Use the relation (U/T)subT=T(P/T)subV P'') = '('') ' ' along with -P along with the Euler chain relation and the inversion rule

Use the relation (ðœ•U/ðœ•T)subT=T(ðœ•P/ðœ•T)subVí µðœ•Pðœ•ð‘ˆâ„ðœ•ð‘‰)� = ð‘‡(ðœ•ð‘ƒâ„ðœ•ð‘‡)� − 𑃠along with -P along with the Euler chain relation and the inversion rule to obtain an expression for the internal pressure (ðœ•U/ðœ•V)subT in terms of P, α, T and κ.