Thermodynamics question

Hi there,

I'm struggling to get my head around a question in 2nd year thermodynamics. I have done similar questions but I'm struggling to get started with this one as I can't arrange my formulae without ending up with two unknown values.

Here is the question...

Air, initially at 300 K and 105 Pa, is contained in an adiabatic piston-cylinder apparatus. The piston has a cross-sectional area of 1 m2 and can be assumed to be massless and of negligible thickness. The air is separated from a copper block of mass 5 kg, initially at 600 K, by an adiabatic membrane. The piston initially rests 1 m above the membrane (h1 = 1 m). At some time, the adiabatic membrane is removed and the air and copper are allowed to come to thermal equilibrium. Find the final temperature (in K) of the air and copper in this equilibrium state. Assume the following air properties: cv = 716 J/kg/K, R = 287 J/kg/K, and the following copper property: c = 385 J/kg/K.


I'm using the first and second laws of thermodynamics combined with the ideal gas law but no matter how I arrange the formulae I end up with T2, final temp (which I'm trying to find),
and V2 final volume in the formulae, both of which are unknowns. I know that final pressure is equal to the start pressure.

I tried using the formulae

T2 = MaCa(T1)+MbCb(T1) / MaCa+MbCb

but I don't think this is correct as I'm working with a gas.

Any help would be greatly appreciated!