Question

The isobaric thermal expansivity ? is defined as ? = 1 ?
(?? ??
)
?

The isothermal compressibility ? is defined as ? = −1 ?
(?? ??
)
?


1. From ? = ?(?,?), show that ?? = ???? −????
2. From ? = ?(?,?), show that ?? = ?? ?
?? −????
3. From ? = ?(?,?), show that ?? = (?? −???)?? +?(?? −??)??
4. From ? = ?(?,?), show that ?? = ???? +?(1−??)??
5. From ? = ?(?,?), show that ?? = −(?+???)?? +?????

Answer 1

1)

Now write dV. This step is common for all the problem.

are the terms at constant pressure and constant temperature respectively.

since and , substitute for and in (2)

thus

Remaining questions can be solved in similar way by using Maxwell Relations.

Second step is common for all the problems. Compare and understand how it is written.

Please find attached the link to remaining solutions for this question.

https://drive.google.com/open?id=13T6HOEVYNx70E_Srsf6nS16l8EwRA76r

Have a good day!