explain the intensive and extensive properties? derive an expression for a state function H i.e. dH= dU+p(dV) AND dH=dU+dnRT...

Properties that do not depend on the amount of the matter present are known as INTENSIVE properties.

 Examples are 

Color

Odor

Luster - How shiny a substance is.

Malleability - The ability of a substance to be beaten into thin sheets.

Ductility - The ability of a substance to be drawn into thin wires.

Conductivity - The ability of a substance to allow the flow of energy or electricity.

Hardness - How easily a substance can be scratched.

Melting/Freezing Point - The temperature at which the solid and liquid phases of a substance are in equilibrium at atmospheric pressure.

Boiling Point - The temperature at which the vapor pressure of a liquid is equal to the pressure on the liquid (generally atmospheric pressure).

Density - The mass of a substance divided by its volume

 

Properties that do depend on the amount of matter present are known as EXTENSIVE properties.

Examples are

• Mass - A measurement of the amount of matter in a object (grams).
• Weight - A measurement of the gravitational force of attraction of the earth acting on an object.
• Volume - A measurement of the amount of space a substance occupies.
• Length

The derivation:

According to the first law, dU = dQ - dW        (for any process, neglecting DKE and DPE)

or after putting the value of W, dU = dQ - pdV

Also, we know  H = U + pV therefore dH = dU + pdV + Vdp

so,  dH = dQ - dW + pdV + Vdp (any process)

or

dH = dQ + Vdp (for any quasi-static process)