Heat Capacity Ratio of Water at 1000°C | 1273.15K

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In summary, the person is trying to find the heat capacity ratio of water at 1000C or 1273.15K, specifically for a rocket engine design. They have tried to find it through various websites but have only found information up to 375C. They mention that the heat capacities can be calculated using Cp/R = a1 + a2 T + a3 T^2 + a4 T^3 + a5 T^4 and that the coefficients can be found in the thermodynamic database. They also provide the coefficients for the H2O entry in the database and mention that they are familiar with using E format for representing powers of 10.
  • #1
dbmorpher
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Hello,
I am trying to find the heat capacity ratio of water at 1000C or 1273.15K.
I have tried to find it through various website but have yet to find anything past 375C. I could find the gamma if I was given any of the two types of heat capacity ratios (volumetric or pressure) I could get it myself. I would like to find this out because it is useful for a rocket engine I am trying to design.
 
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  • #2
The heat capacities are known from experiments and documented in the NASA polynomial databases, e.g. here:
http://www.me.berkeley.edu/gri-mech/data/nasa_plnm.html

There, you see that heat capacity can be calculated using
Cp/R = a1 + a2 T + a3 T^2 + a4 T^3 + a5 T^4
where the coefficients a are given in the thermodynamic database:
http://www.me.berkeley.edu/gri-mech/version30/files30/thermo30.dat

In the thermodynamic database mentioned there, the H2O entry is:
H2O L 8/89H 2O 1 G 200.000 3500.000 1000.000 1
3.03399249E+00 2.17691804E-03-1.64072518E-07-9.70419870E-11 1.68200992E-14 2
-3.00042971E+04 4.96677010E+00 4.19864056E+00-2.03643410E-03 6.52040211E-06 3
-5.48797062E-09 1.77197817E-12-3.02937267E+04-8.49032208E-01 4

the coefficients a1..a5 for the high temperature range 1000 K - 3500 K are given in line 2
 
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  • #3
bigfooted said:
The heat capacities are known from experiments and documented in the NASA polynomial databases, e.g. here:
http://www.me.berkeley.edu/gri-mech/data/nasa_plnm.html

There, you see that heat capacity can be calculated using
Cp/R = a1 + a2 T + a3 T^2 + a4 T^3 + a5 T^4
where the coefficients a are given in the thermodynamic database:
http://www.me.berkeley.edu/gri-mech/version30/files30/thermo30.dat

In the thermodynamic database mentioned there, the H2O entry is:
H2O L 8/89H 2O 1 G 200.000 3500.000 1000.000 1
3.03399249E+00 2.17691804E-03-1.64072518E-07-9.70419870E-11 1.68200992E-14 2
-3.00042971E+04 4.96677010E+00 4.19864056E+00-2.03643410E-03 6.52040211E-06 3
-5.48797062E-09 1.77197817E-12-3.02937267E+04-8.49032208E-01 4

the coefficients a1..a5 for the high temperature range 1000 K - 3500 K are given in line 2

Thank you for the help bigfooted but I am sorry to say that I don't really understand the differences in the different a# coeffficients. I understand what to do with them but do not really know which a is which
 
  • #4
dbmorpher said:
Thank you for the help bigfooted but I am sorry to say that I don't really understand the differences in the different a# coeffficients. I understand what to do with them but do not really know which a is which

a1=3.03399249E+00
a2=2.17691804E-03
a3=-1.64072518E-07
a4=9.70419870E-11
a5=1.68200992E-14

You are familiar with E format for representing powers of 10, correct?
 
  • #5
Yes I am Chestermiller thank you for clarifying the constants for me.
 

1. What is the heat capacity ratio of water at 1000°C?

The heat capacity ratio of water at 1000°C, also known as the specific heat ratio, is approximately 1.065. This means that at 1000°C, water has a slightly higher heat capacity than at lower temperatures.

2. How is the heat capacity ratio of water at 1000°C calculated?

The heat capacity ratio is calculated by dividing the specific heat at constant pressure by the specific heat at constant volume. In the case of water at 1000°C, this is approximately 1.065.

3. Why is it important to know the heat capacity ratio of water at 1000°C?

Knowing the heat capacity ratio of water at 1000°C is important in various industrial and scientific applications. It can help in determining the amount of energy required to heat or cool water, as well as in the design of equipment that involves high temperatures and water as a coolant.

4. Does the heat capacity ratio of water at 1000°C change with pressure?

Yes, the heat capacity ratio of water can change with pressure. At low pressures, water has a heat capacity ratio close to 1, but as pressure increases, the heat capacity ratio also increases. At 1000°C, the heat capacity ratio of water is typically between 1.06 and 1.07 at atmospheric pressure.

5. How does the heat capacity ratio of water at 1000°C compare to other substances?

The heat capacity ratio of water at 1000°C is relatively high compared to other substances. For example, at the same temperature, the heat capacity ratio of air is approximately 1.4, while for metals it can range from 1.1 to 1.3. This high heat capacity ratio of water makes it an effective coolant in various industrial processes.

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