Question

Problem 3. (10 points) A closed and insulated rigid tank (perfectly insulated) is initially divided into halves by a separator. On one side of the separator is 1 m of air at 300 K, 2 bar. On the other side is 1 m of air at 500 K, 1 bar. The separator is removed, and the air from the two sides mixes and reaches equilibrium state Please treat the air as ideal gas with cp-1.001 kJ/kg K and c0.714 kJ/kg K. Determine: (a) (b) (c) the final temperature, in K. the final pressure, in bar. the amount of entropy generated by this mixing. Separa tor o 0 ar 2 bah

Answer 1

C_p = 1.001197 kh k C_v = 0.7141511 kg k C_1 = 0.714 at 300 k C_2 = 0.742 at 500 k a) p_1 v_1 = m_1 R T_1 m_1 = p_1 v_1/R T_1 = 200 times 1/0.227 times 300 p_1 = 2 bar = 200 k pa m_1 = 0.2.322 kg P_2 = 1 bar = 100 K Pa P_2 V_2 = m_2 R T_2 m_2 = p_2 v_2/m R T_2 = 100 times 1/0.207 times 500 m_2 = 0.696 Kg T_f = m_1 c_1 T_1 + m_2 c_2 T_2/m_1 c_1 + m_2 c_2 = 2.322 times 0.714 times 300 + 0.696 times 0.742 times 500/2.312 times 0.714 + 0.696 times 0.742 = T_f = 347.5 k final temperature (c) (Delta s) generation = (Delta s) system + (Delta s) surrounding = (Delta s) system O (Delta s) generation = m_1 c_1 Ln T_f/T_1 + m_2 c_2 L T_f/T_2 = 2.322 times 0.714 Ln (347.5/300) + 0.696 times 0.742 Ln (347.5/500) (Delta s) generation = 0.2436 - 0.187 = 0.0557 b) final pressure v_f =