Team with a quality of 0.7, pressure of 1.5 bar, and flow rate of 10 kg/s enters a steam separator operating at steady state. Sat-urated vapor at 1.5 bar exits the separator at state 2 at a rate of 6.9 kg/s while saturated liquid at 1.5 bar exits the separator at state 3. Neglect-ing kinetic and potential energy effects, determine the rate of heat transfer, in kW, and its associated direction.

Explanation:

The model for the separator is obtained after applying the First Law of Thermodynamics:

The rate of the heat transfer is:

The specific enthalpies of each state are, respectivelly:

-222.649 kW

Explanation:

The first step to solve this problem is to use the first law of thermodynamics:

Note that Q, W, and m represent rate of heat transfer, rate of work, and mass flow rate.

This reduces to:

This equation can be rearranged to solve for rate of heat transfer (Q):

The enthalpy values for this problem can be found from tables. From Fundamentals of Engineering Thermodynamics 9th Edition, the table used was Table A-3: Properties of Saturated Water (Liquid-Vapor): Pressure Table.

The value for is found by using the equation

kJ/kg

The value for is the value for at 1.5 bar due to it being saturated vapor.

= 2693.6 kJ/kg

The value for is the value for at 1.5 bar due to it being saturated liquid.

= 467.11 kJ/kg

Now these values can be substituted back into the equation solving for Q:

Note that kg/s

The equation solving for Q becomes:

kW

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