Temperature Rise of the cooling water

[shaiqbashir]

Hi Guys!

well! I am studying vapor powered cycles nowadays. The topic which I am studying currently is The Rankine Cycle. I came across a question in my book . which i want you to help me out.

It is said that in the rankine cycle, in the condenser, 2000 kg/s of cooling water is used to cool a 36 kg/s of working fluid in each cycle.

Now it is asked to find the temperature rise of the cooling water. Now i know the pressure of the fluid after condensation that is 10 kPa. Now please tell me the way to find it out. I am not asking to solve me the question, just asking any hint so that i may be able to do it. Please help me as soon as possible,

 

[Q_Goest]

In this and all similar analysis, you want to apply the first law of thermodynamics. Drawing control volumes around parts of the system will help to simplify things so you can better apply the first law.

Draw a control volume (CV) around each of the two fluids as they pass each other exchanging heat. You should be able to think of 2 control volumes, one around the water, one around the other fluid. Each of these control volumes has mass flow in, mass flow out, and either heat going in or out.

Applying the first law to each CV, you should notice the following:
1. Kinetic and potential energy can be neglected. This is generally true but you can check it if you have any doubt.
2. There is no fluid stored inside either control volume, so the change in internal energy is zero.
3. There is no work done by or on either control volume.

Once you do this, you should have mass going into each CV which is your enthalpy going in or energy entering the CV. You will also have mass leaving each CV which is the enthalpy going out or energy leaving the CV.

Next, you will have thermal energy either entering or leaving each CV. Energy is entering the water making it hotter, and leaving the other fluid making it cooler.

Now all you need to do is tally up the energy. All energy entering the CV should equal all energy leaving the CV.

One of the problems most students run into is how you calculate the enthalpy. In industry, we have data bases that you can put pressure and temperature in and get enthalpy out. Or you can put enthalpy and pressure in and get temperature out, etc… But you can also calculate enthalpy by using specific heat and temperature.

 

[ravenprp]

Hi there!

The temperature rise of the cooling water can be calculated using the heat balance equation: mCpΔT = Q, where m is the mass flow rate of the cooling water, Cp is the specific heat capacity of water, ΔT is the temperature rise, and Q is the heat transfer rate.

To find Q, you can use the energy balance equation for the condenser: Q = m' (h1 - h2), where m' is the mass flow rate of the working fluid and h1 and h2 are the specific enthalpies of the fluid at the inlet and outlet of the condenser, respectively.

Once you have Q, you can plug it into the heat balance equation and solve for ΔT. Just make sure to convert all units to a consistent system (e.g. SI units) before plugging them into the equations.

I hope this helps! Let me know if you have any further questions. Good luck with your studies!