Types of specific heat of gas :

(a) `text(Molar specific heat :)` Unit mass is taken as one mole

Units `->` J / mole - k

(b) `text(Gram specific heat :)` Unit mass is taken as 1 kg or 1 gm.

Units `->` J / kg-k or J / gm-k

`C_(g r a m) =(C_(mo l a r))/M`

`text(Definition :)`

Amount of heat required to raise temperature of one unit amount (mass or mole) by one unit temperature through a given process is known as specific heat of that process.

`C_(process)=((dQ)/(nDeltaT))_(process)`

`text(Note :)` Thus any gas can have infinite specific heats depending on the infinite different processes.

`DeltaQ=int_(T_1)^(T_2)nCdT` where C is the specific heat for the process through which temperature from `T_1` to `T_2`.

C remains inside the integral because it may be a variable i.e. C may be a function of temperature (directly or indirectly).

`text(Specific Heat at Constant Volume :)`

`C_v=((dQ)/(ndT))_text(constant volume)`

Its experimental value is found to be very close to `(fR)/2`

thus `C_v=(fR)/2`

`text(Specific Heat at Constant Pressure :)`

`C_p=((dQ)/(ndT))_text(constant pressure)`

its experimental value is found to be almost equal to `((f+2)R)/2`

`C_p=((f+2)R)/2`

`text(Adiabatic Exponent)` `gamma` `:`

`gamma=(C_p)/(C_v)`

`=>` `gamma=1+2/f`

`=>` `C_v=R/(gamma-1)`

`=>` `C_p=(gammaR)/(gamma-1)`