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