Question

A refrigerating unit working on Bell Coleman cycle takes air from cold chamber at $-{10}^{\circ }c$ and compressed it from 1 bar to 6.5 bar with index of compression being 1.2. The compressed air is cooled to a temperature of ${30}^{\circ }C$ before it is expanded in the expander, where the index of expansion is 1.35. What is the refrigerating effect?

• A. $28.14kJ/kg$
• B. $36.72kJ/kg$
• C. $41.84kJ/kg$
• D. $48.76kJ/kg$

Answer 1

The correct option is B $36.72kJ/kg$

$W_{net/kg}=\text{Work done on compressor-Work done by expander}$

$=\frac{n_1}{n_1-1}R(T-2-T_1)-\frac{n_2}{n_2-1}R(T_3-T_4)$

$=\frac{n_1}{n_1-1}R{T}_1[{\left(\frac{P_2}{P_1}\right)}^{n_1-1/n_1}-1]\frac{n_2}{n_2-1}R{T}_4[{\left(\frac{P_3}{P_1}\right)}^{n_2-1/n_2}-1]$

where $n_1=1.2R=0.287kJ/kgK$

$T_1=263K,n_2=1.35,T_3=273+30=303K$

$T_4=\frac{T_5}{{\left(\frac{P_2}{P_1}\right)}^{\frac{1.55-1}{1.55}}}=\frac{303}{(6.5{)}^{0.33/1.35}}=186.5K$

$\therefore W_{net}/kg=(\frac{1.2}{1.2-1}\times 0.287\times 263\times \left(\right(5.5{)}^{0.2/1.2}-1))$

$=165.75-129.03=36.72kJ/kg$