# Ideal Gas State Change (5, 2); Isothermal Expansion (5, 3); Polytropic Processes (5, 4); Isentropic Flow (5, 5) - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Example:
Given: T=16.85_ C, P=1_atm, V=25_1, MW=36_g/gmol.
Solution: n=1.0506_gmol, m=3.7820E-2_kg.

## Ideal Gas State Change (5, 2)

Equation:
Example:
Given: Pi=1.5_kPa, Pf=1.5kPa, Vi=2_l, Ti=100_ C, Tf=373.15_K.
Solution: Vf=2_1.

### Isothermal Expansion (5, 3)

These equations apply to an ideal gas.
Equations:
W
=
n R T LN
Example:
Given: Vi=2_l, Vf=125_l, T=300_ C, n=0.25_gmol, MW=64_g/gmol.
Solution: W=4926.4942_J, M=0.016_kg.

### Polytropic Processes (5, 4)

These equations describe a reversible pressure-volume change of an ideal gas such that P V
Special cases include isothermal processes (n=1), isentropic processes (n=k, the specific heat ratio), and
constant-pressure processes (n=0).
Equations:
Pf
Vf
---- -
----- -
=
Pi
Vi
Example:
Given: Pi=15_psi, Pf=35_psi, Vi=1_ft^3, Vf=0.50_ft^3, Ti=75_ F.
Solution: n=1.2224, Tf=164.1117_ F.

### Isentropic Flow (5, 5)

The calculation differs at velocities below and above Mach 1. The Mach number is based on the speed of sound
in the compressible fluid.
5-26 Equation Reference
Pf Vf
Pi Vi
----------------
=
--------------- -
Tf
Ti
Vf
----- -
m
=
n MW
Vi
n 1
----------- -
n –
Tf
Pf
----- -
---- -
=
Ti
Pi
n
n
is constant.