Enthelpy change - Using tables to find specific heat

[JJBladester]

Homework Statement

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

Homework Equations

$$\Delta h = c_{p} \Delta T$$

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

The Attempt at a Solution

$$\Delta h = c_{p,avg} \Delta T$$

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

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 c_p values listed in this table. This makes no sense to me as $c_{p,avg}$ would be (c_p at T₁ + c_p at T₂)/2.

How can the book use the values from a table where c_p values are given for temperature at 300 K?

 

[Coushander]

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 c_p 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 c_p average value at 300K in the first place? They'd do that by conducting experiments to generate c_p values at 300K and averaging those out.

 

[JJBladester]

Are you asking why they would use the c_p 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 c_p 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?

 

[Coushander]

Yes, I'm asking why the solution to this problem is for c_p 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.

 

[asteriatic]

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.