Enthelpy change - Using tables to find specific heat

In summary, The change in enthalpy of argon, in KJ/kg, when cooled from 100 to 25 °C is 39.0 KJ/kg. The specific heat used for the calculation is an average value at 300 K, likely for the sake of convenience on the part of the textbook publisher.
  • #1
JJBladester
Gold Member
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Homework Statement



Calculate the change in the enthalpy of argon, in KJ/kg, when it is cooled from 100 to 25 °C.

Homework Equations



[tex]\Delta h = c_{p} \Delta T[/tex]

Where [itex]\Delta h[/itex] is the change in enthalpy, [itex]c_{p}[/itex] is the specific heat, and [itex]\Delta T[/itex] is the change in temperature.

The Attempt at a Solution



[tex]\Delta h = c_{p,avg} \Delta T[/tex]

[tex]\Delta h_{argon} = c_{p,avg} \Delta T=\left (.5203\frac{kJ}{kg\cdot C} \right )\left (100 C-25C \right )=39.0\frac{kJ}{kg}[/tex]

My book has a table at the back that is labeled Ideal-gas specific heats of various common gases at 300 K. The answer given to this question uses the cp values listed in this table. This makes no sense to me as [itex]c_{p,avg}[/itex] would be (cp at T1 + cp at T2)/2.

How can the book use the values from a table where cp values are given for temperature at 300 K?
 
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  • #2
How can the book use the values from a table where cp values are given for temperature at 300 K?

Are you asking why they would use the cp value for 300K for the solution? That'd be just cause they're lazy and don't actually expect you to know what the specific heat at 373K and at 298K is.

Or are you asking how they can generate a cp average value at 300K in the first place? They'd do that by conducting experiments to generate cp values at 300K and averaging those out.
 
  • #3
Coushander said:
Are you asking why they would use the cp value for 300K for the solution? That'd be just cause they're lazy and don't actually expect you to know what the specific heat at 373K and at 298K is...

Yes, I'm asking why the solution to this problem is for cp at a temperature completely unrelated to the temperatures in the problem. Is it that the average of the temperatures (336K) can be reasonably approximated to be 300K with little error?
 
  • #4
JJBladester said:
Yes, I'm asking why the solution to this problem is for cp at a temperature completely unrelated to the temperatures in the problem. Is it that the average of the temperatures (336K) can be reasonably approximated to be 300K with little error?

I'm assuming that it's a textbook. As I said, it's likely for the sake of convenience on the part of the publisher, because it wouldn't be realistic to publish a huge list of specific heats for every molecule at different temperatures. The list would be astronomical. It's easier and cheaper for them to standardize only one value for the molecule and then write their textbook questions in a range where that standard is reasonably applicable.
 
  • #5


I would suggest double checking the values used in the book and ensuring they are correct. It is possible that the table in the book is using a different unit of measurement or a different reference temperature. If the values are indeed correct, then it is possible that the book is assuming an ideal gas behavior for argon, where the specific heat remains constant regardless of temperature. However, this assumption may not be accurate for all gases, and it would be important to clarify this with the book or consult other sources for more accurate values. Additionally, it would be beneficial to understand the reasoning behind using the average specific heat instead of the individual values at each temperature. Overall, it is important to critically evaluate and question any discrepancies in scientific calculations and seek clarification when needed.
 

1. How is specific heat calculated using tables?

The specific heat of a substance can be calculated by using a table that lists the specific heat values for different substances. The specific heat value for a particular substance can be found by locating the substance within the table and using the corresponding value.

2. Why is specific heat important in thermodynamics?

Specific heat is an important concept in thermodynamics because it helps us understand how much energy is required to raise the temperature of a substance. It also allows us to compare the heat absorption or release capabilities of different substances.

3. Can specific heat change for a substance?

Yes, the specific heat of a substance can change under different conditions such as temperature, pressure, and phase. This is because the amount of energy required to raise the temperature of a substance can vary depending on these factors.

4. How does specific heat affect heat transfer?

The specific heat of a substance is directly related to how much heat energy is required to raise its temperature. A substance with a higher specific heat will require more energy to increase its temperature, while a substance with a lower specific heat will require less energy. This can affect the rate of heat transfer between substances.

5. What units are used to measure specific heat?

The SI unit for specific heat is Joules per kilogram Kelvin (J/kgK). However, it can also be measured in other units such as calories per gram Celsius (cal/g°C) or British thermal units per pound Fahrenheit (BTU/lb°F).

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