Completely stumped on a physics problem - thermodynamics.

[wtfxcore]

I rarely do this, but I'm working on online physics homework (masteringphysics, if anyone is familiar with the website which I believe to be the spawn of satan) and I am absolutely stumped. I'm just wondering if anyone can help me out and point me in the right direction.

On a warm summer day, a large mass of air (atmospheric pressure 1.01*10^5 Pa) is heated by the ground to a temperature of 30.0 *C and then begins to rise through the cooler surrounding air.

Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.10×10^4 Pa. Assume that air is an ideal gas, with γ=1.40 (This rate of cooling for dry, rising air, corresponding to roughly 1*C per 100m of altitude, is called the dry adiabatic lapse rate.)

Thanks so much!

[Qaanol]

Well, the word “adiabatic” in the problem tells me you are meant to assume that no heat flows into or out of the mass of air being observed. That is, the change in temperature stems solely from its change in volume and pressure.

Looking at my intro physics textbook (Giancoli 3e, 2000) in the section on adiabatic expansion of an ideal gas, it derives the result PV^γ=constant. You should be able to find that result in your own physics book and apply it to the problem at hand.

[Animastryfe]

All formulas and information come from my Thermal Physics textbook, written by Baierlein.

The OP should probably use P^(1-\gamma)*T^(\gamma)=constant. This can be derived from the P*V^(\gamma)=constant equation through the use of the ideal gas law. I can derive this equation from scratch for you, if you want.

Back to the question. It appears that the air is in thermal equilibrium, and is undergoing an adiabatic expansion. Using the above adiabatic relation, you know that
(T_initial)^(\gamma)*(P_initial)^(1-\gamma)=(T_final)^(\gamma)*(P_final)^(1-\gamma), and therefore you can find the final temperature.