Question

The pressure, temperature and velocity of air flowing in pipe are 5 bar, 500 K and 50m/s, respectively. The specific heats of air at a constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of he air stream is

• A. 170
• B. 191
• C. 187
• D. 213

Answer 1

The correct option is C 187

(b)
$P_0=100kPa,T_0=300K$
Available energy
$=(h_1-h_0)-T_0(s_1-s_0)+(\frac{v_1^2}{2}-\frac{v_2^2}{2})$
where, $s_1-s_0=c_{p}In\frac{T_1}{T_0}-RIn\frac{p_1}{p_0}$ $(V_2=0)$
$=1.005In\left(\frac{500}{300}\right)-0.287In\left(\frac{5}{1}\right)$
$=0.05147kJ/kgK$
$\therefore$ Available energy
$=1.005(500-300)-300\left(0.5147\right)+\frac{(50{)}^2}{2}\times {10}^{-3}$
$=186.8kJ/kg\approx 187kJ/kg$