Chapter 8, Problem 8.13P

Interpretation Introduction

Interpretation: The relationship between the power for adiabatic compression and the power for isothermal compression is to be determined.

Concept introduction: A process is said to be isothermal which is occurring at the constant temperature and isothermal compression means increase in pressure without any change in temperature. Thus, power required for isothermal compression is,

  ${\text{P}}_{\text{1}}\text{=}\frac{\text{1}\text{.304}\text{×}{\text{10}}^{\text{-4}}{\text{T}}_{\text{a}}{\text{q}}_{\text{0}}}{\text{η}}\text{ln}\left(\frac{{\text{p}}_{\text{b}}}{{\text{p}}_{\text{a}}}\right)\mathrm{.......}\text{(1)}$

Here, T_a= Inlet temperature in $\text{°R}$

  ${\text{q}}_{\text{0}}$ = Volume of compressed gas in std ft³/min

P₁ = Brake horsepower for isothermal compression

  ${\text{p}}_{\text{a}}$ = Inlet Pressure of the gas

  ${\text{p}}_{\text{b}}$ = Outlet Pressure of the gas

  $\text{η}$ = Stage efficiency

A process is said to be adiabatic which is occurring at the constant heat and adiabatic compression means increase in pressure without any change in heat. Thus, power required for adiabatic compression is,

  ${\text{P}}_{\text{2}}\text{=}\frac{\text{1}\text{.304}\text{×}{\text{10}}^{\text{-4}}{\text{T}}_{\text{a}}{\text{q}}_{\text{0}}}{\text{η}}\frac{\text{γ}}{\text{γ-1}}\left[{\left(\frac{{\text{p}}_{\text{b}}}{{\text{p}}_{\text{a}}}\right)}^{\text{1-}\frac{\text{1}}{\text{γ}}}\text{-1}\right]\mathrm{.......}\text{(2)}$

P₂ = Brake horsepower for adiabatic compression

  $\text{γ}\text{=}$ Compressibility ratio