# Determining properties of air

Is there any way to theoretically obtain values of specific volume, internal energy, enthalpy and entropy of air, assuming it's an ideal gas?

Can it be done using ideal gas laws?

• Do you mean changes ($\Delta$) in these properties? Aug 13, 2020 at 8:37
• Well, really, I want an explanation. How does one calculate these. To answer your question, sir––yes.
– Qwin
Aug 13, 2020 at 8:50
• @bobd Sir, do you think there is a way?
– Qwin
Aug 13, 2020 at 10:11
• Sure. See my answer. Aug 13, 2020 at 12:35

You can determine such properties by combining the ideal gas law with the first and/or second laws.

For example, by combining the ideal gas law and the first law of thermodynamics, you can show that, for any process, the change in specific internal energy is a function of temperature only according to

$$\Delta u=c_{V}\Delta T$$

For the derivation see here: $\Delta U$, $C_p$, $C_v$ for an ideal gas process

In a similar way you can show, for air as an ideal gas and a constant pressure process,

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

Combining the ideal gas equation, first and second laws we can show:

$$\Delta s=R ln\frac{v_2}{v_1}$$

as follows:

From the second law, for a reversible isothermal process we have

$$q=T\Delta s$$

From the first law we have

$$\Delta u=q-w$$

Since, for an ideal gas isothermal process, $$\Delta T=0$$, then $$\Delta u=0$$, and $$q=w$$, therefore

$$T\Delta s=w=\int Pdv$$

From ideal gas law, one mole of gas

$$Pv=RT$$

$$P=\frac {RT}{v}$$

$$T\Delta s=\int \frac {RT}{v}dv$$

and finally

$$\Delta s=R ln\frac{v_2}{v_1}$$

Hope this helps.