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To study the heat changes in a chemical reaction at constant temperature and constant pressure, a new thermodynamic function called enthalpy was introduced.

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.

H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.

Change in enthalpy = Enthalpy of products - Enthalpy of reactants

∆H = H_{P}-H_{R}

From the first law of thermodynamics

∆U =qp-P∆V

qp =heat absorbed by the system

-P∆V=work done by the system.

For finite changes at constant pressure,

∆H= ∆U+∆(PV)

∆H=∆U+P∆V (∵ P is constant )

∆H=qp

∆H=-Ve for exothermic reactions

∆H=+Ve for endothermic reactions.

**Relation between ∆H &∆U**:

Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant

∆H=∆U+P∆V

∆H=∆U+P(0)

∆H=∆U

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.

Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is V_{A }and the number of moles in the reactants is n_{A}. Similarly, the volume of the products is V_{B} and the number of moles in the product is n_{B}.

According to the ideal gas equation,

Pv=nRT

pv_{A}=n_{A}RT

pv_{B}= n_{B}RT

Thus

pv_{B-} pv_{A =} n_{B}RT- n_{A}RT

p(v_{B-} v_{A}) =RT(n_{B-}n_{A})

p∆v =∆n_{g}RT

∆H=∆U +p∆v

∆H=∆U+∆n_{g}RT

**Heat capacity: **The capacity to absorb heat energy and store it is known as the heat capacity of a system.

q=C .∆T

Where C is called the heat capacity of the system.

If q calories is the heat absorbed by the mass m and the temperature rises from T_{1} to T_{2}, the heat capacity

C is given by the expression

C = q /T_{2}-T_{1}

Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.

The SI units of molar heat capacity are**J**^{0}k^{-1}mole^{-1}.

**Relation between molar heat capacity at constant volume, which is denoted by Cv and molar heat capacity at constant pressure, which is denoted by Cp:**

q=C∆v

At constant volume

q_{v}=C_{v}∆T =∆U

At constant pressure

q_{p = }C_{p}∆T =∆H

The difference between Cp and CV for one mole of an ideal gas can be derived as follows:

The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)

For 1 mole of gas pv =RT

∆H= ∆U+∆(RT)

R is aconstant

∆H= ∆U+R∆T

C_{p}∆T= C_{v}∆T+R∆T

Since ∆T=1

C_{p}= C_{v }+R

R = C_{p}- C_{v}

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.

H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.

Change in enthalpy = Enthalpy of products - Enthalpy of reactants

∆H = H

From the first law of thermodynamics

∆U =qp-P∆V

qp =heat absorbed by the system

-P∆V=work done by the system.

For finite changes at constant pressure,

∆H= ∆U+∆(PV)

∆H=∆U+P∆V (∵ P is constant )

∆H=qp

∆H=-Ve for exothermic reactions

∆H=+Ve for endothermic reactions.

Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant

∆H=∆U+P∆V

∆H=∆U+P(0)

∆H=∆U

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.

Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is V

According to the ideal gas equation,

Pv=nRT

pv

pv

Thus

pv

p(v

p∆v =∆n

∆H=∆U +p∆v

∆H=∆U+∆n

q=C .∆T

Where C is called the heat capacity of the system.

If q calories is the heat absorbed by the mass m and the temperature rises from T

C is given by the expression

C = q /T

Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.

The SI units of molar heat capacity are

q=C∆v

At constant volume

q

At constant pressure

q

The difference between Cp and CV for one mole of an ideal gas can be derived as follows:

The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)

For 1 mole of gas pv =RT

∆H= ∆U+∆(RT)

R is aconstant

∆H= ∆U+R∆T

C

Since ∆T=1

C

R = C

To study the heat changes in a chemical reaction at constant temperature and constant pressure, a new thermodynamic function called enthalpy was introduced.

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.

H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.

Change in enthalpy = Enthalpy of products - Enthalpy of reactants

∆H = H_{P}-H_{R}

From the first law of thermodynamics

∆U =qp-P∆V

qp =heat absorbed by the system

-P∆V=work done by the system.

For finite changes at constant pressure,

∆H= ∆U+∆(PV)

∆H=∆U+P∆V (∵ P is constant )

∆H=qp

∆H=-Ve for exothermic reactions

∆H=+Ve for endothermic reactions.

**Relation between ∆H &∆U**:

Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant

∆H=∆U+P∆V

∆H=∆U+P(0)

∆H=∆U

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.

Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is V_{A }and the number of moles in the reactants is n_{A}. Similarly, the volume of the products is V_{B} and the number of moles in the product is n_{B}.

According to the ideal gas equation,

Pv=nRT

pv_{A}=n_{A}RT

pv_{B}= n_{B}RT

Thus

pv_{B-} pv_{A =} n_{B}RT- n_{A}RT

p(v_{B-} v_{A}) =RT(n_{B-}n_{A})

p∆v =∆n_{g}RT

∆H=∆U +p∆v

∆H=∆U+∆n_{g}RT

**Heat capacity: **The capacity to absorb heat energy and store it is known as the heat capacity of a system.

q=C .∆T

Where C is called the heat capacity of the system.

If q calories is the heat absorbed by the mass m and the temperature rises from T_{1} to T_{2}, the heat capacity

C is given by the expression

C = q /T_{2}-T_{1}

Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.

The SI units of molar heat capacity are**J**^{0}k^{-1}mole^{-1}.

**Relation between molar heat capacity at constant volume, which is denoted by Cv and molar heat capacity at constant pressure, which is denoted by Cp:**

q=C∆v

At constant volume

q_{v}=C_{v}∆T =∆U

At constant pressure

q_{p = }C_{p}∆T =∆H

The difference between Cp and CV for one mole of an ideal gas can be derived as follows:

The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)

For 1 mole of gas pv =RT

∆H= ∆U+∆(RT)

R is aconstant

∆H= ∆U+R∆T

C_{p}∆T= C_{v}∆T+R∆T

Since ∆T=1

C_{p}= C_{v }+R

R = C_{p}- C_{v}

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.

H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.

Change in enthalpy = Enthalpy of products - Enthalpy of reactants

∆H = H

From the first law of thermodynamics

∆U =qp-P∆V

qp =heat absorbed by the system

-P∆V=work done by the system.

For finite changes at constant pressure,

∆H= ∆U+∆(PV)

∆H=∆U+P∆V (∵ P is constant )

∆H=qp

∆H=-Ve for exothermic reactions

∆H=+Ve for endothermic reactions.

Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, ∆V is insignificant

∆H=∆U+P∆V

∆H=∆U+P(0)

∆H=∆U

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.

Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is V

According to the ideal gas equation,

Pv=nRT

pv

pv

Thus

pv

p(v

p∆v =∆n

∆H=∆U +p∆v

∆H=∆U+∆n

q=C .∆T

Where C is called the heat capacity of the system.

If q calories is the heat absorbed by the mass m and the temperature rises from T

C is given by the expression

C = q /T

Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.

The SI units of molar heat capacity are

q=C∆v

At constant volume

q

At constant pressure

q

The difference between Cp and CV for one mole of an ideal gas can be derived as follows:

The change in enthalpy for one mole of an ideal gas ∆H= ∆U+∆(PV)

For 1 mole of gas pv =RT

∆H= ∆U+∆(RT)

R is aconstant

∆H= ∆U+R∆T

C

Since ∆T=1

C

R = C