![SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P](https://cdn.numerade.com/previews/bebae64c-7fa0-40e5-9d89-f62e32e910b6_large.jpg)
SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P
![The dimensionless coefficients ${\kappa }_{\chi ,\eta }$ and ${{\ell... | Download Scientific Diagram The dimensionless coefficients ${\kappa }_{\chi ,\eta }$ and ${{\ell... | Download Scientific Diagram](https://www.researchgate.net/profile/Peter-Talkner/publication/317101002/figure/fig6/AS:1132483903012873@1647016611255/The-dimensionless-coefficients-kappa-chi-eta-and-ell-chi-eta.jpg)
The dimensionless coefficients ${\kappa }_{\chi ,\eta }$ and ${{\ell... | Download Scientific Diagram
![Cp-Cv for real gas, in terms of alpha & beta, change in internal energy with respect to volume - YouTube Cp-Cv for real gas, in terms of alpha & beta, change in internal energy with respect to volume - YouTube](https://i.ytimg.com/vi/5AhFY7yTcGU/maxresdefault.jpg)
Cp-Cv for real gas, in terms of alpha & beta, change in internal energy with respect to volume - YouTube
![SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P](https://cdn.numerade.com/previews/bebae64c-7fa0-40e5-9d89-f62e32e910b6.gif)
SOLVED:Generally, volume expansivity βand isothermal compressibility κdepend on T and P. Prove that: ((∂β)/(∂P))T=-((∂κ)/(∂T))P
![Thermodynamic mechanism of the density and compressibility anomalies of water in the range − 30 < T (°C) < 100 | Scientific Reports Thermodynamic mechanism of the density and compressibility anomalies of water in the range − 30 < T (°C) < 100 | Scientific Reports](https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41598-022-05038-9/MediaObjects/41598_2022_5038_Fig1_HTML.png)