Answer to Question #117834 in Mechanical Engineering for Solomon Akahkuh

Question

Two tanks A and B contain 1 kg of air at 1 bar, 50oC and 3 bar, 50oC when
atmosphere is at 1 bar, 15oC. Identify the tank in which stored energy is
more. Also find the availability of air in each tank.

Answer 1

The tank B (3 bar, 50°C) has more stored energy.

The availability of the system is

$a=m((u_1-u_0)-T_0(s_1-s_0))=m(c_v(T_1-T_0)-T_0\Delta s)$

$\Delta s_A=c_p\ln\frac{T_1}{T_0}-R\ln\frac{p_1}{p_0}=1.005\ln\frac{50+273}{15+273}-0.287\ln\frac{1}{1}=0.115 \frac{kJ}{kg\cdot K}$

$a_A=m(c_v(T_1-T_0)-T_0\Delta s_A)=1(0.718(323-288)-288\cdot0.115)=-7.99kJ$

$\Delta s_B=c_p\ln\frac{T_2}{T_0}-R\ln\frac{p_2}{p_0}=1.005\ln\frac{50+273}{15+273}-0.287\ln\frac{3}{1}= -0.2\frac{kJ}{kg\cdot K}$

$a_B=m(c_v(T_2-T_0)-T_0\Delta s_B)=1(0.718(323-288)-288\cdot(-0.2))=82.73kJ$