Question

In an experimaental set-up, air flows between two stations $P$ and $Q$ adiabatically. The direction of flow depdns on the pressure and temperature conditions maintained at $P$ and $Q$. The conditions at $P$ are $150kPa$ and $35K$. The temperature at station $Q$ is $300K$. The following are the properties and relations pertaining to air:
Specific heat at constant pressure,
$c_p=1.005kG/kgK;$
Specific heat at constnat volume,
$c_v=0.718kJ/kgK;$
Characteristic gas constnat,
$R=0.287kJ/kgK$
Enthalpy, $h=c_{p}T.$
Internal energy, $u=c_{v}T.$

If the air has to flow from station $P$ to station $Q$, te maximum possible value of pressure in $kPa$ at station $Q$ is close to

• A. $50$
• B. $128$
• C. $150$
• D. $87$

Answer 1

The correct option is D $87$

Method I:
Since air is flowing rom $P$ to $Q$, then to get maximum value of pressure at station $Q,$ process must be reversible.


$c_p=1.005kJ/kgK$
$c_v=0.718kJ/kgK$
$R=0.287kJ/kgK$
$\gamma =\frac{c_p}{c_v}=\frac{1.005}{0.718}=1.4$
For reversible adiabatic process $P-Q$
$\frac{T_Q}{T_P}={\left(\frac{p_Q}{p_P}\right)}^{\frac{\gamma -1}{\gamma }}$
$\frac{p_Q}{150}={\left(\frac{300}{350}\right)}^{3.5}=0.586$
or $p_Q=87.45kPa$

Method II:
Since air is flowing $P$ to $Q$, then to get maximum value of pressure at station $Q$.
Chnage in entropy,
$S_Q-S_P\ge 0$