Enthalpy: It is sum of internal energy and P-V work.

   it is denoted by H.

i.e.H= U + Pv

Heat capacity, specific heat capacity and molar heat capacity

• Heat capacity: It is defined as amount of heat required to raise the temperature of substance by one degree Celsius.

          It is given by  :

       C=(q/∆T)

• Specific heat capacity: It is the amount of heat required to raise the temperature of substance (1g) through one degree Celsius.q =(C x ∆t x m)q= m. C. ∆t
• Molar heat capacity :

  It is the amount of heat required to raise the temperature of 1 mole of substance through one degree Celsius.

Molar heat capacity = c_m = heat capacity for 1mole.

                                            c_m = (c/n)

Where c_m is for one mole, n=total number of moles and c is heat capacity

Types of molar heat capacities:

• Heat capacity at constant volume.
• Heat capacity at constant pressure.

Heat capacity at constant volume: Is defined as rate of change of internal energy with temperature at constant volume.

It is given by: C_v = (dU/dt)

Heat capacity at constant pressure: It is defined as rate of change of internal energy with temperature at constant pressure.

It is given by: C_p= (dH/dt)

Relation between C_p &C_v

If the volume of system is kept constant and heat is added to the system then no work is done by the system.

Thus, the heat absorbed by the system is used up completely to increase the internal energy of the system.

And if pressure is kept constant, then the energy supplied is somehow used in increasing the volume and leftover is used to increase the internal energy.

Therefore the energy required to raise the temperature at constant pressure is always more than the energy required to raise the temperature of substance at constant volume. (C_p> C_v).

We know:

The procedure consists of two steps:

1. Combustion of know mass of substance whose heat of combustion is known: A known mass of compound is taken in platinum cup. Oxygen gas is introduced that is under high pressure in the bomb. A current is passed through the filament immersed in compound.
2. Combustion takes place and the increase in temperature is noted, from this heat capacity can be calculated by:

Change in internal energy =q x change in temperature x m/M

Where M = molecular mass of substance and ‘m’ is mass of substance taken.

Mathematically:

Let’s say initial temperature -> t₁⁰C

In order to find temperature -> t₂⁰C

Rise in temperature -> (t₂ – t₁) ⁰C