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Heat Capacity at Constant Volume

A regenerativ...

Question

A regenerative Brayton refrigeration working between pressure limit of 1 and 3 bar. The temperature and pressure of air at inlet of compressor is 270 K and 1 bar respectively. Compressed air enters regenerative heat exchanger at temperature of 310 K and exit at a temperature of 280 K. The refrigeration effect is 30 kJ/kg. The effectiveness of heat exchanger is ____.
Assume compression and expansion are isentropic
(Take $γ$ for air = 1.4 and $c_{p}$ for air = 1.005 kJ/kgK)
(Correct upto 3 decimal place)
0.397

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Solution

The correct option is A 0.397

. $\frac{T_{4}}{T_{3}} = {(\frac{1}{3})}^{\frac{γ - 1}{γ}}$

$T_{4} = {(\frac{1}{3})}^{\frac{1.4 - 1}{1.4}}$

$T_{4} = 204.57 K$

Refrigeration effect = $c_{p} (T_{b} - T_{4})$

$T_{b} - T_{4} = \frac{30}{1.005}$

$T_{b} = 234.421 K$

So, effectiveness of heat exchanger,

$ϵ = \frac{(T_{a} - T_{5})}{T_{a} - T_{b}}$

$ϵ = \frac{310 - 280}{310 - 234.421} = 0.397$

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