Heat & Work in Int Rev, Polytropic Processes

Equation.
The answer depends on
the value of δ.
How much

boundary work

, in kJ/kg, does it take to increase the pressure on an

ideal gas

in a closed system from 200 kPa to 400 kPa in an

internally reversible

,

polytropic

process ? Assume the specific heats are constant.
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Roll the mouse pointer over the big yellow circles to see more information about each process path.
Equation. = Area under the process path.
This PV Diagram shows how the work required to increase the pressure on a closed system by an internally reversible, polytropic process changes as the value of delta changes.

Heat Capacity Ratio
γ = 1.3985

δ = 0.75

Equation.

Equation.

Equation.

Internally reversible processes in which δ < 1 require even more work than an

isothermal

process because they must reject extra heat in order to cool the system down.
The shaded are shown here represents the boundary work required to accomplish the compression when delta is equal to 0.75.
δ = 1.0 < γ

Equation.

Equation.

Equation.

Internally reversible processes in which δ < γ require more work than an isentropic process and as a result must reject some heat.
: Isothermal
The shaded are shown here represents the boundary work required to accomplish the compression when delta is equal to 1.0.
δ = 1.2 < γ

Equation.

Equation.

Equation.

Internally reversible processes in which δ < γ require even more work than an

isentropic

process and as a result must reject some heat.
Hi
δ = γ = 1.3985

Equation.

Equation.

Equation.

This path represents an

internally reversible

,

adiabatic

process. The

isentropic

process requires the least work of any process that is strictly a compression (no heat added).
: Isentropic
Hi
δ = 2 > γ

Equation.

Equation.

Equation.

The increase in pressure is caused both by

boundary work

and by the addition of

heat

to the system.
Hi
δ = ∞ > γ

Equation.

Equation.

Equation.

The increase in pressure is caused only by the addition of

heat

to the system.
: Isochoric
Hi
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Ch 7, Lesson E, Page 19 - Heat & Work in Int Rev, Polytropic Processes