问一道热学题 帮帮忙...证明若理想气体按V=a/√p的规律膨胀,则气体在该过程中的热容C可由下式表示C=C(v)-a^

由 V = a/√p 得 pV^2 = a^2
p*2VdV + V^2dp = 0 → 2 p dV + Vdp = 0
由 pV = νRT 得 pdv + Vdp = νRdT → Vdp = νRdT - pdv 代入上式得
p dV + νRdT = 0 → p dV = - νRdT
由 pV^2 = a^2 和 pV = νRT 得 νRTV = a^2 → νR = a^2/(TV)
C = dQ/dT = (dE + pdV)/dT
= dE/dT + (- νRdT)/dT
= C(v) - a^2/(TV)