Specific Heat of Gas (Relation b/w Cp & Cv)

1. Specific Heat of a Gas:

“The amount of heat required to produce a given change in temperature of a given mass is known as Heat Capacity “.


Suppose Q is the heat given to a body and its temperature increases by ΔT, then Heat capacity of body is given by :-

See Also:- (i) Heat Internal Energy & Work
                  (ii)Work done during Adiabatic Process
          

Further, Heat Capacity per unit mass is known as Specific Heat Capacity & it is denoted by ‘C’

                          

Thus, ” Specific heat of the material is quantity of heat required to raise the temperature of unit mass by 1°C or 1°K. “


See Also :
 (i) Work done in Isothermal Process  

(ii)  Slope of Adiabatic Curve is more steeper   than Isothermal. 

As a gas is compressible,  then there is a rise in temperature without supplying any heat to the gas,  then,

                     

    
On the other hand, if heat is supplied to gas and gas is allowed to expand such that there is no rise in temperature then, 
   

Hence In order to find the value of Specific heat of gas i.e. the pressure or volume has to be kept constant. 
Hence we have two specific heats :-
(i) Specific Heat at Constant Volume:

It is defined as “the amount of heat required to raise the temperature of unit mass of gas through 1°C, when its volume is kept constant”.
It is denoted by Cv. 




(ii) Specific Heat at Constant Pressure :

It is defined as “the amount of heat required to raise the temperature of unit mass of gas through 1°C, when its pressure  is kept constant”.

It is denoted by Cp. 

The unit of Specific Heat in C. G. S system is cal/gm/°C. 

2. Relation between Cp & Cv :-

When a gas is heated at constant pressure, it expands. Therefore heat supplied at constant pressure is partially used in doing work & remaining in raising the internal energy of the gas. 
On the other hand, when a gas is heated at constant volume no work is done and hence total heat supplied is used to rise the temperature of the gas. 
Thus, more heat is required for increasing the temperature of the gas through 1°C at constant pressure then at constant volume. 
Consider two isothermals AB & CD drawn for 1 mol of ideal gas at closed temperature T & T+ΔT. 
Fig. Isothermals AB & CD
When gas expands at constant volume, then change in internal energy is given by :
When gas expands at constant pressure, then change in Internal Energy :

















Now, From Ideal gas equation:

Now, 


Here,  Cp – Cv = R is required relation. 
This is also known as Mayer’s formula. 
I hope you’ll understand Concept of Specific Heat & Mayer’s Formula.  For any query or suggestions ,write to us in comment section. 

        

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