Thermodynamics of Steam Homework

In summary, the book is saying that if a boiler has an efficiency of 70%, then it will produce 807.62 kg of steam for each kg of fuel burned.
  • #1
mvf
3
0
Here is the question in my homework, but my response does not correspond with the answer given, even though I worked out the answer that was given backwards and it still does not work:

Determine the quantity of heat required, to raise 7.7 kg of water at 90°C, to saturated steam at 1300 kPa and 71.6% dry.

Here is my attempt at a solution:

First, I checked the steam table for water at 90°C. The (hf) value is 376.92. Then I checked the steam table for saturated steam (hg) at 1300 kPa and that is 2787.6.

Then I subtracted hf from hg (2787.6 - 376.92 = 2410.68. Then I multiplied that by 7.7.
(2410.68 X 7.7 = 18562.24). Then I took 71.6 percent of that number which is 13 290.561 KJ required to raise 7.7 kg of water to saturated steam.

The answer the book is giving is 14248.567 KJ required. Is this a typo or am I making a mistake. I would appreciate any help I can get, thank you.
 
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  • #2
mvf said:
Here is the question in my homework, but my response does not correspond with the answer given, even though I worked out the answer that was given backwards and it still does not work:

Determine the quantity of heat required, to raise 7.7 kg of water at 90°C, to saturated steam at 1300 kPa and 71.6% dry.

Here is my attempt at a solution:

First, I checked the steam table for water at 90°C. The (hf) value is 376.92. Then I checked the steam table for saturated steam (hg) at 1300 kPa and that is 2787.6.

Then I subtracted hf from hg (2787.6 - 376.92 = 2410.68. Then I multiplied that by 7.7.
(2410.68 X 7.7 = 18562.24). Then I took 71.6 percent of that number which is 13 290.561 KJ required to raise 7.7 kg of water to saturated steam.

The answer the book is giving is 14248.567 KJ required. Is this a typo or am I making a mistake. I would appreciate any help I can get, thank you.
Hi mvf. Welcome to physics forums!

In the final state, you have a combination of saturated liquid and saturated vapor. So, you can't just use 71.6 percent of the saturated vapor enthalpy and call that the enthalpy of the mixture. You need to find the enthalpy of the saturated liquid at the final state, and determine the final enthalpy of the mixture by weighting their enthalpies in proportion to their amounts.

Chet
 
  • #3
And put units into your calculations!
 
  • #4
Sorry, I'm not sure how to calculate properly. Can you help me out? I'd appreciate it, thanks.
 
  • #5
mvf said:
Sorry, I'm not sure how to calculate properly. Can you help me out? I'd appreciate it, thanks.
1. Write down the specific enthalpy of the saturated liquid
2. Write down the specific enthalpy of the saturated vapor
3. Multiply specific enthalpy of saturated liquid by (0.284)
4. Multiply specific enthalpy of saturated vapor by (0.716)
5. Add results of 3. and 4. to get specific enthalpy for final equilibrium state
6. Multiply 5. by 7.7 kg
7. Subtract enthalpy in initial state.

Chet
 
  • #6
Here is my next question:

A boiler furnace releases 10800 KJ of heat for each kg of fuel burned and produces dry saturated steam at 10000 kPa from feedwater at 190 degrees C. How many kg of steam will be produced for each kg of fuel burned if the boiler had an efficiency of 70%.

Here is as far as got:
ms(h1 - h2)
Boiler efficiency = ------------------- X 70%
Heating value of the fuel

ms (2724.7 - 807.62)
= ------------------------ X 70%
Heating value of the fuel

I'm not sure where to go from there and I would appreciate any help I could get. Thanks.
 
  • #7
mvf said:
Here is my next question:

A boiler furnace releases 10800 KJ of heat for each kg of fuel burned and produces dry saturated steam at 10000 kPa from feedwater at 190 degrees C. How many kg of steam will be produced for each kg of fuel burned if the boiler had an efficiency of 70%.

Here is as far as got:
ms(h1 - h2)
Boiler efficiency = ------------------- X 70%
Heating value of the fuel

ms (2724.7 - 807.62)
= ------------------------ X 70%
Heating value of the fuel

I'm not sure where to go from there and I would appreciate any help I could get. Thanks.
What they are implying is that 70% of the 10800 kJ is available for supplying heat to the water to make steam. If those h's are the enthalpy of the saturated steam at 10000kPa and the feedwater at 190 C, then the amount of steam produced is equal to the heat made available divided by the increase in enthalpy per kg. Just check the units, and they will tell you how to do many problems.

Chet
 

1. What is steam and how is it used?

Steam is the gaseous form of water that is formed when water is heated to a high enough temperature. It is widely used in many industries, including power generation, heating and cooling systems, and various manufacturing processes.

2. What is thermodynamics and how does it relate to steam?

Thermodynamics is the study of energy and its transformations. In the context of steam, thermodynamics is used to understand and analyze the behavior of steam as it undergoes changes in temperature, pressure, and volume.

3. How is the efficiency of steam engines or turbines calculated?

The efficiency of a steam engine or turbine is calculated using the first and second laws of thermodynamics. The first law states that energy cannot be created or destroyed, only transferred. The second law states that the total entropy of a closed system will always increase over time. By applying these laws, the efficiency of a steam engine or turbine can be determined.

4. What is the difference between saturated and superheated steam?

Saturated steam is steam that is in equilibrium with liquid water at a specific temperature and pressure. Superheated steam is steam that has been heated to a temperature above its boiling point without changing its pressure. Superheated steam contains more energy and is used in high-performance applications.

5. How is the quality of steam determined?

The quality of steam is determined by the amount of water droplets present in the steam. This can be measured using a steam quality meter or by performing a steam quality calculation based on the temperature and pressure of the steam.

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