8.02 × 10−1 moles of nitrogen gas ( γ= 1.40) is contained in a volume of 2.00 × 10−2 m3 at a pressure of 1.00 × 105 Pa and temperature of 300 K. The sample is adiabatically compressed to half its original volume. IT behaves as an ideal gas.
(i) What is the change in entropy of the gas?
(ii) Show from the adiabatic condition and the equation of state that TV γ-1
remains constant, and hence determine the final temperature of the gas
PVγ = A (constant)
The Attempt at a Solution
For I, I think that because the compression is a reversible adiabatic process there will be no entropy change.
It is ii, that I am stuck on. I think that the equation of state will need to be rearranged to give P=nRT / V and that this will need to be substituted into the adiabatic condition to give (nRT Vγ) / V = constant which feels close but I cannot think of the last step.
Or is it better to start with PVγ = constant
PVVγ-1 = constant
nRT *Vγ-1 = constant and ignore n and R seeing as they themselves are constants? giving TVγ-1 = constant
(I am not sure whether n and R can just be ignored or whether this method is even correct or valid).
or some other way entirely, any insight would be appreciated.