Question

2- A 2-m3 insulated tank containing ammonia at -20 C, 80% quality, is connected by a valve to a line flowing ammonia at 2 MPa, 60 C. The valve is opened, allowing ammonia to flow into the tank. At what pressure should the vale be closed if the manufacturer wishes to have 15 kg of ammonia inside at the final state?​

Answer 1

Answer:

The valve should be closed at 1081 kPa ⇒ 11 bar

Explanation:

$Q_{C_V} + m_ih_i = m_2u_2 - m_1u_1 + W_{C_V}$

$Q_{C_V} = W_{C_V} = 0$

$m_1 = \frac{V}{v_1} = \frac{2}{0.49927} = 4.006 kg$

$m_i = m_2 - m_1 = 15 - 4.006 = 10.994 kg$

$u_1 = 1057.5, h_i = 1509.9$

$u_2 = m_ih_i + m_1u_1$

$m_2 = \frac{[10.994*1509.9] + [4.006*1057.5]}{15} = 1389.1 kJ/kg$

$v_2 = \frac{V}{m_2} = \frac{2}{15} = 0.1333 m^3/kg$

Therefore, v₂, u₂ fix state 2.  

​By trial and error, P₂ = 1081 kPa & T₂ = 50.4° C

1081 kPa ⇒ 11 bar