = nRT * ln(V2/V1) = -nRT *ln(5)
Q – W = 0 thus Q = W = -nRT ln(5)
You have to do work on the system and it gives off heat in the process. This will be the same if you work it manually for each of the other paths.
If you really wish to work out everything manually, here’s a handy guide:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Thermal/IdealGasProcessesTable.htm
Graham Industries VR1A Double-acting, reversible model steam engine running on air and steam
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