Question

A rigid tank initially contains 1.4 kg saturated liquid water at 200◦C. At this state, 25 percent of the volumeis occupied by water and the rest by air. Now heat is supplied to the water until the tank contains saturatedvapor only. Determine (a) the volume of the tank, (b) the finaltemperature and pressure, and (c) the internalenergy change of the water.

Answer 1

Answer:

given,

liquid water in the rigid tank = 1.4 kg

The saturated liquid properties of water at 200◦C are

$v_f = 0.001157 m^3/s\ and \ u_f = 850.46 kJ/kg$

a) tank initially contains saturated liquid and water so, volume occupied by water

$V_1 = m v_1$

      = 1.4 × 0.001157

      = 0.001619 m³

total volume =

         = $\dfrac{1}{0.25}\times 0.001619$

         = $0.006476 m^3$

b)$v_2 = \dfrac{V}{m} =\dfrac{0.006476}{1.4}$

          =0.004626 kg/m³

for v₂ = 0.004626 kg/m³

T₂ = 371.3 ⁰C  P₂ = 21,367 kPa  u₂ = 2201.5 kJ/kg

c) total internal energy

$\Delta U = m(u_2-u_1)$

              = 1.4 (2201.5 - 850.46) kJ/kg

              = 1892 kJ