Thermal Dynamics

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Thermal Dynamics

thermal dynamics problem?

An 85m^3 rigid vessel contains 10 kg of water (both liquid and vapor in thermal equilibrium at a pressure of 0.01 MPa). Calculate the volume and mass of both the liquid and vapor. Thanks

answer in the back of the book is:
liquid 0.00425m^3 4.21 Kg
Vapor 84.996 m^3 5.79 Kg

Look for a steam table.
e.g. http://www.efunda.com/Materials/water/steamtable_sat.cfm

From this you get the specific volumes of vapor and liquid in thermal equilibrium at that pressure.
For p = 0.01MPa = 10kPa
v_l = 0.0010103 m³/kg
v_v = 14.670 m³/kg

The volumes of liquid and vapor sum up to the total internal volume of the vessel:
V_t = V_l + V_v = m_l?v_l + m_v?v_v
with V = 85m³

Moreover you know the total mass of water in the vessel
m_t = m_l + m_v
with m = 10kg

Hence,
m_l = m_t - m_v
=>
V = (m_t - m_v)?v_l + m_v?v_v
<=>
V = m_t ?v_l + m_v?(v_v - v_l)
=>
m_v = (V - m_t ?v_l) / (v_v - v_l)
= (85m³ - 10kg ? 0.0010103 m³/kg) / (14.67 m³/kg - 0.0010103 m³/kg)
= 5.79 kg
=>
m_l = m_t - m_v = 10kg - 5.79kg = 4.21kg

=>

V_l = m_l ? v_l = 4.21 ? 0.0010103 m³/kg = 0.00425 m³
V_g = V - V_l = 85m³ - 0.00425 m³ = 84.996m³

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