A rigid 10-L vessel initially contains a mixture of liquid and vapor water at 100 °C, with a quality factor of 0.123. The mixture is heated until its temperature is 150 °C. Calculate the heat transfer required for this process. This is problem 4-31 from the textbook.

The vessel is modelled after the First Law of Thermodynamics. Let suppose the inexistence of mass interaction at boundary between vessel and surroundings, changes in potential and kinectic energy are negligible and vessel is a rigid recipient.

[tex]Q_{in} = U_{2} - U_{1}[/tex]

Properties of water at initial and final state are:

State 1 - (Liquid-Vapor Mixture)

[tex]P = 101.42\,kPa[/tex]

[tex]T = 100\,^{\textdegree}C[/tex]

[tex]\nu = 0.2066\,\frac{m^{3}}{kg}[/tex]

[tex]u = 675.761\,\frac{kJ}{kg}[/tex]

[tex]x = 0.123[/tex]

State 2 - (Liquid-Vapor Mixture)

[tex]P = 476.16\,kPa[/tex]

[tex]T = 150\,^{\textdegree}C[/tex]

[tex]\nu = 0.2066\,\frac{m^{3}}{kg}[/tex]

[tex]u = 1643.545\,\frac{kJ}{kg}[/tex]

[tex]x = 0.525[/tex]

The mass stored in the vessel is:

[tex]m = \frac{V}{\nu}[/tex]

[tex]m = \frac{10\times 10^{-3}\,m^{3}}{0.2066\,\frac{m^{3}}{kg} }[/tex]

[tex]m = 0.048\,kg[/tex]

The heat transfer require to the process is:

[tex]Q_{in} = m\cdot (u_{2}-u_{1})[/tex]

[tex]Q_{in} = (0.048\,kg)\cdot (1643.545\,\frac{kJ}{kg} - 675.761\,\frac{kJ}{kg} )[/tex]

[tex]Q_{in} = 46.454\,kJ[/tex]