Chapter 3, Problem 3.94P

Interpretation Introduction

Interpretation:

For an open system in which air is considered as ideal gas is expanding in a home due to heating of air at constant pressure resulting in leakage of air at outdoors, the expression which relate household temperature with time should be derived.

Concept Introduction:

For an open system the mass and energy can exchange from the surrounding, the mass balance is therefore,

  $\frac{dm}{dt}+\Delta m=0$

In terms of moles or material balance is

$\frac{dn}{dt}+\Delta n=0$ Where $\frac{dn}{dt}$ is the rate of change of moles of air inside the room and $\Delta n$ is difference between exit and entrance of number of moles of air.

The energy balance for open system is:

  $\stackrel{•}{Q}+\stackrel{•}{W}=\Delta [(H+\frac{1}{2}{u}^2+gz)\stackrel{•}{n}]+\frac{d(nU)}{dt}$............(1)

And

And for ideal gas

  $n=\frac{P{V}^t}{RT}$........(2)