Solving a Rankine Cycle Problem with 45MW Output

In summary, the question asks for the temperature rise of the cooling water in a steam power plant operating on a simple Rankine cycle. The equation Q=m.Cp.DT can be used to calculate this, using the values for heat transfer, mass flow rate, and temperature difference between inlet and outlet. The specific heat capacity of the cooling water can be calculated using the equation Cp = Cpv + mCpl, using values from tables or online.
  • #1
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Homework Statement



Can anyone help with this particular question

Using a steam power plant that operates on a simple rankine cycle and has a net power output of 45MW. Steam enters the turbine at 70 bar and 500 degrees c and is cooled in the condenser at a pressure of 110kPa by running cooling water, from a lake through tubes to the condenser at a rate of 2000kg/sec. Determine:

The temperature rise of the cooling water?

The Attempt at a Solution



I have calculated the thermal efficiency of the cycle to be at 39% and the mass flow rate of steam to be at 36 kg/sec. Should i be using the equation Q=m.Cp.DT? to calculate the temp rise of the cooling water?...I know all enthalpy figures at each state of the cycle -

h1=3410
h2=2153
h3=192
h4=199

but am still having difficulty knowing what equations to use and what to put in?

Thanks.
 
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  • #2


I would be happy to assist you with this question. Based on the information provided, the equation Q=m.Cp.DT is indeed the correct one to use in order to calculate the temperature rise of the cooling water. This equation calculates the heat transfer from the steam to the cooling water, where Q is the heat transfer, m is the mass flow rate of the cooling water, Cp is the specific heat capacity of the cooling water, and DT is the temperature difference between the inlet and outlet of the cooling water.

In order to calculate the specific heat capacity of the cooling water, you can use the equation Cp = Cpv + mCpl, where Cpv is the specific heat capacity of water vapor and Cpl is the specific heat capacity of liquid water. The values for these can be found in tables or online. Once you have calculated Cp, you can then plug in the values for Q, m, and DT to solve for the temperature rise of the cooling water.

I hope this helps. Let me know if you have any further questions or if you need clarification on any of the equations or values. Good luck with your calculations!
Scientist
 
  • #3


I would suggest using the First Law of Thermodynamics to solve this Rankine cycle problem. This law states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the system is the steam power plant and the heat added is the energy from the steam entering the turbine and the work done is the power output of 45MW.

To calculate the temperature rise of the cooling water, you can use the equation Q=m*Cp*DT, where Q is the heat added, m is the mass flow rate of the cooling water, Cp is the specific heat capacity of water, and DT is the temperature rise. You already have the mass flow rate of the steam, so you can use this equation to solve for DT.

Additionally, you can also use the enthalpy values at each state of the cycle to calculate the heat added and the work done. The enthalpy values can be used to calculate the specific heat of the steam at each state, which can then be used in the First Law of Thermodynamics equation.

I would also suggest checking your calculations and units to ensure accuracy. It is important to use the correct units and equations when solving thermodynamics problems. If you are still having difficulty, I would recommend seeking assistance from a professor or a colleague with expertise in thermodynamics.
 

1. What is a Rankine cycle problem with 45MW output?

A Rankine cycle problem with 45MW output refers to a thermodynamic cycle used to generate power in a steam turbine, with an output of 45 megawatts (MW). This type of problem is commonly encountered in the field of engineering and energy production.

2. How is a Rankine cycle problem with 45MW output solved?

Solving a Rankine cycle problem with 45MW output involves using thermodynamic equations and principles to calculate the various parameters involved in the cycle, such as temperature, pressure, and heat transfer. This can be done manually or with the help of computer software.

3. What factors affect the output of a Rankine cycle problem?

The output of a Rankine cycle problem can be affected by several factors, including the efficiency of the steam turbine, the temperature and pressure of the steam, and any losses in the system due to friction or heat transfer. The choice of working fluid and design of the cycle also play a role in the output.

4. What are the applications of solving a Rankine cycle problem with 45MW output?

Solving a Rankine cycle problem with 45MW output is important in the design and optimization of power plants and other energy generation systems. It can also be used to analyze and improve the performance of existing systems, as well as in research and development of new technologies.

5. What are some challenges in solving a Rankine cycle problem with 45MW output?

Some challenges in solving a Rankine cycle problem with 45MW output include accurately modeling the complex thermodynamic processes involved, accounting for real-world limitations and losses, and ensuring the safety and efficiency of the system. Additionally, variations in operating conditions and changes in design parameters can also present challenges in solving these types of problems.

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