2. APPLICATIONS

APPLICATIONS

• Work (Pressure-volume Work)
Let us consider a cylinder which contains one mole of an ideal gas in which a frictionless piston is fitted.

• Work Done in Isothermal and Reversible Expansion of Ideal Gas

 • Isothermal and Free Expansion of an Ideal Gas

For isothermal (T = constant) expansion of an

ideal gas into vacuum ; w = 0 since pex = 0.

Also, Joule determined experimentally that

q = 0; therefore, ∆U = 0

• Enthalpy (H)
It is defined as total heat content of the system. It is equal to the sum of internal energy and pressure-volume work.
Mathematically, H = U + PV
Change in enthalpy: Change in enthalpy is the heat absorbed or evolved by the system at constant pressure.
ΔH = q_p
For exothermic reaction (System loses energy to Surroundings),
ΔH and q_p both are -Ve.
For endothermic reaction (System absorbs energy from the Surroundings).
ΔH and q_p both are +Ve.
Relation between ΔH and Δu.

Let us consider a general reaction A B

Let H_A be the enthalpy of reactant A and H_B be that of the products.

∴ H_A = U_A + PV_A

H_B = U_B + PV_B

 ΔH = H_B - H_A

= (U_B + PV_B) – (U_A + PV_A)

ΔH = ΔU + PΔV (H_B – H_A)

 ΔH = ΔU + PΔV

At constant pressure and temperature using ideal gas law,

PV_A = n_A RT (for reactant A)

PV_B = n_B RT (for reactant B)

Thus,   PV_B – PV_A = n_B RT - n_A RT

= ( n_B – n_A) RT

PΔV = Δn_g RT

∴ ΔH = ΔU + Δn_g RT
• Extensive property
An extensive property is a property whose value depends on the quantity or size of matter present in the system.
For example: Mass, volume, enthalpy etc. are known as extensive property.
• Intensive property
Intensive properties do not depend upon the size of the matter or quantity of the matter present in the system.
For example: temperature, density, pressure etc. are called intensive properties.
• Heat capacity
The increase in temperature is proportional to the heat transferred.
q = coeff. x ΔT
q = CΔT
Where, coefficient C is called the heat capacity.
C is directly proportional to the amount of substance.
C_m = C/n
It is the heat capacity for 1 mole of the substance.

• Molar heat capacity
It is defined as the quantity of heat required to raise the temperature of a substance by 1° (kelvin or Celsius).
• Specific Heat Capacity
It is defined as the heat required to raise the temperature of one unit mass of a substance by 1° (kelvin or Celsius).
q = C x m x ΔT
where m = mass of the substance
ΔT = rise in temperature.
• Relation Between C_p and C_v for an Ideal Gas
At constant volume heat capacity = C_v
At constant pressure heat capacity = C_p
At constant volume q_v= C_vΔT = ΔU
At constant pressure q_p = C_p ΔT = ΔH
For one mole of an ideal gas
ΔH = ΔU + Δ (PV) = ΔU + Δ (RT)
ΔH = ΔU + RΔT
On substituting the values of ΔH and Δu, the equation is modified as

C_p ΔT = C_vΔT + RΔT
or C_p-C_v = R