# Wb for Polytropic, Int Rev Processes: Summary

Here is a summary of the equations for the

for

,

processes for

#### ideal gases

with constant heat capacities in a closed system.
δ = 0
δ = 1
δ = γ
δ = ∞
(Isobaric)
(Isothermal)
(Isentropic)
(Isochoric)
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### Ch 7, Lesson E, Page 18 - Wb for Polytropic, Int Rev Processes: Summary

• We only derived the boundary work equations for the isothermal and isentropic processes.
• The other two are pretty straightforward.
• When the pressure is a constant, the integral of p ΔVwiggle is just P times ΔVwiggle.
• When the molar volume is constant, the boundary work is zero for a closed system.
• Please take careful note of the cases for which these equations apply.
• Polytropic processes.  Internally reversible, closed system, ideal gas, constant heat capacities.
• You’ve seen so many equations in this chapter that it is easy to get confused and use an equation that is not applicable to a process that you are analyzing.
• So, be careful.
• Next, let’s make a little comparison about the boundary work requirement for a compression process.