# Adiabatic Compression of an Ideal Gas

1. Feb 28, 2017

### Tom2017

Hello

My question is attached to this post ("Question") along with relevant equations I use. ("Image1" "Image2")
This is my attempted method.

First Law of thermodynamics --> DU = Q - W --> Adiabatic Process so Q = 0 --> DU = -W

W = ∫ P Dv Using the upper limit V2 Lower limit V1...

I obtain V1 by using the ideal gas law
I obtain V2 by using the equation in "Image 1"

To solve the integral I will use the ideal gas law and replace P with nRT/V and make use of equation in "Image 2" to calculate W.

Then to obtain the change in enthalpy DH, I will use the following --> DH = DU = -W

Thank you for your help. Is this method correct?

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2. Mar 1, 2017

### stevendaryl

Staff Emeritus
I didn't look over your figures in detail (in general, it's much nicer to learn to write your equations in LaTex, instead of using attachment pictures). It seems that your reasoning is mostly right, except when you wrote:

$dH = dU$

$H$ is defined to be $H = U + PV$, so $\Delta H = \Delta U + \Delta(PV)$

$\Delta(PV)$ is nonzero for an adiabatic change. (It's zero for an isothermal change).

3. Mar 1, 2017

### Staff: Mentor

There was no need to use the first law of thermodynamics on this, since Eqns. 1 and 2 already contain the result of integrating the first law for adiabatic compression or expansion of an ideal gas. Your first step should have been to eliminate the V's from Eqns. 1 and 2 to express the temperatures in terms of the pressures. What do you get when you do this? From the equation you derived, what is the final temperature? Once you know the final temperature, you know the temperature change $\Delta T$. What do you get for $\Delta T$? You are now in perfect position to calculate the internal energy change $\Delta U$ and the enthalpy change $\Delta H$. How is $\Delta U$ related to $C_v$, n, and $\Delta T$? How is $\Delta H$ related to $C_p$, n, and $\Delta T$. Since you know the heat capacity ratio $\gamma$, you can get $C_v$ and $C_p$. What are the values of these heat capacities?