# Enthalpy change - Using tables to find specific heat

1. Feb 13, 2012

### JJBladester

1. The problem statement, all variables and given/known data

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

2. Relevant 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.

3. 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 cp values listed in this table. This makes no sense to me as $c_{p,avg}$ 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?

2. Feb 13, 2012

### Coushander

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. Feb 13, 2012

### JJBladester

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. Feb 13, 2012

### Coushander

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.

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