A sample of 3 mol of a diatomic perfect gas at 200K is compressed reversibly and adiabatically until its temperature reaches 250K. Given that Cv,m=27.5 JK-1mol-1, calculate q, w, ΔU, ΔH and ΔS.
dS = dq/T
ΔU = n(Cv,m)ΔT
ΔH = n(Cp,m)ΔT
The Attempt at a Solution
(skipped the part of q and ΔS)
ΔU = q+w = w
w = -∫PdV = -PΔV = -nRΔT = -1247.2 J
ΔU = -1247.2 J
ΔH = ΔU+Δ(PV) = -2494.4 J
the model answer:
w= ΔU = CvΔT = +4.1 kJ
ΔH = CpΔT = +5.4 kJ
here are my questions:
what's wrong with my answer?
i should not assume Pressure is constant?
if the problem is that Pressure does vary in the process,
why ΔH is still calculated by Cp,m (i know ΔH=q in an isobaric process) ?
why can't i use ΔH = ΔU -w in this case?
is ΔU always equal to CvΔT for isobaric and isochoric process,
and equal to 0 for isothermal process?
i have read my physical chemistry book but i am still confused!