Question

An air refrigeration system works on reversed Brayton cycle and used for $10$ tones of refrigeration capacity. Air enters the compressor at $-{20}^{o}C$ and $1.4$ bar and compressed to $4.2$ bar. Compressed air is cooled in the cooler to ${50}^{o}C$ with a loss in pressure of $0.2$ bar. What is theoretical piston displacement ?

• A. $50m^3/min$
• B. $1.01617m^3/min$
• C. $79.1m^3/min$
• D. $63.7m^3/min$

Answer 1

The correct option is C $79.1m^3/min$


As loss an pressure is given in cooler, so,

$P_s=4.2-0.2=4$ bar

3-4 is isentroic expansion process,

$\frac{T_4}{T_3}={\left(\frac{P_4}{P_3}\right)}^{(\gamma -1)/\gamma }$

$T_4=\frac{T_4}{{\left(\frac{4}{1.4}\right)}^{(\gamma -1)/\gamma }}$

$[T_3=50+273=323K]$

$T_4=239.3K$

Let $\dot{m}$ is the mass flow rate of air.

So, Regirgeration capacity $=\dot{m}\times c_p(T_1-T_4)$

$[T_1=273-20=253K]$

$10\times 3.5=\dot{m}\times \left(1.005\right(253-239.3)$

$\dot{m}=2.542kg/s$

Theoretical piston displacement $={\dot{V}}_1)$

$P_1{V}_1=\dot{m}R{T}_1$

${\dot{V}}_1=\frac{2.542\times 0.287\times 253}{L4\times {10}^2}$

${\dot{V}}_1=13184m^3/s=79.104m^3/mm$