Define the State Postulate. Why is it so important in thermodynamics?

$($ii$)$ Explain why for a compressible substance, the specific heat CP is always larger than the

specific heat Cv$.$

$($iii$)$ Explain why for an incompressible substance the internal energy u$($P$,$T$)$ can be accurately

approximated as u$($T$).$

$($iv$)$ Explain using a sketch of a phase diagram for water $($P versus T$)$ what happens to the melting

and boiling temperatures as a function of the pressure.

$($v$)$ Consider the two systems shown below. If the systems are brought in contact with one

another, in which direction will energy flow? Why?

$($vi$)$ Air is compressed in an isothermal process. Assuming air to be an ideal gas, derive an

expression for the work required to compress mass M in a closed system from V$1,$ P$1$ to V$2,$

P$2$ at temperature T$,$ where V$1>$ V$2.$