Adiabatic Process: Derive Temp Change w/ Pressure

[KingBigness]

Homework Statement

Derive an expression for the change in temperature with pressure for an adiabatic process. If a dry air parcel is lifted adiabatically from 1000hPa to 800hPa what is the final temperature if it was initally at 20$^{o}$C?$^{}$

Homework Equations

$PV^{k}=constant$
I derived an equation $\frac{T_{2}}{T_{1}}= \frac{P_{2}}{P_{1}}^{\frac{k-1}{k}}$

Not sure if this is the correct equation?

The Attempt at a Solution

$k = \frac{c_{p}}{c_{v}}$

I'm not sure if this is even the right direction for this question, and if it is where can I get the value of the c's?

Any help would be appreciated. thanks =D

 

[Andrew Mason]

Homework Statement

Derive an expression for the change in temperature with pressure for an adiabatic process. If a dry air parcel is lifted adiabatically from 1000hPa to 800hPa what is the final temperature if it was initally at 20$^{o}$C?$^{}$

Homework Equations

$PV^{k}=constant$
I derived an equation $\frac{T_{2}}{T_{1}}= \frac{P_{2}}{P_{1}}^{\frac{k-1}{k}}$

Not sure if this is the correct equation?

What is your reasoning? Assume air is an ideal gas.

Express V in terms of P and T and substitute into $PV^{k}=constant$

AM