Energy Balance for closed rigid container

In summary, the problem involves heating initially saturated vapor in a closed, rigid container until its temperature reaches 400 °C. The specific volume of the vapor remains constant throughout the process. To find the internal energy at the final state, linear interpolation is used with the available superheated vapor tables. Different tables may have different pressure increments, so it is important to find the table with a pressure value closest to the given specific volume at the given temperature. The formula used for linear interpolation is (v1-v)/(v1-v2)=(u2-u)/(u1-u2), where v1 and u1 are the specific volume and internal energy at the initial state, and v2 and u2 are the specific volume and internal energy at the
  • #1
jdawg
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Homework Statement


Water, initially saturated vapor at 4 bar, fills a closed, rigid container, The water is heated until its temperature is 400C. For the water, determine the heat transfer in KJ per kg of water .

Homework Equations

The Attempt at a Solution


Assume potential and kinetic energy=0, W=0,Steady state

I got the energy balance right: Q/m=(u2-u1)

Found v1 and u1 from steam tables:
specific volume: v1=v2=0.4625 m3/kg
u1 = 2553.6 KJ/kg

I know that state two is super heated, but how do I know what the pressure is?? What values do I interpolate with to get u2??
 
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  • #2
jdawg said:

Homework Statement


Water, initially saturated vapor at 4 bar, fills a closed, rigid container, The water is heated until its temperature is 400C. For the water, determine the heat transfer in KJ per kg of water .

Homework Equations

The Attempt at a Solution


Assume potential and kinetic energy=0, W=0,Steady state

I got the energy balance right: Q/m=(u2-u1)

Found v1 and u1 from steam tables:
specific volume: v1=v2=0.4625 m3/kg
u1 = 2553.6 KJ/kg

I know that state two is super heated, but how do I know what the pressure is?? What values do I interpolate with to get u2??
Well, you have a closed, rigid container. What does that tell you about the kind of heating process which is going on when the vapor is heated to 400° C?
 
  • #3
I'm not really sure, the change in internal energy is what causes the increase in heat? Or is there an increase in temperature because the pressure increases?
 
  • #4
jdawg said:
I'm not really sure, the change in internal energy is what causes the increase in heat? Or is there an increase in temperature because the pressure increases?
Think about the container.

It's rigid, so does its volume change with increasing pressure inside? Does the amount of water inside change while it is being heated?

So what property must be the same at the start of heating and when it is finished?
 
  • #5
I know the specific volume is constant, but I'm still confused about how to do the interpolating. I guess I'm supposed to use specific volume and internal energy to interpolate? I'm really lost at this part.
 
  • #6
jdawg said:
I know the specific volume is constant, but I'm still confused about how to do the interpolating. I guess I'm supposed to use specific volume and internal energy to interpolate? I'm really lost at this part.
How can you use the internal energy to interpolate? Isn't that what you're looking for, the internal energy of the vapor after it has been superheated?

If you know the specific volume is constant, what does this tell you about finding the properties of the superheated vapor?
 
  • #7
I really don't know :( In the solution I have they used the table p=5bar and p=10 bar to interpolate. I don't understand how they knew to use these tables.
 
  • #8
But then another solution said to use p=5bar and p=7bar instead...
 
  • #9
jdawg said:
I really don't know :( In the solution I have they used the table p=5bar and p=10 bar to interpolate. I don't understand how they knew to use these tables.

jdawg said:
But then another solution said to use p=5bar and p=7bar instead...

Different steam tables are tabulated differently. Some may tabulate superheated properties for pressure increments of 5 bar, some for closer increments of pressure.

You've answered your own question, and apparently you don't realize it. If the vapor has a constant specific volume, that's the property you search for when interpolating the superheated vapor tables at T = 400° C.
 
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  • #10
I think both solutions are using the same tables. What you said makes sense, so I just look for the pressure table that has a value close to my constant specific volume at my given temperature.

What formula are they using here though: (0.4397-0.4625)/(0.4397-0.6173)=(2960.9-u2)/(2960.9-2963.2)
I feel like this is different than the formula I was given to use.
 
  • #11
jdawg said:
I think both solutions are using the same tables. What you said makes sense, so I just look for the pressure table that has a value close to my constant specific volume at my given temperature.

What formula are they using here though: (0.4397-0.4625)/(0.4397-0.6173)=(2960.9-u2)/(2960.9-2963.2)
I feel like this is different than the formula I was given to use.
It looks like someone is using linear interpolation to find the value of u for T = 400 °C and v = 0.4625 m3 / kg

https://en.wikipedia.org/wiki/Linear_interpolation

Check the property values in the superheated vapor table.
 
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  • #12
Thanks so much!
 

What is energy balance for a closed rigid container?

Energy balance for a closed rigid container is the principle that states energy cannot be created or destroyed within a closed system. This means that the total amount of energy within the container remains constant, and any changes in energy must be accounted for.

Why is energy balance important for a closed rigid container?

Energy balance is important for a closed rigid container because it allows us to understand and predict the behavior of the system. By keeping track of the energy entering and leaving the container, we can determine how the container will respond to different conditions.

What are the types of energy involved in energy balance for a closed rigid container?

The types of energy involved in energy balance for a closed rigid container include thermal energy, mechanical energy, chemical energy, and nuclear energy. These forms of energy can be converted from one to another, but the total amount remains the same.

How is energy balance calculated for a closed rigid container?

Energy balance for a closed rigid container is calculated by adding up all the energy inputs and subtracting all the energy outputs. This can be represented by the equation: Energy input = Energy output + Energy stored.

What factors can affect energy balance in a closed rigid container?

Several factors can affect energy balance in a closed rigid container, including changes in temperature, pressure, and the addition or removal of substances. Any change in the container's surroundings or contents can impact the energy balance within the system.

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