Another nasty question, RE: superheated wet steam?

[nickbone59]

Homework Statement

A gas fired superheater takes wet steam at a pressure of 40 bar and a dryness fraction of 0.95 and heats it isobarically such that it leaves at 380c. Assuming no losses occur, sketch the process on a ts diagram and determine;

i)the rise in specific entropy through the superheater
ii)the necessary rate of heat transfer to the steam, neglecting kinetic and potential energy changes, if the steam flowrate is 1.2 Kg/s
iii)the volumetric flow rate of gas in m^3/hr needed to fire the super heater, if combustion is 100% efficient and the gas has a calorific value (LCV) of 17,500 kJ/m^3
iv)the annual cost of firing the superheater if the combustion efficiency is now 85% and the gas costs 2.1p/m^3

Homework Equations

Don't know where to start or what equations to use?

The Attempt at a Solution

Haven't got a clue, searched the internet for similar examples or relevant equation, nothing in my notes either or in the books i have from the library!
HELP! please.

 

[KataKoniK]

Thank you for your post. I am happy to help you with your problem. To start, we need to understand the basic concepts involved in this process. A superheater is a device that is used to increase the temperature of steam above its saturation point. In your problem, the wet steam enters the superheater at a pressure of 40 bar and a dryness fraction of 0.95. This means that the steam is mostly in vapor form with a small amount of liquid water.

To solve this problem, we will use the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. We will also use the ideal gas law, which relates the pressure, volume, and temperature of a gas. This law can be written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature.

Now, let's draw the process on a T-s diagram. The T-s diagram is a graph that shows the temperature and specific entropy of a substance. The process can be represented by a straight line on the T-s diagram, as the pressure and dryness fraction remain constant. The initial state of the steam is at point A (40 bar, 0.95 dryness fraction) and the final state is at point B (380°C, 0.95 dryness fraction). The rise in specific entropy through the superheater can be calculated by finding the difference between the specific entropy of point B and point A.

Next, we need to calculate the necessary rate of heat transfer to the steam. This can be done using the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system. In this case, we can neglect the work done by the system as it is isobaric (constant pressure) and assume no losses occur. Therefore, the heat transfer to the steam can be calculated as Q = mΔU, where m is the mass flow rate of steam and ΔU is the change in internal energy. You can use the ideal gas law to find the change in internal energy.

To determine the volumetric flow rate of gas needed to fire the superheater, we

 

[piercas]

Dear student,

Thank you for your question. I understand your frustration when faced with a complex problem and not knowing where to start. However, it is important to remember that problem-solving is a crucial skill in science and it requires breaking down the problem into smaller, manageable parts.

To begin with, let's start by defining some key terms in the problem. Superheated wet steam is a type of steam that is heated above its boiling point without losing its liquid form. This means that it still contains some water droplets, hence the term "wet". The process of heating this steam is called superheating and it is done isobarically, meaning at a constant pressure.

Now, let's address the first part of the question: sketching the process on a ts diagram and determining the rise in specific entropy. A ts diagram, also known as a temperature-entropy diagram, is a graphical representation of the thermodynamic processes of a substance. It shows the relationship between temperature and entropy, and is commonly used to analyze and visualize the performance of thermodynamic systems. To sketch the process on a ts diagram, you will need to plot the initial state of the steam (given by the pressure and dryness fraction) and the final state (given by the temperature). This will give you a line on the ts diagram, representing the process of superheating the steam. To determine the rise in specific entropy, you will need to use the Clausius-Clapeyron equation, which relates the change in entropy to the heat transfer and temperature. This will give you the answer to the first part of the question.

Moving on to the second part of the question, we need to determine the necessary rate of heat transfer to the steam. This can be calculated using the specific heat capacity of water and the change in temperature of the steam. Since we are neglecting kinetic and potential energy changes, we can use the equation Q=mCpΔT, where Q is the heat transfer, m is the mass flow rate of steam, Cp is the specific heat capacity of water, and ΔT is the change in temperature. This will give you the answer in joules, so you will need to convert it to the appropriate units.

For the third part of the question, we need to calculate the volumetric flow rate of gas needed to fire the superheater. This can be done by using the ideal gas law, which relates the volume of a gas