We known 1

(Molar Heat capacity at constant Pressure)

^{st }law of thermodynamics
dU=dq+dW

If P

_{ext}=constant
Then dW= -PdV

and dU=dq- PdV

dq=dU-PdV

dq=(U

_{2}-U_{1})+P(V_{2}-V_{1})
dq=(U2+PV2)-(U1+PV1)

dQ=H2-H1 ( H

_{2}=U_{2}+PV_{2}and H_{1}=U_{1}+PV_{1})**dq=dH**

hence

The enthalpy of a system is defined as:

H
= U + PV

DH = DU + D(PV)

Where

H is the enthalpy of the system

U is the internal energy of the system

P is the
pressure at the boundary of the system and its environment.

(1) In thermodynamics the quantity

**U + PV**is a new state function and known as the enthalpy of the system and is denoted by**H=U+PV**. It represents the total energy stored in the system.
(2) It may be noted that change in
enthalpy is equal to heat exchange at constant pressure.(3) Enthalpy
is also an

**extensive property**as well as a**state function**. (4)The absolute value of enthalpy cannot be determined, however the change in enthalpy can be experimentally determined.**DH = DU + D(PV)**

(5) Change in enthalpy is a more useful quantity than its
absolute value.

(6) The unit of measurement for

**enthalpy (SI) is joule.**
(7)The enthalpy is the preferred expression of system energy
changes in many chemical and physical measurements, because it simplifies
certain descriptions of energy transfer. This is because a change in enthalpy
takes account of energy transferred to the environment through the expansion of
the system under study.

(8)The change

**d****H is positive in endothermic reactions**, and**negative in exothermic**processes. dH of a system is equal to the sum of non-mechanical work done on it and the heat supplied to it.
(9) For quasi static processes under constant pressure,

**d****H is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings**. This means that the change in enthalpy under such conditions is the heat absorbed (or released) by a chemical reaction.**NOTE:**

Transfer of heat at

**constant volume**brings about a change in the internal energy(**DU**) of the system whereas that at**constant pressure**brings about a change in the enthalpy (**DH**) of the system.
For Ideal
gas

H=U+PV and U=f(T)

PV=nRT

H=U+nRT and H=f(T) only for ideal gas

For other
substance and real gas

H=U+PV

U=f(P,V,T)
and H=f(,PV,T)

So H=f(P,T)/ f(V,T)/ f(P,V)

H=f(T,P)

dH=(dH/dT)

_{p }dT+(dH/dP)_{T }dP------------------------------------- (1)
H=f(V,T)

dH=(dH/dV)

_{T }dV+(dH/dT)_{V }dT------------------------------------- (2)
H=f(P,V)

dH=(dH/dV)

_{P }dV+(dH/dP)_{V }dP------------------------------------- (3)
Out of the
above three relation

**H**as function on of (T,P) Has a greater significance. The above differential equation simplified for different substance for different condition.**For isobaric process :**dP = 0

We known

Q

_{P}=nC_{pm}dT (Molar Heat capacity at constant Pressure)
C

dQ=dH at dP=0_{pm}= (dQ/dT)_{P }for 1 mole of gas
then

**C**_{pm}= (dH/dT)_{P}

**For an ideal gas:**change in enthalpy at constant temperature with change in

pressure is zero. i.e.

Continue...........

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