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## Homework Statement

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.

## Homework Equations

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?

Thank You!

i have read my physical chemistry book but i am still confused!